Research ArticleEnd-Point Static Control of Basic OxygenFurnace (BOF) Steelmaking Based on WaveletTransform Weighted Twin Support Vector Regression

Chuang Gao12 Minggang Shen 1 Xiaoping Liu3 Lidong Wang2 and Maoxiang Chu2

1School of Materials and Metallurgy University of Science and Technology Liaoning Anshan Liaoning China2School of Electronic and Information Engineering University of Science and Technology Liaoning Anshan Liaoning China3School of Information and Electrical Engineering Shandong Jianzhu University Jinan Shandong China

Correspondence should be addressed to Minggang Shen lnassmg163com

Received 6 July 2018 Revised 22 October 2018 Accepted 10 December 2018 Published 1 January 2019

Academic Editor Michele Scarpiniti

Copyright copy 2019 Chuang Gao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A static control model is proposed based on wavelet transform weighted twin support vector regression (WTWTSVR) Firstly newweighted matrix and coefficient vector are added into the objective functions of twin support vector regression (TSVR) to improvethe performance of the algorithm The performance test confirms the effectiveness of WTWTSVR Secondly the static controlmodel is established based on WTWTSVR and 220 samples in real plant which consists of prediction models control modelsregulating units controller and BOF Finally the results of proposed prediction models show that the prediction error bound with0005 in carbon content and 10∘C in temperature can achieve a hit rate of 92 and 96 respectively In addition the double hitrate of 90 is the best result by comparing with four existingmethodsThe results of the proposed static controlmodel indicate thatthe control error bound with 800 Nm3 in the oxygen blowing volume and 55 tons in the weight of auxiliary materials can achieve ahit rate of 90 and 88 respectively Therefore the proposed model can provide a significant reference for real BOF applicationsand also it can be extended to the prediction and control of other industry applications

1 Introduction

With the development of end-point control technology forbasic oxygen furnace (BOF) the static control model can beestablished to overcome the randomness and inconsistencyof the artificial experience control models According to theinitial conditions of hot metal the relative calculations canbe carried out to guide production The end-point hit ratewould be improved through this approach Unfortunatelythe control parameters would not be adjusted during thesmelting process which restricts the further improvement ofthe end-point hit rate To solve this problem the sublancebased dynamic control model could be adopted by usingthe sublance technology By combining the static model withthe dynamic model the end-point hit rate of BOF could beguaranteed The establishment of the static control model isthe foundation of the dynamic model The accuracy of thestatic model will directly affect the hit rates of the dynamic

control model thus it plays an important role in the parame-ter optimization of BOF control process Therefore the staticcontrol model is still a practical and reliable technologyto guide the production and improve the technology andmanagement level of steelmaking plants

In recent years some significant developments of BOFprediction and control modelling have been achieved Blancoet al [1] designed a mixed controller for carbon and siliconin a steel converter in 1993 In 2002 three back propaga-tion models are adopted to predict the end-blow oxygenvolume and the weight of coolant additions [2] In 2006 adynamic model is constructed to predict the carbon contentand temperature for the end-blow stage of BOF [3] Basedon multivariate data analysis the slopping prediction wasproposed by Bramming et al [4] In 2014 the multi-levelrecursive regression model was established for the predictionof end-point phosphorus content during BOF steelmakingprocess [5] An antijamming endpoint prediction model

HindawiComplexityVolume 2019 Article ID 7408725 16 pageshttpsdoiorg10115520197408725

2 Complexity

of extreme learning machine (ELM) was proposed withevolving membrane algorithm [6] By applying input vari-ables selection technique the input weighted support vectormachinemodellingwas proposed [7] and then the predictionmodel was established on the basis of improving a case-based reasoning method [8] The neural network predictionmodellings [9ndash12] were carried out to achieve aimed end-point conditions in liquid steel A fuzzy logic control schemewas given for the basic oxygen furnace in [13] Most ofthese achievements are based on the statistical and intelligentmethods

As an intelligent method Jayadeva et al [14] proposeda twin support vector machine (TSVM) algorithm in 2007The advantage of this method is that the computational com-plexity of modelling can be reduced by solving two quadraticprogramming problems instead of one in traditional methodIt is also widely applied to the classification applications In2010 Peng [15] proposed a twin support vector regression(TSVR) which can be used to establish the prediction modelfor industrial data After that some improved TSVRmethods[16ndash22] were proposed By introducing a K-nearest neighbor(KNN) weighted matrix into the optimization problem inTSVR the modified algorithms [16 19] were proposed toimprove the performance of TSVR A V-TSVR [17] andasymmetric V-TSVR [20] were proposed to enhance the gen-eralization ability by tuning new model parameters To solvethe ill-conditioned problem in the dual objective functionsof the traditional TSVR an implicit Lagrangian formulationfor TSVR [18] was proposed to ensure that the matrices inthe formulation are always positive semidefinite matricesParastalooi et al [21] added a new term into the objectivefunction to obtain structural information of the input dataBy comparing with the neural network technology thedisadvantage of neural network is that the optimizationprocess may fall into the local optimum The optimization ofTSVR is a pair of quadratic programming problems (QPPs)which means there must be a global optimal solution foreach QPP All above modified TSVR algorithms are focusedon the improvements of the algorithm accuracy and thecomputation speed Currently the TSVR algorithm has neverbeen adopted in the BOF applications Motivated by this theTSVR algorithm can be used to establish a BOF model

Wavelet transform can fully highlight the characteristicsof some aspects of the problem which has attracted moreand more attention and been applied to many engineeringfields In this paper the wavelet transform technique isused to denoise the output samples during the learningprocess and it is a new application of the combinationof wavelet transform and support vector machine methodThen a novel static control model is proposed based onwavelet transform weighted twin support vector regression(WTWTSVR) which is an extended model of our previouswork In [23] we proposed an end-point prediction modelwith WTWTSVR for the carbon content and temperature ofBOF and the accuracy of the prediction model is expectedHowever the prediction model cannot be used to guidereal BOF production directly Hence a static control modelshould be established based on the prediction model tocalculate the oxygen volume and the weight of auxiliary raw

materials and the accuracy of the calculations affects thequality of the steel Therefore the proposed control modelcan provide a guiding significance for real BOF productionIt is also helpful to other metallurgical prediction and controlapplications To improve the performance of the controlmodel an improvement of the traditional TSVR algorithmis carried out A new weighted matrix and a coefficientvector are added into the objective function of TSVR Alsothe parameter 120576 in TSVR is not adjustable anymore whichmeans it is a parameter to be optimized Finally the staticcontrol model is established based on the real datasetscollected from the plant The performance of the proposedmethod is verified by comparing with other four existingregression methods The contributions of this work includethe following (1) It is the first attempt to establish the staticcontrol model of BOF by using the proposed WTWTSVRalgorithm (2)Newweightedmatrix and coefficient vector aredetermined by the wavelet transform theory which gives anew idea for the optimization problem inTSVR areas (3)Theproposed algorithm is an extension of the TSVR algorithmwhich is more flexible and accurate to establish a predictionand control model (4)The proposed control model providesa new approach for the applications of BOF control Theapplication range of the proposed method could be extendedto other metallurgical industries such as the prediction andcontrol in the blast furnace process and continuous castingprocess

Remark 1 Themaindifference betweenprimalKNNWTSVR[16] and the proposed method is that the proposed algo-rithm utilizes the wavelet weighted matrix instead of KNNweighted matrix for the squared Euclidean distances fromthe estimated function to the training points Also a waveletweighted vector is introduced into the objective functions forthe slack vectors 1205761 and 1205762 are taken as the optimized param-eters in the proposed algorithm to enhance the generalizationability Another difference is that the optimization problemsof the proposed algorithm are solved in the Lagrangian dualspace and that of KNNWTSVR are solved in the primal spacevia unconstrained convex minimization

Remark 2 By comparing with available weighted techniquelike K-nearest neighbor the advantages of the wavelet trans-form weighting scheme are embodied in the following twoaspects

(1) The Adaptability of the Samples The proposed method issuitable for dealing with timespatial sequence samples (suchas the samples adopted in this paper) due to the character ofwavelet transform Thewavelet transform inherits and devel-ops the idea of short-time Fourier transform The weights ofsample points used in the proposed algorithm are determinedby calculating the difference between the sample valuesand the wavelet-regression values for Gaussian functionwhich can mitigate the noise especially the influence ofoutliers While KNN algorithm determines the weight of thesample points by calculating the number of adjacent points(determined by Euclidian distance) which is more suitablefor the samples of multi-points clustering type distribution

Complexity 3

(2)TheComputational Complexity KNNalgorithm requires alarge amount of computations because the distance betweeneach sample to all known samples must be computed toobtain its K nearest neighbors By comparing with KNNweighting scheme the wavelet transform weighting schemehas less computational complexity because it is dealingwith one dimensional output samples and the computationcomplexity is proportional to the number of samples l KNNscheme is dealing with the input samples the computationcomplexity of KNN scheme is proportional to 1198972 With theincreasing of dimensions and number of the samples it willhave a large amount of computations

Therefore the wavelet transform weighting scheme ismore competitive than KNN weighting scheme for the timesequence samples due to its low computational complexity

2 Background

21 Description of BOF Steelmaking BOF is used to producethe steel with wide range of carbon alloy and special alloysteels Normally the capacity of BOF is between 100 tonsand 400 tons When the molten iron is delivered to theconverter through the rail the desulphurization process isfirstly required In BOF the hot metal and scrap lime andother fluxes are poured into the converter The oxidationreaction is carried out with carbon silicon phosphorusmanganese and some iron by blowing in a certain volumeof oxygen The ultimate goal of steelmaking is to produce thesteel with specific chemical composition at suitable tappingtemperature The control of BOF is difficult because thewhole smelting process is only half an hour and there isno opportunity for sampling and analysis in the smeltingprocess The proportion of the iron and scrap is about 31 inBOF The crane loads the waste into the container and thenpours the molten iron into the converter The water cooledoxygen lance enters the converter the high purity oxygenis blown into BOF at 16000 cubic feet per minute and theoxygen is reacted with carbon and other elements to reducethe impurity in the molten metal and converts it into a cleanhigh quality liquid steel The molten steel is poured into theladle and sent to the metallurgical equipment of the ladle [13]

Through the oxidation reaction of oxygen blown in BOFthe molten pig iron and the scrap can be converted into steelIt is a widely used steelmaking method with its higher pro-ductivity and low production cost [3] However the physicaland chemical process of BOF is very complicated Also thereare various types of steel produced in the same BOF whichmeans that the grade of steel is changed frequently Thereforethe BOF modelling is a challenge task The main objective ofthe modelling is to obtain the prescribed end-point carboncontent and temperature

22 Nonlinear Twin Support Vector Regression Support vec-tor regression (SVR) was proposed for the applications ofregression problems For the nonlinear case it is based onthe structural riskminimization andVapnik 120576-insensitive lossfunction In order to improve the training speed of SVR Pengproposed a TSVR algorithm in 2010 The difference betweenTSVR and SVR is that SVR solves one large QPP problem and

TSVR solves two smallQPPproblems to improve the learningefficiency Assume that a sample is an 119899-dimensional vectorand the number of the samples is 119897 which can be expressedas (x1 1199101) (x119897 119910119897) Let A = [x1 x119897]119879 isin 119877119897times119899 be theinput data set of training samples y = [1199101 y119897]119879 isin 119877119897 bethe corresponding output and e = [1 1]119879 be the onesvector with appropriate dimensions Assume119870( ) denotes anonlinear kernel function Let119870(AA119879) be the kernel matrixwith order 119897 and its (119894 119895)-th element (119894 119895 = 1 2 119897) bedefined by

[119870 (AA119879)]119894119895= 119870 (x119894 x119895) = (Φ (x119894) sdot Φ (x119895)) isin 119877 (1)

Here the kernel function 119870(x x119894) represents the inner prod-uct of the nonlinear mapping functions Φ(x119894) and Φ(x119895) inthe high dimensional feature space Because there are variouskernel functions the performance comparisons of kernelfunctions will be discussed later In this paper the radial basiskernel function (RBF) is chosen as follows

119870 (x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816221205902 ) (2)

where 120590 is the width of the kernel function Let 119870(x119879A119879) =(119870(x x1) 119870(x x2) 119870(x x119897)) be a row vector in 119877119897 Thentwo 120576-insensitive bound functions 1198911(x) = 119870(x119879A119879)1205961 + 1198871and1198912(x) = 119870(x119879A119879)1205962+1198872 can be obtained where12059611205962 isin119877119897 are the normal vectors and 1198871 1198872 isin 119877 are the bias valuesTherefore the final regression function 119891(x) is determined bythe mean of 1198911(x) and 1198912(x) that is

119891 (x) = 12 (1198911 (x) + 1198912 (x))= 12119870 (x119879A119879) (1205961 + 1205962) + 12 (1198871 + 1198872)

(3)

Nonlinear TSVR can be obtained by solving two QPPs asfollows

min1205961 1198871120585

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus 1205761e minus (119870(AA119879)1205961 + 1198871e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198881e119879120585st y minus (119870 (AA119879)1205961 + 1198871e) ge 1205761e minus 120585 120585 ge 0119890 (4)

and

min1205962 1198872120574

12 1003816100381610038161003816100381610038161003816100381610038161003816y + 1205762e minus (119870 (AA119879)1205962 + 1198872e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198882e119879120574st 119870(AA119879)1205962 + 1198872e minus y ge 1205762e minus 120574 120574 ge 0e (5)

