research article a hybrid model based on ensemble...

Research ArticleA Hybrid Model Based on Ensemble Empirical ModeDecomposition and Fruit Fly Optimization Algorithm forWind Speed Forecasting

Zongxi Qu1 Kequan Zhang1 Jianzhou Wang2 Wenyu Zhang1 and Wennan Leng1

1Key Laboratory of Arid Climatic Change and Reducing Disaster of Gansu Province College of Atmospheric SciencesLanzhou University Lanzhou 730000 China2School of Statistics Dongbei University of Finance and Economics Dalian 116025 China

Correspondence should be addressed to Kequan Zhang zhangkqlzueducn

Received 26 February 2016 Revised 10 July 2016 Accepted 4 August 2016

Academic Editor Ferhat Bingol

Copyright copy 2016 Zongxi Qu 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

As a type of clean and renewable energy the superiority of wind power has increasingly captured the worldrsquos attention Reliable andprecise wind speed prediction is vital for wind power generation systems Thus a more effective and precise prediction model isessentially needed in the field of wind speed forecasting Most previous forecastingmodels could adapt to various wind speed seriesdata however these models ignored the importance of the data preprocessing and model parameter optimization In view of itsimportance a novel hybrid ensemble learning paradigm is proposed In this model the original wind speed data is firstly dividedinto a finite set of signal components by ensemble empirical mode decomposition and then each signal is predicted by severalartificial intelligencemodels with optimized parameters by using the fruit fly optimization algorithm and the final prediction valueswere obtained by reconstructing the refined series To estimate the forecasting ability of the proposed model 15min wind speeddata for wind farms in the coastal areas of China was performed to forecast as a case study The empirical results show that theproposed hybrid model is superior to some existing traditional forecasting models regarding forecast performance

1 Introduction

The worldrsquos current sources of fossil fuels will eventually bedepleted mainly due to high demand and in some situationsextravagant consumption [1] The recently posted EnergyOutlook 2035 of British Petroleum predicts that primaryenergy consumption will increase by 37 between 2013and 2035 with growth averaging 14 per year Approx-imately 96 of the expected growth will be in countriesthat are not members of the Organization for EconomicCooperation and Development (OECD) with energy con-sumption growing at 22 per year [2] According to somestatistics energy demand worldwide will grow rapidly byone-third from 2010 to 2035 and China and India willbecome the largest contributors accounting for 50 percent ofthe growth during that period Moreover China is expectedto be the largest oil importer by 2020 [2 3] To cope withthe growing demand for energy countries such as China can

look to renewable energy sources to provide an opportunityfor sustainable development The significance of renewablesources was recently underpinned by a plethora of advocatesand reports which have mostly focused on wind energystudied by the related institutions and energy commissionsof several countries [2 4ndash7] According to reports from theChina National Renewable Energy Center (CNREC) windresources inChina are rich and promising prospects carryinga potential of more than 30 TW mostly in the Three NorthAreas with an onshore potential of more than 26 TW Before2020 land-based wind power will dominate with offshorewind power in the demonstration status Furthermore theannual discharge of carbon dioxide will be reduced to 15billion tons and 30 billion tons in 2050 in the conservativeand aggressive scenarios and an estimated 720 000 jobsand 1 440 000 jobs will be created respectively [4 5] Basedon these figures wind energy should be regarded as anappealing energy option because it is both abundant and

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2016 Article ID 3768242 14 pageshttpdxdoiorg10115520163768242

2 Advances in Meteorology

environmentally friendly as such wind energy will be ableto satisfy the growing demand for electricity

Wind energy has great influence on power grid securitypower system operation and market economics due to itsintermittent nature especially in areas with high wind powerpenetrationThus the analysis and assessment ofwind energyare a meaningful but markedly difficult task for researchBecause wind power generation hinges on wind speedobtaining accurate wind speeds is important To improvethe precision of wind speed predictions numerous methodshave been proposed and developed in recent decades Thesemethods can be divided into three general types physicalmodels conventional statistical models and artificial intelli-gence models [8ndash11] Physical models use weather predictiondata such as temperature pressure orography obstacles andsurface roughness for the best forecasting accuracy but arepoor at short-term wind speed simulation Conventional sta-tistical models in contrast draw on vast historical data basedonmathematical models usually involving conventional timeseries analysis such as ARMA ARIMA or seasonal ARIMAmodels [12 13] and achieve more accurate short-term windspeed predictions than physical models However conven-tional statistical models are imperfect The fluctuating andintermittent characteristics of wind speed sequences requiremore complicated functions to capture the nonlinear rela-tionships rather than assuming a linear correlation structure[14] Given the development of statistical models along withthe advent of artificial intelligence techniques artificial intel-ligence models including artificial neural networks (ANNs)and other mixed methods have been proposed and are usedin the field of wind speed forecasting [15ndash20] For instancebecause of the chaotic nature of wind time series Alaniset al [15] proposed a higher order neural network (HONN)based on an extendedKalman filter formodel training whichprovides accurate one-step-ahead predictions Guo et al [20]proposed a hybrid wind speed forecastingmethod employinga backpropagation (BP) neural network and seasonal expo-nential