By introducing the Lagrangian function and Karush-Kuhn-Tucker conditions the dual formulations of (4) and (5)can be derived as follows

max120572

minus 12120572119879G (G119879G)minus1G119879120572 + g119879G (G119879G)minus1G119879120572minus g119879120572

st 0e le 120572 le 1198881e(6)

4 Complexity

and

max120573

minus 12120573119879G (G119879G)minus1G119879120573 minus h119879G (G119879G)minus1G119879120573+ h119879120573

st 0e le 120573 le 1198882e(7)

whereG = [119870(AA119879) e] g = y minus 1205761e and h = y + 1205762eTo solve the above QPPs (6) and (7) the vectors1205961 1198871 and1205962 1198872 can be obtained

[12059611198871 ] = (G119879G)minus1G119879 (g minus 120572) (8)

and

[12059621198872 ] = (G119879G)minus1G119879 (h + 120573) (9)

By substituting the above results into (3) the final regres-sion function can be obtained

23 Nonlinear Wavelet Transform Based Weighted TwinSupport Vector Regression

231 Model Description of Nonlinear WTWTSVR In 2017Xu el al [20] proposed the asymmetric V-TSVR algorithmbased on pinball loss functions This new algorithm canenhance the generalization ability by tuning new modelparametersTheQPPs of nonlinear asymmetric V-TSVR wereproposed as follows

min1205961 11988711205761120585

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205961 + 1198871e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198881V11205761+ 1119897 1198881e119879120585

st y minus (119870 (AA119879)1205961 + 1198871e)ge minus1205761e minus 2 (1 minus 119901) 120585 120585 ge 0e 1205761 ge 0

(10)

and

min1205962 11988721205762 120574

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205962 + 1198872e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198882V21205762+ 1119897 1198882e119879120585lowast

st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 2119901120585lowast120585lowast ge 0e 1205762 ge 0

(11)

where 1198881 1198882 V1 V2 ge 0 are regulating parameters and theparameter 119901 isin (0 1) is used to apply a slightly differentpenalty for the outliers The contributions of this method arethat 1205761 and 1205762 are introduced into the objective functions ofQPPs and the parameters V1 and V2 are used to regulate thewidth of 1205761 and 1205762 tubes Also the parameter 119901 is designed togive an unbalance weight for the slack vectors 120585 and 120585lowast Basedon the concept of asymmetric V-TSVR a nonlinear waveletstransform based weighted TSVR is firstly proposed in thispaper By comparing with the traditional TSVR algorithmthe proposed algorithm introduces awavelet transform basedweighted matrix D1 and a coefficient vector D2 into theobjective function of TSVR Also the parameters 1205761 and 1205762are not adjustable by user anymore which means they areboth introduced into the objective functions Simultaneouslythe regularization is also considered to obtain the optimalsolutions Therefore the QPPs of nonlinear WTWTSVR areproposed as follows

min1205961 11988711205851205761

12 (y minus (119870(AA119879)1205961 + 1198871e))119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)st y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585 120585 ge 0e 1205761 ge 0

(12)

and

min1205962 1198872120585

lowast 1205762

12 (y minus (119870 (AA119879)1205962 + 1198872e))119879D1 (y minus (119870 (AA119879)1205962 + 1198872e)) + 11988832 (12059611987921205962 + 11988721) + 1198884 (D1198792 120585lowast + V21205762)st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 120585lowast 120585lowast ge 0e 1205762 ge 0

(13)

where 1198881 1198882 1198883 1198884 V1 V2 ge 0 are regulating parametersD1 is adiagonal matrix with the order of 119897 times 119897 and D2 is a coefficient

vector with the length of 119897 times 1 The determination of D1 andD2 will be discussed later

Complexity 5

The first term in the objective function of (12) or (13) isused to minimize the sums of squared Euclidean distancesfrom the estimated function 1198911(x) = 119870(x119879A119879)1205961 + 1198871 or1198912(x) = 119870(x119879A119879)1205962 + 1198872 to the training points The matrixD1 gives different weights for each Euclidean distance Thesecond term is the regularization term to avoid the over-fitting problem The third term minimizes the slack vector120585 or 120585lowast and the width of 1205761-tube or 1205762-tube The coefficientvector D2 is a penalty vector for the slack vector To solve theproblem in (12) the Lagrangian function can be introducedthat is

119871 (1205961 1198871 120585 1205761120572120573 120574)= 12 (y minus (119870 (AA119879)1205961 + 1198871e))119879sdotD1 (y minus (119870 (AA119879)1205961 + 1198871e))+ 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)minus 120572119879 (y minus (119870(AA119879)1205961 + 1198871e) + 1205761e + 120585) minus 120573119879120585minus 1205741205761

(14)

where 120572 120573 and 120574 are the positive Lagrangian multipliers Bydifferentiating 119871 with respect to the variables 1205961 1198871 120585 1205761 wehave

1205971198711205971205961 = minus119870(AA119879)119879D1 (y minus (119870(AA119879)1205961 + 1198871e))+ 119870(AA119879)119879 120572 + 11988811205961 = 0

(15)

1205971198711205971198871 = minuse119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + e119879120572

+ 11988811198871 = 0 (16)

120597119871120597120585 = 1198882D2 minus 120572 minus 120573 = 0 (17)

1205971198711205971205761 = 1198882V1 minus e119879120572 minus 120574 = 0 (18)

The KKT conditions are given by

y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585120585 ge 0e

120572119879 (y minus (119870 (AA119879)1205961 + 1198871e) + 1205761e + 120585) = 0120572 ge 0e

120573119879120585 = 0120573 ge 0e

1205741205761 = 0 120574 ge 0

(19)

Combining (15) and (16) we obtain

minus [[119870(AA119879)119879

e119879]]D1 (y minus (119870 (AA119879)1205961 + 1198871e))

+ [[119870(AA119879)119879

e119879]]120572 + 1198881 [

12059611198871 ] = 0(20)

Let H = [119870(AA119879)e] and u1 = [1205961198791 1198871]119879 and (20) can berewritten as

minusH119879D1y + (H119879D1H + 1198881I) u1 +H119879120572 = 0 (21)

where I is an identity matrix with appropriate dimensionFrom (21) we get

u1 = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (22)

From (15) (16) and (19) the following constraints can beobtained

e119879120572 le 1198882V1 0e le 120572 le 1198882D2 (23)

Substituting (22) into Lagrangian function 119871 we can getthe dual formulation of (12)

min120572

12120572119879H (H119879D1H + 1198881I)minus1H119879120572 + y119879120572

minus y119879D1H (H119879D1H + 1198881I)minus1H119879120572st 0e le 120572 le 1198882D2 e119879120572 le 1198882V1

(24)

Similarly the dual formulation of (13) can be derived asfollows

min120578

12120578119879H (H119879D1H + 1198883I)minus1H119879120578+ y119879D1H (H119879D1H + 1198883I)minus1H119879120578 minus y119879120578

119904119905 0e le 120578 le 1198884D2 e119879120578 le 1198884V2(25)

To solve the above QPPs the vectors 1205961 1198871 and 1205962 1198872 canbe expressed by

[12059611198871 ] = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (26)

and

[12059621198872 ] = (H119879D1H + 1198883I)minus1H119879 (D1y + 120578) (27)

By substituting the above results into (3) the final regres-sion function can be obtained

232 Determination of Wavelets Transform Based WeightedMatrixD1 and aCoefficientVectorD2 Thewavelet transformcan be used to denoise the time series signal Based onthe work of Ingrid Daubechies the Daubechies wavelets

6 Complexity

are a family of orthogonal wavelets for a discrete wavelettransform There is a scaling function (called father wavelet)for each wavelet type which generates an orthogonal mul-tiresolution analysis Daubechies orthogonal wavelets 1198891198871 minus11988911988710 are commonly used

The wavelet transform process includes three stagesdecomposition signal processing and reconstruction Ineach step of decomposition the signal can be decomposedinto two sets of signals high frequency signal and lowfrequency signal Suppose that there is a time series signal SAfter the first step of decomposition it generates two signalsone is high frequency part Sh1 and another is low frequencypart Sl1 Then in the second step of decomposition the lowfrequency signal Sl1 can be decomposed further into Sh2and Sl2 After 119896 steps of decomposition 119896 + 1 groups ofdecomposed sequence (Sh1 Sh2 Sh119896 Sl119896) are obtainedwhere Sl119896 represents the contour of the original signal Sand Sh1 Sh2 Sh119896 represent the subtle fluctuations Thedecomposition process of signal S is shown in Figure 1 anddefined as follows

Sl119896 (119899) = 119897119896minus1sum119898=1

120601 (119898 minus 2119899) Sl119896minus1 (119898) (28)

Sh119896 (119899) = 119897119896minus1sum119898=1

120593 (119898 minus 2119899) Sl119896minus1 (119898) (29)

where Sl119896minus1 with the length 119897119896minus1 is the signal to be decom-posed Sl119896 and Sh119896 are the results in the 119896-th step 120601(119898 minus 2119899)and 120593(119898 minus 2119899) are called scaling sequence (low pass filter)and wavelets sequence respectively [24] In this paper 1198891198872wavelet with the length of 4 is adopted After wavelet trans-forming appropriate signal processing can be carried outIn the stage of reconstruction the processed high frequencysignal Shlowast119896 and low frequency signal Sllowast119896 are reconstructed togenerate the target signal Slowast Let P and Q be the matrix withthe order of 119897119896times119897119896minus1 P119899119898 = 120601(119898minus2119899) andQ119899119898 = 120593(119898minus2119899)The reconstruction process is shown in Figure 2 Therefore(28) and (29) can be rewritten as follows

Sl119896 (119899) = P sdot Sl119896minus1 (119898) (30)

Sh119896 (119899) = Q sdot Sl119896minus1 (119898) (31)

The signal Sllowast119896minus1 can be generated by reconstructing Sllowast119896and Shlowast119896

Sllowast119896minus1 (119898) = Pminus1 sdot Sllowast119896 (119899) +Qminus1 sdot Shlowast119896 (119899) (32)

If the output vector S = [1198781 1198782 119878119897]119879 of a predictionmodel is a time sequence then the wavelets transform canbe used to denoise the output of the training samples Afterthe decomposition signal processing and reconstructionprocess a denoising sequence Slowast = [119878lowast1 119878lowast2 119878lowast119897 ]119879 can beobtained The absolute difference vector 119903119894 = |119878119894 minus 119878lowast119894 | 119894 =1 2 119897 and r = [1199031 1199032 119903119897]119879 between 119878 and 119878lowast denote thedistance from the training samples to the denoising samplesIn the WTWTSVR a small 119903119894 reflects a large weight on thedistance between the estimated value and training value of the

S

Sh1

Sl1Sh2

Sl2

Slk

Shk

Figure 1 The process of decomposition

SlowastShlowastk-1

Sllowastk-1

Sllowast1

Sllowastk

Shlowastk

Shlowast

1

Figure 2 The process of reconstruction

119894-th sample which can be defined as the following Gaussianfunction

119889119894 = exp(minus 11990321198942120590lowast2) 119894 = 1 2 119897 (33)

where 119889119894 denotes the weight coefficient and 120590lowast is the widthof the Gaussian function Therefore the wavelets transformbased weighted matrix D1 and the coefficient vector D2can be determined by D1 = diag(1198891 1198892 119889119897) and D2 =[1198891 1198892 119889119897]119879233 Computational Complexity Analysis The computationcomplexity of the proposed algorithm is mainly determinedby the computations of a pair of QPPs and a pair of inversematrices If the number of the training samples is l then thetraining complexity of dual QPPs is about 119874(21198973) while thetraining complexity of the traditional SVR is about 119874(81198973)which implies that the training speed of SVR is about fourtimes the proposed algorithm Also a pair of inverse matriceswith the size (119897 + 1) times (119897 + 1) in QPPs have the samecomputational cost 119874(1198973) During the training process itis a good way to cache the pair of inverse matrices withsome memory cost in order to avoid repeated computationsIn addition the proposed algorithm contains the wavelettransform weighted matrix and db2 wavelet with length of4 is used in this paper Then the complexity of wavelettransform is less than 8l By comparingwith the computationsof QPPs and inverse matrix the complexity of computing thewavelet matrix can be ignored Therefore the computationcomplexity of the proposed algorithm is about 119874(31198973)3 Establishment of Static Control Model

The end-point carbon content (denoted as C) and the tem-perature (denoted as T) are main factors to test the qualityof steelmaking The ultimate goal of steelmaking is to control

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

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40 45 50 55 60 65 70

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)

plusmn000510

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∘C)

Actual value (∘C)

Pred

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d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

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0

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minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

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155

16

Oxy

gen

volu

me (

NＧ

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Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 3

(2)TheComputational Complexity KNNalgorithm requires alarge amount of computations because the distance betweeneach sample to all known samples must be computed toobtain its K nearest neighbors By comparing with KNNweighting scheme the wavelet transform weighting schemehas less computational complexity because it is dealingwith one dimensional output samples and the computationcomplexity is proportional to the number of samples l KNNscheme is dealing with the input samples the computationcomplexity of KNN scheme is proportional to 1198972 With theincreasing of dimensions and number of the samples it willhave a large amount of computations

Therefore the wavelet transform weighting scheme ismore competitive than KNN weighting scheme for the timesequence samples due to its low computational complexity

2 Background

21 Description of BOF Steelmaking BOF is used to producethe steel with wide range of carbon alloy and special alloysteels Normally the capacity of BOF is between 100 tonsand 400 tons When the molten iron is delivered to theconverter through the rail the desulphurization process isfirstly required In BOF the hot metal and scrap lime andother fluxes are poured into the converter The oxidationreaction is carried out with carbon silicon phosphorusmanganese and some iron by blowing in a certain volumeof oxygen The ultimate goal of steelmaking is to produce thesteel with specific chemical composition at suitable tappingtemperature The control of BOF is difficult because thewhole smelting process is only half an hour and there isno opportunity for sampling and analysis in the smeltingprocess The proportion of the iron and scrap is about 31 inBOF The crane loads the waste into the container and thenpours the molten iron into the converter The water cooledoxygen lance enters the converter the high purity oxygenis blown into BOF at 16000 cubic feet per minute and theoxygen is reacted with carbon and other elements to reducethe impurity in the molten metal and converts it into a cleanhigh quality liquid steel The molten steel is poured into theladle and sent to the metallurgical equipment of the ladle [13]

Through the oxidation reaction of oxygen blown in BOFthe molten pig iron and the scrap can be converted into steelIt is a widely used steelmaking method with its higher pro-ductivity and low production cost [3] However the physicaland chemical process of BOF is very complicated Also thereare various types of steel produced in the same BOF whichmeans that the grade of steel is changed frequently Thereforethe BOF modelling is a challenge task The main objective ofthe modelling is to obtain the prescribed end-point carboncontent and temperature

22 Nonlinear Twin Support Vector Regression Support vec-tor regression (SVR) was proposed for the applications ofregression problems For the nonlinear case it is based onthe structural riskminimization andVapnik 120576-insensitive lossfunction In order to improve the training speed of SVR Pengproposed a TSVR algorithm in 2010 The difference betweenTSVR and SVR is that SVR solves one large QPP problem and

TSVR solves two smallQPPproblems to improve the learningefficiency Assume that a sample is an 119899-dimensional vectorand the number of the samples is 119897 which can be expressedas (x1 1199101) (x119897 119910119897) Let A = [x1 x119897]119879 isin 119877119897times119899 be theinput data set of training samples y = [1199101 y119897]119879 isin 119877119897 bethe corresponding output and e = [1 1]119879 be the onesvector with appropriate dimensions Assume119870( ) denotes anonlinear kernel function Let119870(AA119879) be the kernel matrixwith order 119897 and its (119894 119895)-th element (119894 119895 = 1 2 119897) bedefined by

[119870 (AA119879)]119894119895= 119870 (x119894 x119895) = (Φ (x119894) sdot Φ (x119895)) isin 119877 (1)

Here the kernel function 119870(x x119894) represents the inner prod-uct of the nonlinear mapping functions Φ(x119894) and Φ(x119895) inthe high dimensional feature space Because there are variouskernel functions the performance comparisons of kernelfunctions will be discussed later In this paper the radial basiskernel function (RBF) is chosen as follows

119870 (x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816221205902 ) (2)

where 120590 is the width of the kernel function Let 119870(x119879A119879) =(119870(x x1) 119870(x x2) 119870(x x119897)) be a row vector in 119877119897 Thentwo 120576-insensitive bound functions 1198911(x) = 119870(x119879A119879)1205961 + 1198871and1198912(x) = 119870(x119879A119879)1205962+1198872 can be obtained where12059611205962 isin119877119897 are the normal vectors and 1198871 1198872 isin 119877 are the bias valuesTherefore the final regression function 119891(x) is determined bythe mean of 1198911(x) and 1198912(x) that is

119891 (x) = 12 (1198911 (x) + 1198912 (x))= 12119870 (x119879A119879) (1205961 + 1205962) + 12 (1198871 + 1198872)

(3)

Nonlinear TSVR can be obtained by solving two QPPs asfollows

min1205961 1198871120585

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus 1205761e minus (119870(AA119879)1205961 + 1198871e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198881e119879120585st y minus (119870 (AA119879)1205961 + 1198871e) ge 1205761e minus 120585 120585 ge 0119890 (4)

and

min1205962 1198872120574

12 1003816100381610038161003816100381610038161003816100381610038161003816y + 1205762e minus (119870 (AA119879)1205962 + 1198872e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198882e119879120574st 119870(AA119879)1205962 + 1198872e minus y ge 1205762e minus 120574 120574 ge 0e (5)

By introducing the Lagrangian function and Karush-Kuhn-Tucker conditions the dual formulations of (4) and (5)can be derived as follows

max120572

minus 12120572119879G (G119879G)minus1G119879120572 + g119879G (G119879G)minus1G119879120572minus g119879120572

st 0e le 120572 le 1198881e(6)

4 Complexity

and

max120573

minus 12120573119879G (G119879G)minus1G119879120573 minus h119879G (G119879G)minus1G119879120573+ h119879120573

st 0e le 120573 le 1198882e(7)

whereG = [119870(AA119879) e] g = y minus 1205761e and h = y + 1205762eTo solve the above QPPs (6) and (7) the vectors1205961 1198871 and1205962 1198872 can be obtained

[12059611198871 ] = (G119879G)minus1G119879 (g minus 120572) (8)

and

[12059621198872 ] = (G119879G)minus1G119879 (h + 120573) (9)

By substituting the above results into (3) the final regres-sion function can be obtained

23 Nonlinear Wavelet Transform Based Weighted TwinSupport Vector Regression

231 Model Description of Nonlinear WTWTSVR In 2017Xu el al [20] proposed the asymmetric V-TSVR algorithmbased on pinball loss functions This new algorithm canenhance the generalization ability by tuning new modelparametersTheQPPs of nonlinear asymmetric V-TSVR wereproposed as follows

min1205961 11988711205761120585

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205961 + 1198871e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198881V11205761+ 1119897 1198881e119879120585

st y minus (119870 (AA119879)1205961 + 1198871e)ge minus1205761e minus 2 (1 minus 119901) 120585 120585 ge 0e 1205761 ge 0

(10)

and

min1205962 11988721205762 120574

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205962 + 1198872e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198882V21205762+ 1119897 1198882e119879120585lowast

st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 2119901120585lowast120585lowast ge 0e 1205762 ge 0

(11)

where 1198881 1198882 V1 V2 ge 0 are regulating parameters and theparameter 119901 isin (0 1) is used to apply a slightly differentpenalty for the outliers The contributions of this method arethat 1205761 and 1205762 are introduced into the objective functions ofQPPs and the parameters V1 and V2 are used to regulate thewidth of 1205761 and 1205762 tubes Also the parameter 119901 is designed togive an unbalance weight for the slack vectors 120585 and 120585lowast Basedon the concept of asymmetric V-TSVR a nonlinear waveletstransform based weighted TSVR is firstly proposed in thispaper By comparing with the traditional TSVR algorithmthe proposed algorithm introduces awavelet transform basedweighted matrix D1 and a coefficient vector D2 into theobjective function of TSVR Also the parameters 1205761 and 1205762are not adjustable by user anymore which means they areboth introduced into the objective functions Simultaneouslythe regularization is also considered to obtain the optimalsolutions Therefore the QPPs of nonlinear WTWTSVR areproposed as follows

min1205961 11988711205851205761

12 (y minus (119870(AA119879)1205961 + 1198871e))119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)st y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585 120585 ge 0e 1205761 ge 0

(12)

and

min1205962 1198872120585

lowast 1205762

12 (y minus (119870 (AA119879)1205962 + 1198872e))119879D1 (y minus (119870 (AA119879)1205962 + 1198872e)) + 11988832 (12059611987921205962 + 11988721) + 1198884 (D1198792 120585lowast + V21205762)st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 120585lowast 120585lowast ge 0e 1205762 ge 0

(13)

where 1198881 1198882 1198883 1198884 V1 V2 ge 0 are regulating parametersD1 is adiagonal matrix with the order of 119897 times 119897 and D2 is a coefficient

vector with the length of 119897 times 1 The determination of D1 andD2 will be discussed later

Complexity 5

The first term in the objective function of (12) or (13) isused to minimize the sums of squared Euclidean distancesfrom the estimated function 1198911(x) = 119870(x119879A119879)1205961 + 1198871 or1198912(x) = 119870(x119879A119879)1205962 + 1198872 to the training points The matrixD1 gives different weights for each Euclidean distance Thesecond term is the regularization term to avoid the over-fitting problem The third term minimizes the slack vector120585 or 120585lowast and the width of 1205761-tube or 1205762-tube The coefficientvector D2 is a penalty vector for the slack vector To solve theproblem in (12) the Lagrangian function can be introducedthat is

119871 (1205961 1198871 120585 1205761120572120573 120574)= 12 (y minus (119870 (AA119879)1205961 + 1198871e))119879sdotD1 (y minus (119870 (AA119879)1205961 + 1198871e))+ 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)minus 120572119879 (y minus (119870(AA119879)1205961 + 1198871e) + 1205761e + 120585) minus 120573119879120585minus 1205741205761

(14)

where 120572 120573 and 120574 are the positive Lagrangian multipliers Bydifferentiating 119871 with respect to the variables 1205961 1198871 120585 1205761 wehave

1205971198711205971205961 = minus119870(AA119879)119879D1 (y minus (119870(AA119879)1205961 + 1198871e))+ 119870(AA119879)119879 120572 + 11988811205961 = 0

(15)

1205971198711205971198871 = minuse119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + e119879120572

+ 11988811198871 = 0 (16)

120597119871120597120585 = 1198882D2 minus 120572 minus 120573 = 0 (17)

1205971198711205971205761 = 1198882V1 minus e119879120572 minus 120574 = 0 (18)

The KKT conditions are given by

y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585120585 ge 0e

120572119879 (y minus (119870 (AA119879)1205961 + 1198871e) + 1205761e + 120585) = 0120572 ge 0e

120573119879120585 = 0120573 ge 0e

1205741205761 = 0 120574 ge 0

(19)

Combining (15) and (16) we obtain

minus [[119870(AA119879)119879

e119879]]D1 (y minus (119870 (AA119879)1205961 + 1198871e))

+ [[119870(AA119879)119879

e119879]]120572 + 1198881 [

12059611198871 ] = 0(20)

Let H = [119870(AA119879)e] and u1 = [1205961198791 1198871]119879 and (20) can berewritten as

minusH119879D1y + (H119879D1H + 1198881I) u1 +H119879120572 = 0 (21)

where I is an identity matrix with appropriate dimensionFrom (21) we get

u1 = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (22)

From (15) (16) and (19) the following constraints can beobtained

e119879120572 le 1198882V1 0e le 120572 le 1198882D2 (23)

Substituting (22) into Lagrangian function 119871 we can getthe dual formulation of (12)

min120572

12120572119879H (H119879D1H + 1198881I)minus1H119879120572 + y119879120572

minus y119879D1H (H119879D1H + 1198881I)minus1H119879120572st 0e le 120572 le 1198882D2 e119879120572 le 1198882V1

(24)

Similarly the dual formulation of (13) can be derived asfollows

min120578

12120578119879H (H119879D1H + 1198883I)minus1H119879120578+ y119879D1H (H119879D1H + 1198883I)minus1H119879120578 minus y119879120578

119904119905 0e le 120578 le 1198884D2 e119879120578 le 1198884V2(25)

To solve the above QPPs the vectors 1205961 1198871 and 1205962 1198872 canbe expressed by

[12059611198871 ] = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (26)

and

[12059621198872 ] = (H119879D1H + 1198883I)minus1H119879 (D1y + 120578) (27)

By substituting the above results into (3) the final regres-sion function can be obtained

232 Determination of Wavelets Transform Based WeightedMatrixD1 and aCoefficientVectorD2 Thewavelet transformcan be used to denoise the time series signal Based onthe work of Ingrid Daubechies the Daubechies wavelets

6 Complexity

are a family of orthogonal wavelets for a discrete wavelettransform There is a scaling function (called father wavelet)for each wavelet type which generates an orthogonal mul-tiresolution analysis Daubechies orthogonal wavelets 1198891198871 minus11988911988710 are commonly used

The wavelet transform process includes three stagesdecomposition signal processing and reconstruction Ineach step of decomposition the signal can be decomposedinto two sets of signals high frequency signal and lowfrequency signal Suppose that there is a time series signal SAfter the first step of decomposition it generates two signalsone is high frequency part Sh1 and another is low frequencypart Sl1 Then in the second step of decomposition the lowfrequency signal Sl1 can be decomposed further into Sh2and Sl2 After 119896 steps of decomposition 119896 + 1 groups ofdecomposed sequence (Sh1 Sh2 Sh119896 Sl119896) are obtainedwhere Sl119896 represents the contour of the original signal Sand Sh1 Sh2 Sh119896 represent the subtle fluctuations Thedecomposition process of signal S is shown in Figure 1 anddefined as follows

Sl119896 (119899) = 119897119896minus1sum119898=1

120601 (119898 minus 2119899) Sl119896minus1 (119898) (28)

Sh119896 (119899) = 119897119896minus1sum119898=1

120593 (119898 minus 2119899) Sl119896minus1 (119898) (29)

where Sl119896minus1 with the length 119897119896minus1 is the signal to be decom-posed Sl119896 and Sh119896 are the results in the 119896-th step 120601(119898 minus 2119899)and 120593(119898 minus 2119899) are called scaling sequence (low pass filter)and wavelets sequence respectively [24] In this paper 1198891198872wavelet with the length of 4 is adopted After wavelet trans-forming appropriate signal processing can be carried outIn the stage of reconstruction the processed high frequencysignal Shlowast119896 and low frequency signal Sllowast119896 are reconstructed togenerate the target signal Slowast Let P and Q be the matrix withthe order of 119897119896times119897119896minus1 P119899119898 = 120601(119898minus2119899) andQ119899119898 = 120593(119898minus2119899)The reconstruction process is shown in Figure 2 Therefore(28) and (29) can be rewritten as follows

Sl119896 (119899) = P sdot Sl119896minus1 (119898) (30)

Sh119896 (119899) = Q sdot Sl119896minus1 (119898) (31)

The signal Sllowast119896minus1 can be generated by reconstructing Sllowast119896and Shlowast119896

Sllowast119896minus1 (119898) = Pminus1 sdot Sllowast119896 (119899) +Qminus1 sdot Shlowast119896 (119899) (32)

If the output vector S = [1198781 1198782 119878119897]119879 of a predictionmodel is a time sequence then the wavelets transform canbe used to denoise the output of the training samples Afterthe decomposition signal processing and reconstructionprocess a denoising sequence Slowast = [119878lowast1 119878lowast2 119878lowast119897 ]119879 can beobtained The absolute difference vector 119903119894 = |119878119894 minus 119878lowast119894 | 119894 =1 2 119897 and r = [1199031 1199032 119903119897]119879 between 119878 and 119878lowast denote thedistance from the training samples to the denoising samplesIn the WTWTSVR a small 119903119894 reflects a large weight on thedistance between the estimated value and training value of the

S

Sh1

Sl1Sh2

Sl2

Slk

Shk

Figure 1 The process of decomposition

SlowastShlowastk-1

Sllowastk-1

Sllowast1

Sllowastk

Shlowastk

Shlowast

1

Figure 2 The process of reconstruction

119894-th sample which can be defined as the following Gaussianfunction

119889119894 = exp(minus 11990321198942120590lowast2) 119894 = 1 2 119897 (33)

where 119889119894 denotes the weight coefficient and 120590lowast is the widthof the Gaussian function Therefore the wavelets transformbased weighted matrix D1 and the coefficient vector D2can be determined by D1 = diag(1198891 1198892 119889119897) and D2 =[1198891 1198892 119889119897]119879233 Computational Complexity Analysis The computationcomplexity of the proposed algorithm is mainly determinedby the computations of a pair of QPPs and a pair of inversematrices If the number of the training samples is l then thetraining complexity of dual QPPs is about 119874(21198973) while thetraining complexity of the traditional SVR is about 119874(81198973)which implies that the training speed of SVR is about fourtimes the proposed algorithm Also a pair of inverse matriceswith the size (119897 + 1) times (119897 + 1) in QPPs have the samecomputational cost 119874(1198973) During the training process itis a good way to cache the pair of inverse matrices withsome memory cost in order to avoid repeated computationsIn addition the proposed algorithm contains the wavelettransform weighted matrix and db2 wavelet with length of4 is used in this paper Then the complexity of wavelettransform is less than 8l By comparingwith the computationsof QPPs and inverse matrix the complexity of computing thewavelet matrix can be ignored Therefore the computationcomplexity of the proposed algorithm is about 119874(31198973)3 Establishment of Static Control Model

The end-point carbon content (denoted as C) and the tem-perature (denoted as T) are main factors to test the qualityof steelmaking The ultimate goal of steelmaking is to control

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

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1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

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lue (

NＧ

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Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

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minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

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145

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Oxy

gen

volu

me (

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Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

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eigh

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Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

4 Complexity

and

max120573

minus 12120573119879G (G119879G)minus1G119879120573 minus h119879G (G119879G)minus1G119879120573+ h119879120573

st 0e le 120573 le 1198882e(7)

whereG = [119870(AA119879) e] g = y minus 1205761e and h = y + 1205762eTo solve the above QPPs (6) and (7) the vectors1205961 1198871 and1205962 1198872 can be obtained

[12059611198871 ] = (G119879G)minus1G119879 (g minus 120572) (8)

and

[12059621198872 ] = (G119879G)minus1G119879 (h + 120573) (9)

By substituting the above results into (3) the final regres-sion function can be obtained

23 Nonlinear Wavelet Transform Based Weighted TwinSupport Vector Regression

231 Model Description of Nonlinear WTWTSVR In 2017Xu el al [20] proposed the asymmetric V-TSVR algorithmbased on pinball loss functions This new algorithm canenhance the generalization ability by tuning new modelparametersTheQPPs of nonlinear asymmetric V-TSVR wereproposed as follows

min1205961 11988711205761120585

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205961 + 1198871e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198881V11205761+ 1119897 1198881e119879120585

st y minus (119870 (AA119879)1205961 + 1198871e)ge minus1205761e minus 2 (1 minus 119901) 120585 120585 ge 0e 1205761 ge 0

(10)

and

min1205962 11988721205762 120574

12 1003816100381610038161003816100381610038161003816100381610038161003816y minus (119870 (AA119879)1205962 + 1198872e)10038161003816100381610038161003816100381610038161003816100381610038162 + 1198882V21205762+ 1119897 1198882e119879120585lowast

st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 2119901120585lowast120585lowast ge 0e 1205762 ge 0

(11)

where 1198881 1198882 V1 V2 ge 0 are regulating parameters and theparameter 119901 isin (0 1) is used to apply a slightly differentpenalty for the outliers The contributions of this method arethat 1205761 and 1205762 are introduced into the objective functions ofQPPs and the parameters V1 and V2 are used to regulate thewidth of 1205761 and 1205762 tubes Also the parameter 119901 is designed togive an unbalance weight for the slack vectors 120585 and 120585lowast Basedon the concept of asymmetric V-TSVR a nonlinear waveletstransform based weighted TSVR is firstly proposed in thispaper By comparing with the traditional TSVR algorithmthe proposed algorithm introduces awavelet transform basedweighted matrix D1 and a coefficient vector D2 into theobjective function of TSVR Also the parameters 1205761 and 1205762are not adjustable by user anymore which means they areboth introduced into the objective functions Simultaneouslythe regularization is also considered to obtain the optimalsolutions Therefore the QPPs of nonlinear WTWTSVR areproposed as follows

min1205961 11988711205851205761

12 (y minus (119870(AA119879)1205961 + 1198871e))119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)st y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585 120585 ge 0e 1205761 ge 0

(12)

and

min1205962 1198872120585

lowast 1205762

12 (y minus (119870 (AA119879)1205962 + 1198872e))119879D1 (y minus (119870 (AA119879)1205962 + 1198872e)) + 11988832 (12059611987921205962 + 11988721) + 1198884 (D1198792 120585lowast + V21205762)st 119870(AA119879)1205962 + 1198872e minus y ge minus1205762e minus 120585lowast 120585lowast ge 0e 1205762 ge 0

(13)

where 1198881 1198882 1198883 1198884 V1 V2 ge 0 are regulating parametersD1 is adiagonal matrix with the order of 119897 times 119897 and D2 is a coefficient

vector with the length of 119897 times 1 The determination of D1 andD2 will be discussed later

Complexity 5

The first term in the objective function of (12) or (13) isused to minimize the sums of squared Euclidean distancesfrom the estimated function 1198911(x) = 119870(x119879A119879)1205961 + 1198871 or1198912(x) = 119870(x119879A119879)1205962 + 1198872 to the training points The matrixD1 gives different weights for each Euclidean distance Thesecond term is the regularization term to avoid the over-fitting problem The third term minimizes the slack vector120585 or 120585lowast and the width of 1205761-tube or 1205762-tube The coefficientvector D2 is a penalty vector for the slack vector To solve theproblem in (12) the Lagrangian function can be introducedthat is

119871 (1205961 1198871 120585 1205761120572120573 120574)= 12 (y minus (119870 (AA119879)1205961 + 1198871e))119879sdotD1 (y minus (119870 (AA119879)1205961 + 1198871e))+ 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)minus 120572119879 (y minus (119870(AA119879)1205961 + 1198871e) + 1205761e + 120585) minus 120573119879120585minus 1205741205761

(14)

where 120572 120573 and 120574 are the positive Lagrangian multipliers Bydifferentiating 119871 with respect to the variables 1205961 1198871 120585 1205761 wehave

1205971198711205971205961 = minus119870(AA119879)119879D1 (y minus (119870(AA119879)1205961 + 1198871e))+ 119870(AA119879)119879 120572 + 11988811205961 = 0

(15)

1205971198711205971198871 = minuse119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + e119879120572

+ 11988811198871 = 0 (16)

120597119871120597120585 = 1198882D2 minus 120572 minus 120573 = 0 (17)

1205971198711205971205761 = 1198882V1 minus e119879120572 minus 120574 = 0 (18)

The KKT conditions are given by

y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585120585 ge 0e

120572119879 (y minus (119870 (AA119879)1205961 + 1198871e) + 1205761e + 120585) = 0120572 ge 0e

120573119879120585 = 0120573 ge 0e

1205741205761 = 0 120574 ge 0

(19)

Combining (15) and (16) we obtain

minus [[119870(AA119879)119879

e119879]]D1 (y minus (119870 (AA119879)1205961 + 1198871e))

+ [[119870(AA119879)119879

e119879]]120572 + 1198881 [

12059611198871 ] = 0(20)

Let H = [119870(AA119879)e] and u1 = [1205961198791 1198871]119879 and (20) can berewritten as

minusH119879D1y + (H119879D1H + 1198881I) u1 +H119879120572 = 0 (21)

where I is an identity matrix with appropriate dimensionFrom (21) we get

u1 = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (22)

From (15) (16) and (19) the following constraints can beobtained

e119879120572 le 1198882V1 0e le 120572 le 1198882D2 (23)

Substituting (22) into Lagrangian function 119871 we can getthe dual formulation of (12)

min120572

12120572119879H (H119879D1H + 1198881I)minus1H119879120572 + y119879120572

minus y119879D1H (H119879D1H + 1198881I)minus1H119879120572st 0e le 120572 le 1198882D2 e119879120572 le 1198882V1

(24)

Similarly the dual formulation of (13) can be derived asfollows

min120578

12120578119879H (H119879D1H + 1198883I)minus1H119879120578+ y119879D1H (H119879D1H + 1198883I)minus1H119879120578 minus y119879120578

119904119905 0e le 120578 le 1198884D2 e119879120578 le 1198884V2(25)

To solve the above QPPs the vectors 1205961 1198871 and 1205962 1198872 canbe expressed by

[12059611198871 ] = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (26)

and

[12059621198872 ] = (H119879D1H + 1198883I)minus1H119879 (D1y + 120578) (27)

By substituting the above results into (3) the final regres-sion function can be obtained

232 Determination of Wavelets Transform Based WeightedMatrixD1 and aCoefficientVectorD2 Thewavelet transformcan be used to denoise the time series signal Based onthe work of Ingrid Daubechies the Daubechies wavelets

6 Complexity

are a family of orthogonal wavelets for a discrete wavelettransform There is a scaling function (called father wavelet)for each wavelet type which generates an orthogonal mul-tiresolution analysis Daubechies orthogonal wavelets 1198891198871 minus11988911988710 are commonly used

The wavelet transform process includes three stagesdecomposition signal processing and reconstruction Ineach step of decomposition the signal can be decomposedinto two sets of signals high frequency signal and lowfrequency signal Suppose that there is a time series signal SAfter the first step of decomposition it generates two signalsone is high frequency part Sh1 and another is low frequencypart Sl1 Then in the second step of decomposition the lowfrequency signal Sl1 can be decomposed further into Sh2and Sl2 After 119896 steps of decomposition 119896 + 1 groups ofdecomposed sequence (Sh1 Sh2 Sh119896 Sl119896) are obtainedwhere Sl119896 represents the contour of the original signal Sand Sh1 Sh2 Sh119896 represent the subtle fluctuations Thedecomposition process of signal S is shown in Figure 1 anddefined as follows

Sl119896 (119899) = 119897119896minus1sum119898=1

120601 (119898 minus 2119899) Sl119896minus1 (119898) (28)

Sh119896 (119899) = 119897119896minus1sum119898=1

120593 (119898 minus 2119899) Sl119896minus1 (119898) (29)

where Sl119896minus1 with the length 119897119896minus1 is the signal to be decom-posed Sl119896 and Sh119896 are the results in the 119896-th step 120601(119898 minus 2119899)and 120593(119898 minus 2119899) are called scaling sequence (low pass filter)and wavelets sequence respectively [24] In this paper 1198891198872wavelet with the length of 4 is adopted After wavelet trans-forming appropriate signal processing can be carried outIn the stage of reconstruction the processed high frequencysignal Shlowast119896 and low frequency signal Sllowast119896 are reconstructed togenerate the target signal Slowast Let P and Q be the matrix withthe order of 119897119896times119897119896minus1 P119899119898 = 120601(119898minus2119899) andQ119899119898 = 120593(119898minus2119899)The reconstruction process is shown in Figure 2 Therefore(28) and (29) can be rewritten as follows

Sl119896 (119899) = P sdot Sl119896minus1 (119898) (30)

Sh119896 (119899) = Q sdot Sl119896minus1 (119898) (31)

The signal Sllowast119896minus1 can be generated by reconstructing Sllowast119896and Shlowast119896

Sllowast119896minus1 (119898) = Pminus1 sdot Sllowast119896 (119899) +Qminus1 sdot Shlowast119896 (119899) (32)

If the output vector S = [1198781 1198782 119878119897]119879 of a predictionmodel is a time sequence then the wavelets transform canbe used to denoise the output of the training samples Afterthe decomposition signal processing and reconstructionprocess a denoising sequence Slowast = [119878lowast1 119878lowast2 119878lowast119897 ]119879 can beobtained The absolute difference vector 119903119894 = |119878119894 minus 119878lowast119894 | 119894 =1 2 119897 and r = [1199031 1199032 119903119897]119879 between 119878 and 119878lowast denote thedistance from the training samples to the denoising samplesIn the WTWTSVR a small 119903119894 reflects a large weight on thedistance between the estimated value and training value of the

S

Sh1

Sl1Sh2

Sl2

Slk

Shk

Figure 1 The process of decomposition

SlowastShlowastk-1

Sllowastk-1

Sllowast1

Sllowastk

Shlowastk

Shlowast

1

Figure 2 The process of reconstruction

119894-th sample which can be defined as the following Gaussianfunction

119889119894 = exp(minus 11990321198942120590lowast2) 119894 = 1 2 119897 (33)

where 119889119894 denotes the weight coefficient and 120590lowast is the widthof the Gaussian function Therefore the wavelets transformbased weighted matrix D1 and the coefficient vector D2can be determined by D1 = diag(1198891 1198892 119889119897) and D2 =[1198891 1198892 119889119897]119879233 Computational Complexity Analysis The computationcomplexity of the proposed algorithm is mainly determinedby the computations of a pair of QPPs and a pair of inversematrices If the number of the training samples is l then thetraining complexity of dual QPPs is about 119874(21198973) while thetraining complexity of the traditional SVR is about 119874(81198973)which implies that the training speed of SVR is about fourtimes the proposed algorithm Also a pair of inverse matriceswith the size (119897 + 1) times (119897 + 1) in QPPs have the samecomputational cost 119874(1198973) During the training process itis a good way to cache the pair of inverse matrices withsome memory cost in order to avoid repeated computationsIn addition the proposed algorithm contains the wavelettransform weighted matrix and db2 wavelet with length of4 is used in this paper Then the complexity of wavelettransform is less than 8l By comparingwith the computationsof QPPs and inverse matrix the complexity of computing thewavelet matrix can be ignored Therefore the computationcomplexity of the proposed algorithm is about 119874(31198973)3 Establishment of Static Control Model

The end-point carbon content (denoted as C) and the tem-perature (denoted as T) are main factors to test the qualityof steelmaking The ultimate goal of steelmaking is to control

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 5

The first term in the objective function of (12) or (13) isused to minimize the sums of squared Euclidean distancesfrom the estimated function 1198911(x) = 119870(x119879A119879)1205961 + 1198871 or1198912(x) = 119870(x119879A119879)1205962 + 1198872 to the training points The matrixD1 gives different weights for each Euclidean distance Thesecond term is the regularization term to avoid the over-fitting problem The third term minimizes the slack vector120585 or 120585lowast and the width of 1205761-tube or 1205762-tube The coefficientvector D2 is a penalty vector for the slack vector To solve theproblem in (12) the Lagrangian function can be introducedthat is

119871 (1205961 1198871 120585 1205761120572120573 120574)= 12 (y minus (119870 (AA119879)1205961 + 1198871e))119879sdotD1 (y minus (119870 (AA119879)1205961 + 1198871e))+ 11988812 (12059611987911205961 + 11988721 ) + 1198882 (D1198792 120585 + V11205761)minus 120572119879 (y minus (119870(AA119879)1205961 + 1198871e) + 1205761e + 120585) minus 120573119879120585minus 1205741205761

(14)

where 120572 120573 and 120574 are the positive Lagrangian multipliers Bydifferentiating 119871 with respect to the variables 1205961 1198871 120585 1205761 wehave

1205971198711205971205961 = minus119870(AA119879)119879D1 (y minus (119870(AA119879)1205961 + 1198871e))+ 119870(AA119879)119879 120572 + 11988811205961 = 0

(15)

1205971198711205971198871 = minuse119879D1 (y minus (119870(AA119879)1205961 + 1198871e)) + e119879120572

+ 11988811198871 = 0 (16)

120597119871120597120585 = 1198882D2 minus 120572 minus 120573 = 0 (17)

1205971198711205971205761 = 1198882V1 minus e119879120572 minus 120574 = 0 (18)

The KKT conditions are given by

y minus (119870 (AA119879)1205961 + 1198871e) ge minus1205761e minus 120585120585 ge 0e

120572119879 (y minus (119870 (AA119879)1205961 + 1198871e) + 1205761e + 120585) = 0120572 ge 0e

120573119879120585 = 0120573 ge 0e

1205741205761 = 0 120574 ge 0

(19)

Combining (15) and (16) we obtain

minus [[119870(AA119879)119879

e119879]]D1 (y minus (119870 (AA119879)1205961 + 1198871e))

+ [[119870(AA119879)119879

e119879]]120572 + 1198881 [

12059611198871 ] = 0(20)

Let H = [119870(AA119879)e] and u1 = [1205961198791 1198871]119879 and (20) can berewritten as

minusH119879D1y + (H119879D1H + 1198881I) u1 +H119879120572 = 0 (21)

where I is an identity matrix with appropriate dimensionFrom (21) we get

u1 = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (22)

From (15) (16) and (19) the following constraints can beobtained

e119879120572 le 1198882V1 0e le 120572 le 1198882D2 (23)

Substituting (22) into Lagrangian function 119871 we can getthe dual formulation of (12)

min120572

12120572119879H (H119879D1H + 1198881I)minus1H119879120572 + y119879120572

minus y119879D1H (H119879D1H + 1198881I)minus1H119879120572st 0e le 120572 le 1198882D2 e119879120572 le 1198882V1

(24)

Similarly the dual formulation of (13) can be derived asfollows

min120578

12120578119879H (H119879D1H + 1198883I)minus1H119879120578+ y119879D1H (H119879D1H + 1198883I)minus1H119879120578 minus y119879120578

119904119905 0e le 120578 le 1198884D2 e119879120578 le 1198884V2(25)

To solve the above QPPs the vectors 1205961 1198871 and 1205962 1198872 canbe expressed by

[12059611198871 ] = (H119879D1H + 1198881I)minus1H119879 (D1y minus 120572) (26)

and

[12059621198872 ] = (H119879D1H + 1198883I)minus1H119879 (D1y + 120578) (27)

By substituting the above results into (3) the final regres-sion function can be obtained

232 Determination of Wavelets Transform Based WeightedMatrixD1 and aCoefficientVectorD2 Thewavelet transformcan be used to denoise the time series signal Based onthe work of Ingrid Daubechies the Daubechies wavelets

6 Complexity

are a family of orthogonal wavelets for a discrete wavelettransform There is a scaling function (called father wavelet)for each wavelet type which generates an orthogonal mul-tiresolution analysis Daubechies orthogonal wavelets 1198891198871 minus11988911988710 are commonly used

The wavelet transform process includes three stagesdecomposition signal processing and reconstruction Ineach step of decomposition the signal can be decomposedinto two sets of signals high frequency signal and lowfrequency signal Suppose that there is a time series signal SAfter the first step of decomposition it generates two signalsone is high frequency part Sh1 and another is low frequencypart Sl1 Then in the second step of decomposition the lowfrequency signal Sl1 can be decomposed further into Sh2and Sl2 After 119896 steps of decomposition 119896 + 1 groups ofdecomposed sequence (Sh1 Sh2 Sh119896 Sl119896) are obtainedwhere Sl119896 represents the contour of the original signal Sand Sh1 Sh2 Sh119896 represent the subtle fluctuations Thedecomposition process of signal S is shown in Figure 1 anddefined as follows

Sl119896 (119899) = 119897119896minus1sum119898=1

120601 (119898 minus 2119899) Sl119896minus1 (119898) (28)

Sh119896 (119899) = 119897119896minus1sum119898=1

120593 (119898 minus 2119899) Sl119896minus1 (119898) (29)

where Sl119896minus1 with the length 119897119896minus1 is the signal to be decom-posed Sl119896 and Sh119896 are the results in the 119896-th step 120601(119898 minus 2119899)and 120593(119898 minus 2119899) are called scaling sequence (low pass filter)and wavelets sequence respectively [24] In this paper 1198891198872wavelet with the length of 4 is adopted After wavelet trans-forming appropriate signal processing can be carried outIn the stage of reconstruction the processed high frequencysignal Shlowast119896 and low frequency signal Sllowast119896 are reconstructed togenerate the target signal Slowast Let P and Q be the matrix withthe order of 119897119896times119897119896minus1 P119899119898 = 120601(119898minus2119899) andQ119899119898 = 120593(119898minus2119899)The reconstruction process is shown in Figure 2 Therefore(28) and (29) can be rewritten as follows

Sl119896 (119899) = P sdot Sl119896minus1 (119898) (30)

Sh119896 (119899) = Q sdot Sl119896minus1 (119898) (31)

The signal Sllowast119896minus1 can be generated by reconstructing Sllowast119896and Shlowast119896

Sllowast119896minus1 (119898) = Pminus1 sdot Sllowast119896 (119899) +Qminus1 sdot Shlowast119896 (119899) (32)

If the output vector S = [1198781 1198782 119878119897]119879 of a predictionmodel is a time sequence then the wavelets transform canbe used to denoise the output of the training samples Afterthe decomposition signal processing and reconstructionprocess a denoising sequence Slowast = [119878lowast1 119878lowast2 119878lowast119897 ]119879 can beobtained The absolute difference vector 119903119894 = |119878119894 minus 119878lowast119894 | 119894 =1 2 119897 and r = [1199031 1199032 119903119897]119879 between 119878 and 119878lowast denote thedistance from the training samples to the denoising samplesIn the WTWTSVR a small 119903119894 reflects a large weight on thedistance between the estimated value and training value of the

S

Sh1

Sl1Sh2

Sl2

Slk

Shk

Figure 1 The process of decomposition

SlowastShlowastk-1

Sllowastk-1

Sllowast1

Sllowastk

Shlowastk

Shlowast

1

Figure 2 The process of reconstruction

119894-th sample which can be defined as the following Gaussianfunction

119889119894 = exp(minus 11990321198942120590lowast2) 119894 = 1 2 119897 (33)

where 119889119894 denotes the weight coefficient and 120590lowast is the widthof the Gaussian function Therefore the wavelets transformbased weighted matrix D1 and the coefficient vector D2can be determined by D1 = diag(1198891 1198892 119889119897) and D2 =[1198891 1198892 119889119897]119879233 Computational Complexity Analysis The computationcomplexity of the proposed algorithm is mainly determinedby the computations of a pair of QPPs and a pair of inversematrices If the number of the training samples is l then thetraining complexity of dual QPPs is about 119874(21198973) while thetraining complexity of the traditional SVR is about 119874(81198973)which implies that the training speed of SVR is about fourtimes the proposed algorithm Also a pair of inverse matriceswith the size (119897 + 1) times (119897 + 1) in QPPs have the samecomputational cost 119874(1198973) During the training process itis a good way to cache the pair of inverse matrices withsome memory cost in order to avoid repeated computationsIn addition the proposed algorithm contains the wavelettransform weighted matrix and db2 wavelet with length of4 is used in this paper Then the complexity of wavelettransform is less than 8l By comparingwith the computationsof QPPs and inverse matrix the complexity of computing thewavelet matrix can be ignored Therefore the computationcomplexity of the proposed algorithm is about 119874(31198973)3 Establishment of Static Control Model

The end-point carbon content (denoted as C) and the tem-perature (denoted as T) are main factors to test the qualityof steelmaking The ultimate goal of steelmaking is to control

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

6 Complexity

are a family of orthogonal wavelets for a discrete wavelettransform There is a scaling function (called father wavelet)for each wavelet type which generates an orthogonal mul-tiresolution analysis Daubechies orthogonal wavelets 1198891198871 minus11988911988710 are commonly used

The wavelet transform process includes three stagesdecomposition signal processing and reconstruction Ineach step of decomposition the signal can be decomposedinto two sets of signals high frequency signal and lowfrequency signal Suppose that there is a time series signal SAfter the first step of decomposition it generates two signalsone is high frequency part Sh1 and another is low frequencypart Sl1 Then in the second step of decomposition the lowfrequency signal Sl1 can be decomposed further into Sh2and Sl2 After 119896 steps of decomposition 119896 + 1 groups ofdecomposed sequence (Sh1 Sh2 Sh119896 Sl119896) are obtainedwhere Sl119896 represents the contour of the original signal Sand Sh1 Sh2 Sh119896 represent the subtle fluctuations Thedecomposition process of signal S is shown in Figure 1 anddefined as follows

Sl119896 (119899) = 119897119896minus1sum119898=1

120601 (119898 minus 2119899) Sl119896minus1 (119898) (28)

Sh119896 (119899) = 119897119896minus1sum119898=1

120593 (119898 minus 2119899) Sl119896minus1 (119898) (29)

where Sl119896minus1 with the length 119897119896minus1 is the signal to be decom-posed Sl119896 and Sh119896 are the results in the 119896-th step 120601(119898 minus 2119899)and 120593(119898 minus 2119899) are called scaling sequence (low pass filter)and wavelets sequence respectively [24] In this paper 1198891198872wavelet with the length of 4 is adopted After wavelet trans-forming appropriate signal processing can be carried outIn the stage of reconstruction the processed high frequencysignal Shlowast119896 and low frequency signal Sllowast119896 are reconstructed togenerate the target signal Slowast Let P and Q be the matrix withthe order of 119897119896times119897119896minus1 P119899119898 = 120601(119898minus2119899) andQ119899119898 = 120593(119898minus2119899)The reconstruction process is shown in Figure 2 Therefore(28) and (29) can be rewritten as follows

Sl119896 (119899) = P sdot Sl119896minus1 (119898) (30)

Sh119896 (119899) = Q sdot Sl119896minus1 (119898) (31)

The signal Sllowast119896minus1 can be generated by reconstructing Sllowast119896and Shlowast119896

Sllowast119896minus1 (119898) = Pminus1 sdot Sllowast119896 (119899) +Qminus1 sdot Shlowast119896 (119899) (32)

If the output vector S = [1198781 1198782 119878119897]119879 of a predictionmodel is a time sequence then the wavelets transform canbe used to denoise the output of the training samples Afterthe decomposition signal processing and reconstructionprocess a denoising sequence Slowast = [119878lowast1 119878lowast2 119878lowast119897 ]119879 can beobtained The absolute difference vector 119903119894 = |119878119894 minus 119878lowast119894 | 119894 =1 2 119897 and r = [1199031 1199032 119903119897]119879 between 119878 and 119878lowast denote thedistance from the training samples to the denoising samplesIn the WTWTSVR a small 119903119894 reflects a large weight on thedistance between the estimated value and training value of the

S

Sh1

Sl1Sh2

Sl2

Slk

Shk

Figure 1 The process of decomposition

SlowastShlowastk-1

Sllowastk-1

Sllowast1

Sllowastk

Shlowastk

Shlowast

1

Figure 2 The process of reconstruction

119894-th sample which can be defined as the following Gaussianfunction

119889119894 = exp(minus 11990321198942120590lowast2) 119894 = 1 2 119897 (33)

where 119889119894 denotes the weight coefficient and 120590lowast is the widthof the Gaussian function Therefore the wavelets transformbased weighted matrix D1 and the coefficient vector D2can be determined by D1 = diag(1198891 1198892 119889119897) and D2 =[1198891 1198892 119889119897]119879233 Computational Complexity Analysis The computationcomplexity of the proposed algorithm is mainly determinedby the computations of a pair of QPPs and a pair of inversematrices If the number of the training samples is l then thetraining complexity of dual QPPs is about 119874(21198973) while thetraining complexity of the traditional SVR is about 119874(81198973)which implies that the training speed of SVR is about fourtimes the proposed algorithm Also a pair of inverse matriceswith the size (119897 + 1) times (119897 + 1) in QPPs have the samecomputational cost 119874(1198973) During the training process itis a good way to cache the pair of inverse matrices withsome memory cost in order to avoid repeated computationsIn addition the proposed algorithm contains the wavelettransform weighted matrix and db2 wavelet with length of4 is used in this paper Then the complexity of wavelettransform is less than 8l By comparingwith the computationsof QPPs and inverse matrix the complexity of computing thewavelet matrix can be ignored Therefore the computationcomplexity of the proposed algorithm is about 119874(31198973)3 Establishment of Static Control Model

The end-point carbon content (denoted as C) and the tem-perature (denoted as T) are main factors to test the qualityof steelmaking The ultimate goal of steelmaking is to control

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 7

WTWTSVRVM

Control ModelController BOF

R2 +

WTWTSVRCT

Prediction Model

R1 +

+

-

+

-

V

W

x1

x7

CP

TP

Tr

CrCgTg

Figure 3 Structure of proposed BOF control model

C and T to a satisfied region BOF steelmaking is a complexphysicochemical process so its mathematical model is verydifficult to establish Therefore the intelligent method such asTSVR can be used to approximate the BOF model From thecollected samples it is easy to see that the samples are listedas a time sequence which means they can be seen as a timesequence signal Hence the proposedWTWTSVR algorithmis appropriate to establish a model for BOF steelmaking

In this section a novel static control model for BOF isestablished based on WTWTSVR algorithm According tothe initial conditions of the hot metal and the desired end-point carbon content (denoted as 119862119892) and the temperature(denoted as119879119892) the relative oxygen blowing volume (denotedas V) and the weight of auxiliary raw material (denotedas W) can be calculated by the proposed model Figure 3shows the structure of the proposed BOF control modelwhich is composed of a prediction model for carbon contentand temperature (CT prediction model) a control modelfor oxygen blowing volume and the weight of auxiliary rawmaterials (VW control model) two parameter regulatingunits (R1 and R2) and a controller and a basic oxygenfurnace in any plant Firstly the WTWTSVR CT predictionmodel should be established by using the historic BOFsamples which consists of two individual models (C modeland T model) C model represents the prediction model ofthe end-point carbon content and T model represents theprediction of the end-point temperature The inputs of twomodels both include the initial conditions of the hot metaland the outputs of them are C and T respectively Theparameters of the prediction models can be regulated by R1to obtain the optimized models Secondly the WTWTSVRVW control model should be established based on theproposed prediction models and the oxygen blowing volumecan be calculated by V model and the weight of auxiliaryraw materials can be determined by W model The inputsof the control models both include the initial conditions ofthe hot metal the desired end-point carbon content 119862119892) and

the end-point temperature 119879119892The outputs of them areV andW respectively The parameters of the control models can beregulated by R2 After the regulation of R1 and R2 the staticcontrol model can be established For any future hot metalthe static control model can be used to calculate V and Wby the collected initial conditions and 119862119892 and 119879119892 Then thecalculated values of V and W will be sent to the controllerFinally the relative BOF system is controlled by the controllerto reach the satisfactory end-point region

31 Establishment of WTWTSVR CT Prediction Model Torealize the static BOF control an accurate prediction modelof BOF should be designed firstly The end-point predictionmodel is the foundation of the control model By collectingthe previous BOF samples the abnormal samples must bediscarded which may contain the wrong information ofBOF Through the mechanism analysis of BOF the influencefactors on the end-point information are mainly determinedby the initial conditions of hot metal which means theinfluence factors are taken as the independent input variablesof the predictionmodelsThe relative input variables are listedin Table 1 Note that the input variable x9 denotes the sumof the weight of all types of auxiliary materials which areincluding the light burned dolomite the dolomite stone thelime ore and scrap etc It has a guiding significance for realproduction and the proportion of the components can bedetermined by the experience of the userThe output variableof the model is the end-point carbon content C or the end-point temperature T

According to the prepared samples of BOF andWTWTSVR algorithm the regression function 119891119862119879(119909)can be given by

119891119862119879 (x) = 12119870 (x119879A119879) (1205961 + 1205962)119879 + 12 (1198871 + 1198872) (34)

where119891119862119879(x) denotes the estimation function of C model orT model and x = [1199091 1199092 1199099]119879

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

8 Complexity

Table 1 Independent input variables of prediction models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Oxygen blowing volume 1199098 (V) Nm3

Silicon content 1199094 Total weight of auxiliary raw materials 1199099 (W) tonsManganese content 1199095

Out of the historical data collected from one BOF of 260tons in some steel plant in China 220 samples have beenselected and prepared In order to establish the WTWTSVRprediction models the first 170 samples are taken as thetraining data and 50 other samples are taken as the test data toverify the accuracy of the proposed models In the regulatingunit R1 the appropriate model parameters (1198881 1198882 1198883 1198884 V1 V2and 1205901 120590lowast1 ) are regulatedmanually and then theC model andT model can be established In summary the process of themodelling can be described as follows

Step 1 Initialize the parameters of the WTWTSVR predic-tion model and normalize the prepared 170 training samplesfrom its original range to the range [-1 1] by mapminmaxfunction in Matlab

Step 2 Denoise the end-point carbon content C =[1198621 1198622 119862119897]119879 or temperature T = [1198791 1198792 119879119897]119879 in thetraining samples by using the wavelet transform describedin the previous section Then the denoised samples Clowast =[119862lowast1 119862lowast2 119862lowast119897 ]119879 and Tlowast = [119879lowast1 119879lowast2 119879lowast119897 ]119879 can beobtained

Step 3 By selecting the appropriate parameter 120590lowast1 in (33)determine the wavelets transform based weighted matrix D1and the coefficient vector D2

Step 4 Select appropriate values of 1198881 1198882 1198883 1198884 V1 V2 and 1205901 inthe regulating unit 1198771Step 5 Solve the optimization problems in (24) and (25) by119902119906119886119889119901119903119900119892 function in Matlab and return the optimal vector120572 or 120578

Step 6 Calculate the vectors1205961 1198871 and1205962 1198872 by (26) and (27)Step 7 Substitute the parameters in Step 5 into (3) to obtainthe function 119891119862119879(x)Step 8 Substitute the training samples into (34) to calculatethe relative criteria of the model which will be described indetails later

Step 9 If the relative criteria are satisfactory then theC model or T model is established Otherwise return toSteps from 4 to 8

32 Establishment of WTWTSVR VW Control Model Oncethe WTWTSVR CT prediction models are established theWTWTSVRVW control models are ready to build In order

to control the end-point carbon content and temperature tothe satisfactory region for any future hot metal the relativeoxygen blowing volume V and the total weight of auxiliaryraw materialsW should be calculated based on VW controlmodels respectively Through the mechanism analysis theinfluence factors on V and W are mainly determined by theinitial conditions of hot metal and the desired conditions ofthe steel are also considered as the the influence factorsThenthe independent input variables of the control models arelisted in Table 2 where the input variables x1-x7 are the sameas the CT prediction model and other two input variablesare the desired carbon content 119862119892 and desired temperature119879119892 respectively The output variable of the control model isVorW defined above

Similar to (34) the regression function 119891119881119882(x) can bewritten as

119891119881119882 (x) = 12119870 (x119879A119879) (1205963 + 1205964)119879 + 12 (1198873 + 1198874) (35)

where 119891119881119882(x) denotes the estimation function of V modelorW model and x = [1199091 1199092 1199099]119879

In order to establish the WTWTSVR control models thetraining samples and the test samples are the same as thatof the prediction models The regulating unit 1198772 is used toregulate the appropriate model parameters (1198885 1198886 1198887 1198888 V3 V4and 1205902 120590lowast2 ) manually then the V model and W model canbe established In summary the process of the modelling canbe described as follows

Steps 1ndash7 Similar to those in the section of establishing theprediction models except for the input variables listed inTable 2 and the output variable being the oxygen blowingvolume V = [1198811 1198812 119881119897]119879 or the total weight of auxiliarymaterials W = [11988211198822 119882119897]119879 Also select appropriatevalues of 1198885 1198886 1198887 1198888 V3 V4 and 1205902 in the regulating unit 1198772then the function 119891119881119882(x) is obtainedStep 8 Substitute the training samples into (35) to calculatethe relative predicted values 119881 and of V and W respec-tively

Step 9 and are combined with the input variables 1199091minus1199097in Table 1 to obtain 50 new input samples Then substitutingthem into the C model and T model 50 predicted values119862 and can be obtained Finally calculate the differencesbetween the desired values 119862119892 119879119892 and the predicted values119862 Also other relative criteria of the model should bedetermined

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 9

Table 2 Independent input variables of control models

Name of input variable Symbol Units Name of input variable Symbol UnitsInitial carbon content 1199091 Sulphur content 1199096 Initial temperature 1199092 ∘C Phosphorus content 1199097 Charged hot metal 1199093 tons Desired carbon content 1199098 (Cg) Nm3

Silicon content 1199094 Desired temperature 1199099 (Tg) tonsManganese content 1199095

Step 10 If the obtained criteria are satisfactory then theV model or W model is established Otherwise return toSteps from 4 to 9

4 Results and Discussion

In order to verify the performances ofWTWTSVR algorithmand proposed models the artificial functions and practicaldatasets are adopted respectively All experiments are carriedout in Matlab R2011b on Windows 7 running on a PC withIntel (R) Core (TM) i7-4510U CPU 260GHz with 8GB ofRAM

The evaluation criteria are specified to evaluate theperformance of the proposed method Assume that the totalnumber of testing samples is 119899 119910119894 is the actual value at thesample point 119909119894 119910119894 is the estimated value of 119910119894 and 119910119894 =(sum119899119894=1 119910119894)119899 is the mean value of 1199101 1199102 119910119899 Therefore thefollowing criteria can be defined

119877119872119878119864 = radic 1119899119899sum119894=1

(119910119894 minus 119910119894)2 (36)

119872119860119864 = 1119899119899sum119894=1

1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 (37)

119878119878119864119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (38)

119878119878119877119878119878119879 = sum119899119894=1 (119910119894 minus 119910119894)2sum119899119894=1 (119910119894 minus 119910119894)2 (39)

119867119877 = Number of 1003816100381610038161003816119910119894 minus 1199101198941003816100381610038161003816 lt 119890119903119903119900119903 119887119900119906119899119889119899times 100 (40)

In the above equations RMSE denotes the root meansquared error MAE denotes the mean absolute error andSSE SST and SSR represent the sum of the squared devia-tion between any two of 119910119894 119910119894 119910119894 respectively Normally asmaller value of SSESST reflects that the model has a betterperformance The decrease in SSESST reflects the increasein SSRSST However if the value of SSESST is extremelysmall it will cause the overfitting problem of the regressor Animportant criteria for evaluating the performance of the BOFmodel is hit rate (119867119877) calculated by (40) which is defined as

the ratio of the number of the satisfactory samples over thetotal number of samples For any sample in the dataset if theabsolute error between the estimated value and actual valueis smaller than a certain error bound then the results of thesample hit the end point A large number of hit rate indicate abetter performance of the BOFmodel Generally a hit rate of90 for C or T is a satisfactory value in the real steel plants

41 Performance Test of WTWTSVR In this section theartificial function named Sinc function is used to testthe regression performance of the proposed WTWTSVRmethod which can be defined as 119910 = sin 119909119909 119909 isin [minus4120587 4120587]

In order to evaluate the proposed method effectivelythe training samples are polluted by four types of noiseswhich include the Gaussian noises with zero means andthe uniformly distributed noises For the train samples(119909119894 119910119894) 119894 = 1 2 119897 we have119910119894 = sin 119909119894119909119894 + 120579119894

119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 012) (41)

119910119894 = sin 119909119894119909119894 + 120579119894119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119873(0 022) (42)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 01] (43)

119910119894 = sin 119909119894119909119894 + 120579119894 119909 sim 119880 [minus4120587 4120587] 120579119894 sim 119880 [0 02] (44)

where 119880[119898 119899] and 119873(119901 1199022) denote the uniformly randomvariable in [119898 119899] and the Gaussian variable with the mean119901 and variance 1199022 respectively For all regressions of theabove four Sinc functions 252 training samples and 500 testsamples are selected Note that the test samples are uniformlysampled from the Sinc functions without any noise For allalgorithms in this paper the following sets of parameters areexplored the penalty coefficient c is searched from the set1198941000 119894100 11989410 | 119894 = 1 2 10 The tube regulationcoefficient v is selected from the set 1 2 10Thewaveletcoefficient 120590 and kernel parameter 120590lowast are both searched overthe range 1198941000 119894100 11989410 119894 | 119894 = 1 2 10 In order toreduce the number of combinations in the parameter searchthe following relations are chosen c1= c3 c2= c4 and v1= v2

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

10 Complexity

minus15 minus10 minus5 0 5 10 15minus06minus04minus02

002040608

112

Outlier

OutlierOutlier

Outlier

Training samplesSinc(x)WTWTSVRWTWTSVR with outliersUpminusdown bound

Figure 4 Performance of WTWTSVR on Sinc function with and without outliers

Firstly the choice of kernel function should be consid-ered RBF kernel is an effective and frequently used kernelfunction in TSVR research papers Also the performanceof RBF has been evaluated by comparing with other threeexisting kernel functions (listed in Table 3) and the resultsare shown in Table 4 It is easy to see that the RBF kernelachieves the optimal results Then the average results of theproposed methods and other four existing methods (TSVR[15] V-TSVR [17] KNNWTSVR [19] and Asy V-TSVR [20])with 10 independent runs are shown in Table 5 whereType A B C and D denote four different types of noises(41)-(44) Obviously the results of Table 5 show that theproposed method achieves the optimal result of SSE Alsothe proposedmethod achieves the smallest SSESST results infour regressions of Sinc functions which are 00029 0012400231 and 00903 Especially the obvious performances areenhanced in Type A and B The SSRSST of the proposedmethod takes the first position in Type B the second positionin Type A and C and the third position in Type D Fromthe aspect of training time it can be seen that the proposedmethod achieves the optimal result in Type B In TypeA C and D the training time of the proposed method isfaster than that of TSVR and KNNWTSVR and close tov-Type and Asy v-Type It verifies that the computationalcomplexity of wavelet transform weighting scheme is lowerthan KNN weighting scheme For the effect of outliers wehave verified the performance of the proposed method onthe Sinc function with Type A noise Figure 4 shows that theprediction performance of the proposed method is satisfiedagainst the outliers as shown in the blue line and the resultsof SSE SSESST and SSRSST achieve 01911 00036 and10372 respectively By comparing with the results in Table 5it can be concluded that the overall performance of theproposed method with outliers is still better than TSVR v-TSVR and KNNWTSVRTherefore it can be concluded thatthe overall regression performance of the proposed methodis optimal

42 Verification of the Proposed BOF Models In order toverify the effectiveness of the proposed model 240 heatssamples for low carbon steel of 260119905119900119899119904 BOF were collected

Table 3 Type and functions of four existing kernel functions

Kernel Type Function

Radial Basis FunctionKernel (RBF) 119870(x x119894) = exp(minus10038161003816100381610038161003816100381610038161003816x minus x119894

10038161003816100381610038161003816100381610038161003816221205902 )Rational QuadraticKernel (RQ) 119870(x x119894) = 1 minus 10038161003816100381610038161003816100381610038161003816x minus x119894

100381610038161003816100381610038161003816100381610038162(10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 120590)

Multiquadric Kernel 119870(x x119894) = (10038161003816100381610038161003816100381610038161003816x minus x119894100381610038161003816100381610038161003816100381610038162 + 1205902)05

Log Kernel 119870(x x119894) = minus log (1 + 10038161003816100381610038161003816100381610038161003816x minus x11989410038161003816100381610038161003816100381610038161003816120590)

from some steel plant in China Firstly the preprocessing ofthe samples should be carried out The abnormal sampleswith the unexpected information must be removed whichexceeds the actual range of the signals It may be caused bythe wrong sampling operation Then 220 qualified samplesare obtained The next step is to analyze the informationof the qualified samples The end-point carbon content andtemperature are mainly determined by the initial conditionsof the iron melt the total blowing oxygen volume and theweight of material additions Therefore the unrelated infor-mation should be deleted such as the heat number the dateof the steelmaking and so on According to the informationof Tables 1 and 2 the datasets for the relative prediction andcontrol models can be well prepared After that the proposedmodels are ready to be established More details of the modelhave beendescribed in Section 3Theproposed controlmodelconsists of two prediction models (C model and T model)and two control models (V model and W model) For eachindividual model there are 8 parameters that need to beregulated to achieve the satisfactory results The regulationprocesses are related to the units R1 and R2 in Figure 3First of all the prediction models need to be establishedIn order to meet the requirements of the real productionthe prediction errors bound with 0005 for C model and10∘C for T model are selected Similarly the control errorsbound with 800 Nm3 for V model and 55 tons forW modelare selected The accuracy of each model can be reflected bythe hit rate with its relative error bound and a hit rate of90 within each individual error bound is a satisfied result

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 11

Table 4 Comparisons of WTWTSVR on Sinc functions with different kernel functions

Noise Kernel Type SSE SSESST SSRSST

Type A

RBF 01577plusmn00099 00029plusmn00018 09972plusmn00264RQ 01982plusmn00621 00037plusmn00012 10157plusmn00297

Multiquadric 02884plusmn00762 00054plusmn00014 09911plusmn00345Log 04706plusmn01346 00088plusmn00025 10115plusmn00306

Type B

RBF 06659plusmn02456 00124plusmn00046 10161plusmn00564RQ 11662plusmn03175 00217plusmn00059 09834plusmn00385

Multiquadric 11101plusmn05028 00206plusmn00093 10030plusmn00867Log 18157plusmn06026 00338plusmn00112 10366plusmn00802

Type C

RBF 12425plusmn01444 00231plusmn00027 10228plusmn00153RQ 35697plusmn15023 00664plusmn00279 10421plusmn01584

Multiquadric 36438plusmn14810 00678plusmn00275 10494plusmn00641Log 69962plusmn22691 01301plusmn00422 11208plusmn01682

Type D

RBF 48557plusmn04009 00903plusmn00075 10768plusmn00283RQ 61541plusmn18766 01144plusmn00349 10829plusmn01923

Multiquadric 56597plusmn24049 01052plusmn00447 11015plusmn01908Log 149196plusmn34583 02774plusmn00643 13255plusmn02159

Table 5 Comparisons of four regression methods on Sinc functions with different noises

Noise Regressor SSE SSESST SSRSST Time s

Type A

WTWTSVR 01577plusmn00099 00029plusmn00018 09972plusmn00264 17997TSVR 02316plusmn01288 00043plusmn00024 10050plusmn00308 23815v-TSVR 04143plusmn01261 00077plusmn00023 09501plusmn00270 17397

Asy V-TSVR 01742plusmn01001 00032plusmn00019 10021plusmn00279 17866KNNWTSVR 02044plusmn00383 00038plusmn00007 10177plusmn00202 35104

Type B

WTWTSVR 06659plusmn02456 00124plusmn00046 10161plusmn00564 18053TSVR 08652plusmn03006 00161plusmn00056 10185plusmn00615 23296V-TSVR 08816plusmn03937 00164plusmn00073 09631plusmn00548 18582

Asy V-TSVR 07900plusmn02588 00147plusmn00048 10168plusmn00599 18450KNNWTSVR 06891plusmn02571 00128plusmn00048 09679plusmn00392 36175

Type C

WTWTSVR 12425plusmn01444 00231plusmn00027 10228plusmn00153 18010TSVR 12505plusmn00650 00233plusmn00012 10217plusmn00091 23054V-TSVR 15351plusmn01172 00285plusmn00022 09750plusmn00111 17888

Asy V-TSVR 12464plusmn00934 00232plusmn00017 10256plusmn00125 16888KNNWTSVR 22027plusmn07245 00410plusmn00135 10148plusmn01556 41230

Type D

WTWTSVR 48557plusmn04009 00903plusmn00075 10768plusmn00283 17803TSVR 50090plusmn02172 00931plusmn00040 10890plusmn00131 22556V-TSVR 52580plusmn02935 00978plusmn00055 10386plusmn00125 17578

Asy V-TSVR 49659plusmn02925 00923plusmn00054 10889plusmn00128 17441KNNWTSVR 49751plusmn13262 00925plusmn00274 10262plusmn01538 44397

Also an end-point double hit rate (119863119867119877) of the predictionmodel is another important criterion for the real productionwhich means the hit rates of end-point carbon content andtemperature are both hit for the same sample Hence 170samples are used to train the prediction and control modelsand 50 samples are adopted to test the accuracy of themodelsFor each runof the relativemodelling the results are returnedto the user with the information of the evaluation criteria Itshows the accuracy and fitness of the models with the specific

parameters Smaller values of RMSEMAE and SSESST andlarger values of SSRSST and hit rate are preferred whichmeans the model has a better generalization and higheraccuracy The regulation units R1 and R2 are used to balancethe above criteria by selecting the appropriate values of theparameters Note that the principle of the parameter selectionis satisfactory if the following results are obtained 119878119878119877119878119878119879 gt05 and119867119877 gt 85 with the smallest SSESST Especially thedouble hit rate DHR should be greater than 80 or higher For

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

12 Complexity

1670 1675 1680 1685 1690 1695 17001670

1675

1680

1685

1690

1695

1700WTWTSVR

plusmn

125 13 135 14 145 15 155 16125

13

135

14

145

15

155

16 x WTWTSVR

40 45 50 55 60 65 70

WTWTSVR

Actual value (tons)

40

45

50

55

60

65

70

Pred

icte

d va

lue (

tons

)

plusmn55t

003 0035 004 0045 005003

0035

004

0045

005WTWTSVR

Actual value ()

Pred

icte

d va

lue (

)

plusmn000510

∘CPred

icte

d va

lue (

∘C)

Actual value (∘C)

Pred

icte

d va

lue (

NＧ

3)

Actual value (NＧ3)

plusmn800NＧ3

104

x 104

Figure 5 Performance of errors between predicted values and actual values with proposed static control model

the collected samples the parameters of WTWTSVR modelsare specified and shown in Table 6

By using these parameters the proposed BOF controlmodel has been established In order to evaluate the perfor-mance of the proposed method more simulations of otherexisting regression methods with the samples are carried outwhich are TSVR V-TSVR Asy V-TSVR and KNNWTSVRrespectively The comparison results of the carbon contentprediction are listed in Table 7 From the results it can be seenthat the results of RMSEMAE and SSESST in the proposedmethod are 00023 00026 and 11977 respectively Theyare all smaller than those of other three existing methodsand the SSRSST of 06930 is the highest result The errorperformance and distribution of end-point carbon contentbetween the predicted values and actual values are shown inFigures 5 and 6 It is clear that the proposed C model canachieve the hit rate of 92 which is better than other fourmethods From above analysis it illustrates that the proposedC model has the best fitting behaviour for carbon contentprediction

Similarly the performance comparisons of the tempera-ture prediction are also listed in Table 7 From the results ofTable 7 the best results of RMSE and SSESST and secondbest result of MAE of the proposed method are obtainedThe results of SSRSST is in the third position Figures 5and 6 show that the proposed T model can achieve thehit rate of 96 which is the optimal results by comparingwith other methods In addition the double hit rate is also

the key criterion in the real BOF applications the proposedmethod can achieve a double hit rate of 90 which is thebest result although the temperature hit rate of V-TSVR andKNNWTSVR method can also achieve 96 However theirdouble hit rates only achieve 80 and 84 respectively Inthe real applications a double hit rate of 90 is satisfactoryTherefore the proposed model is more efficient to providea reference for the real applications Also it meets therequirement of establishing the static control model

Based on the prediction models the control models(V model and W model) can be established by using therelative parameters in Table 6 The performance of theproposed V model is shown in Figure 7 By comparing theproposedmethod with the existing methods the comparisonresults of the oxygen blowing volume calculation are listedin Table 8 which shows that the results of RMSE MAEand SSESST in the proposed method are 3713953 4117855and 12713 respectively They are all smaller than those ofother four existing methods and the 119878119878119877119878119878119879 of 10868 is inthe fourth position Figures 5 and 6 show that the predictedvalues of the proposedmodel agreewell with the actual valuesof oxygen volume and the proposed V model has a best hitrate of 90 It verifies that the proposed V model has thebest fitting behaviour for the calculation of oxygen blowingvolume

Similarly the performance of the proposed W model isshown in Figure 8 and the performance comparisons of theweight of the auxiliary materials are also listed in Table 8

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 13

WTWTSVR

Hit rate is 92

plusmn0005

WTWTSVR

Hit rate is 96

plusmn

minus1500 minus1000 minus500 0 500 1000 15000

5

10

15WTWTSVR

Freq

uenc

y

Hit rate is 90

0

5

10

15WTWTSVR

Freq

uenc

y

plusmn55t

Hit rate is 88

0

5

10

15Fr

eque

ncy

0

5

10

15

Freq

uenc

y

minus0005 0 0005 001minus001Predictive error of carbon content ()

minus10 minus5 0 5 10 15minus15

minus5 0 5 10minus10Predictive error of auxiliary raw materials (tons)

plusmn800NＧ3

Predictive error of oxygen volume (NＧ3)

Predictive error of temperature (∘C)

10∘C

Figure 6 Performance of error distributions with proposed static control model

Table 6 Specified parameters of prediction and control models

Prediction Model c1 = c3 c2 = c4 V1 = V2 1205901 120590lowast1C model 0005 002 3 0005 1T model 0002 005 5 004 03Control Model c5 = c7 c6= c8 V3 = V4 1205902 120590lowast2V model 0002 001 2 02 3W model 0001 002 1 05 5

Table 7 Performance comparisons of CT prediction models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

C model (plusmn0005 )RMSE 00023 00026 00026 00026 00025MAE 00026 00031 00031 00031 00030

SSESST 11977 16071 15675 15214 14680SSRSST 06930 04616 03514 03835 03500HR 92 82 84 84 88Time s 04523 02915 03706 03351 05352

T model (plusmn10 ∘C)RMSE 40210 42070 43630 41013 40272MAE 47380 50363 51461 47970 47165

SSESST 17297 18935 20365 17996 17351SSRSST 07968 06653 07578 09141 08338HR 96 94 92 96 96Time s 00977 01181 00861 00538 02393DHR 90 78 78 80 84

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

14 Complexity

Table 8 Performance comparisons of VW control models with four methods

Model Criteria WTWTSVR TSVR v-TSVR Asy v-TSVR KNNWTSVR

V model (plusmn800 Nm3)RMSE 3713953 3830249 3832387 3998635 3997568MAE 4117855 4163151 4230260 4270896 4270415

SSESST 12713 13522 13537 14737 14729SSRSST 10868 11288 09691 09326 09319HR 90 86 84 86 86Time s 06196 04397 05177 04883 07014

W model (plusmn55 tons)RMSE 24158 28824 28431 36781 29077MAE 27057 31254 31632 39979 32588

SSESST 03791 05398 05251 08789 05493SSRSST 06505 05868 06739 04376 06725HR 88 86 80 80 84Time s 01269 01230 00837 00609 02999

Hit ratesHR (C) 86 82 88 90 86HR (T) 92 94 94 80 94DHR 82 78 82 82 82

0 5 10 15 20 25 30 35 40 45 50Heat

Actual valuePredicted value

Ｒ 104

125

13

135

14

145

15

155

16

Oxy

gen

volu

me (

NＧ

3)

Figure 7 Performance of proposed V model

The proposedmodel achieves the best results of RMSEMAEand SSESST Figures 5 and 6 show that the proposed methodachieves the best hit rate of 88 In addition the training timeof the proposed models is faster than that of KNNWTSVRmethod and slower than that of other three methods Itillustrates that the weighting scheme takes more time toobtain higher accuracy and the performance of proposedweighting scheme is better than that of KNN weightingscheme for time sequence samples For 50 test samplesthere are 50 calculated values of V and W by V model andW modelThen they are taken as the input variables into theproposed C model and T model to verify the end-point hitrate From the results in Table 8 the proposed models canachieve a hit rate of 86 in C 92 in T and 82 in 119863119867119877is in the optimal result and the same as that of V-TSVR AsyV-TSVR and KNNWTSVR In the real productions 119863119867119877 ispaid more attention rather than the individual HR in C or T

Actual valuePredicted value

35

40

45

50

55

60

65

70W

eigh

t of a

uxili

ary

raw

mat

eria

ls (to

ns)

5 10 15 20 25 30 35 40 45 500Heat

Figure 8 Performance of proposedW model

Therefore the proposed control models are verified to be ableto guide the real production

Based on above analysis it can be concluded that theproposed static control model is effective and feasible the hitrate canmeet the requirements of the real productions for lowcarbon steel For other types of steels the proposed modelis still suitable for use Firstly the specific samples of theheats should be obtained and preprocessed and the analysisof the influence factors on the specific type of steel shouldbe carried out to obtain the input variables of the modelThe output variables are the same as the relative proposedmodels Secondly the end-point criteria should be specifiedwhich is determined by the type of steelThen the parametersof the relative models can be regulated and determined toachieve the best criteria Finally the BOF control model for

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

Complexity 15

the specific type of steel is established to guide the productionin the plant

BOF steelmaking is a complex physicochemical processthe proposed static control model can be established basedon the real samples collected from the plant However theremust be some undetected factors during the steelmakingprocess which will affect the accuracy of the calculations ofV and W To solve this problem the following strategies canbe introduced at the early stage of the oxygen blowing theproposed control model is used to calculate the relative Vand W and guide the BOF production Then the sublancetechnology is adopted at the late stage of oxygen blowingbecause the physical and chemical reactions tend to be stablein this stage Hence the information of the melt liquid canbe collected by the sublance Therefore another dynamiccontrol model can be established with the sublance samplesto achieve a higher end-point hit rate For medium and smallsteel plants the proposed static model is a suitable choice toreduce the consumption and save the cost

Remark 3 Although this paper is mainly based on staticcontrol model the prediction scheme is also compatiblefor other datasets over the globe Especially the proposedalgorithm is competitive for the regression of time sequencedatasets such as the prediction of the blast furnace processand continuous casting process in the metallurgical industry

5 Conclusion

In this paper a WTWTSVR control model has been pro-posed The new weighted matrix and the coefficient vectorhave been determined by the wavelet transform theory andadded into the objective function of TSVR to improve theperformance of the algorithm The simulation results haveshown that the proposed models are effective and feasibleThe prediction error bound with 0005 in C and 10∘C inT can achieve a hit rate of 92 and 96 respectively Inaddition the double hit rate of 90 is the best result bycomparing with other three existing methods The controlerror bound with 800 Nm3 in V and 55 tons in W canachieve the hit rate of 90 and 88 respectively Thereforethe proposed method can provide a significant reference forreal BOF applications For the further work on the basis ofthe proposed control model a dynamic control model couldbe established to improve the end-point double hit rate ofBOF up to 90 or higher

Data Availability

The Excel data (Research Dataxls) used to support thefindings of this study is included within the SupplementaryMaterials (available here)

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by Liaoning Province PhD Start-Up Fund (No 201601291) and Liaoning Province Ministry ofEducation Scientific Study Project (No 2017LNQN11)

Supplementary Materials

The supplementary material contains the Excel research datafor our simulations There are 220 numbers of preprocessedsamples collected from one steel plant in China Due to thelimitations of confidentiality agreement we cannot providethe name of the company The samples include the historicalinformation of hot metal total oxygen volume total weightof auxiliary raw materials and end-point information Inthe excel table the variables from column A to K aremainly used to establish the static control model for BOFColumns H I J and K are the output variables for C modelT model V model andW model in the manuscript respec-tively The input variables of the relative models are listedin Tables 1 and 2 By following the design procedure ofthe manuscript the proposed algorithm and other existingalgorithms can be evaluated by using the provided researchdata (Supplementary Materials)

References

[1] C Blanco and M Dıaz ldquoModel of Mixed Control for Carbonand Silicon in a Steel ConverterrdquoTransactions of the Iron amp SteelInstitute of Japan vol 33 pp 757ndash763 2007

[2] I J Cox R W Lewis R S Ransing H Laszczewski andG Berni ldquoApplication of neural computing in basic oxygensteelmakingrdquo Journal of Materials Processing Technology vol120 no 1-3 pp 310ndash315 2002

[3] A M Bigeev and V V Baitman ldquoAdapting a mathematicalmodel of the end of the blow of a converter heat to existingconditions in the oxygen-converter shop at the MagnitogorskMetallurgical CombinerdquoMetallurgist vol 50 no 9-10 pp 469ndash472 2006

[4] M Bramming B Bjorkman and C Samuelsson ldquoBOF ProcessControl and Slopping Prediction Based on Multivariate DataAnalysisrdquo Steel Research International vol 87 no 3 pp 301ndash3102016

[5] Z Wang F Xie B Wang et al ldquoThe control and predictionof end-point phosphorus content during BOF steelmakingprocessrdquo Steel Research International vol 85 no 4 pp 599ndash6062014

[6] M Han and C Liu ldquoEndpoint prediction model for basicoxygen furnace steel-making based on membrane algorithmevolving extreme learning machinerdquo Applied Soft Computingvol 19 pp 430ndash437 2014

[7] X Wang M Han and J Wang ldquoApplying input variablesselection technique on input weighted support vector machinemodeling for BOF endpoint predictionrdquo Engineering Applica-tions of Artificial Intelligence vol 23 no 6 pp 1012ndash1018 2010

[8] M Han and Z Cao ldquoAn improved case-based reasoningmethod and its application in endpoint prediction of basicoxygen furnacerdquoNeurocomputing vol 149 pp 1245ndash1252 2015

[9] L X Kong P D Hodgson and D C Collinson ldquoModellingthe effect of carbon content on hot strength of steels using a

16 Complexity

modified artificial neural networkrdquo ISIJ International vol 38no 10 pp 1121ndash1129 1998

[10] A M F Fileti T A Pacianotto and A P Cunha ldquoNeuralmodeling helps the BOS process to achieve aimed end-pointconditions in liquid steelrdquo Engineering Applications of ArtificialIntelligence vol 19 no 1 pp 9ndash17 2006

[11] S M Xie J Tao and T Y Chai ldquoBOF steelmaking endpointcontrol based on neural networkrdquo Control Theory Applicationsvol 20 no 6 pp 903ndash907 2003

[12] J Jimenez JMochon J S de Ayala and FObeso ldquoBlast furnacehot metal temperature prediction through neural networks-based modelsrdquo ISIJ International vol 44 no 3 pp 573ndash5802004

[13] C Kubat H Taskin R Artir and A Yilmaz ldquoBofy-fuzzylogic control for the basic oxygen furnace (BOF)rdquo Robotics andAutonomous Systems vol 49 no 3-4 pp 193ndash205 2004

[14] Jayadeva R Khemchandani and S Chandra ldquoTwin supportvector machines for pattern classificationrdquo IEEE Transactionson Pattern Analysis and Machine Intelligence vol 29 no 5 pp905ndash910 2007

[15] X Peng ldquoTSVR an efficient Twin Support Vector Machine forregressionrdquo Neural Networks vol 23 no 3 pp 365ndash372 2010

[16] D Gupta ldquoTraining primal K-nearest neighbor based weightedtwin support vector regression via unconstrained convex mini-mizationrdquo Applied Intelligence vol 47 no 3 pp 962ndash991 2017

[17] R Rastogi P Anand and S Chandra ldquoA ]-twin support vectormachine based regression with automatic accuracy controlrdquoApplied Intelligence vol 46 pp 1ndash14 2016

[18] M Tanveer K Shubham M Aldhaifallah and K S Nisar ldquoAnefficient implicit regularized Lagrangian twin support vectorregressionrdquoApplied Intelligence vol 44 no 4 pp 831ndash848 2016

[19] Y Xu and L Wang ldquoK-nearest neighbor-based weighted twinsupport vector regressionrdquoApplied Intelligence vol 41 no 1 pp299ndash309 2014

[20] Y Xu X Li X Pan and Z Yang ldquoAsymmetric v-twin supportvector regressionrdquo Neural Computing and Applications vol no2 pp 1ndash16 2017

[21] N Parastalooi A Amiri and P Aliheidari ldquoModified twinsupport vector regressionrdquo Neurocomputing vol 211 pp 84ndash972016

[22] Y-F Ye L Bai X-Y Hua Y-H Shao Z Wang and N-YDeng ldquoWeighted Lagrange 120576-twin support vector regressionrdquoNeurocomputing vol 197 pp 53ndash68 2016

[23] C Gao M Shen and L Wang ldquoEnd-point Prediction ofBOF Steelmaking Based onWavelet Transform BasedWeightedTSVRrdquo in Proceedings of the 2018 37th Chinese Control Confer-ence (CCC) pp 3200ndash3204 Wuhan July 2018

[24] J Shen and G Strang ldquoAsymptotics of Daubechies filtersscaling functions and waveletsrdquo Applied and ComputationalHarmonic Analysis vol 5 no 3 pp 312ndash331 1998

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom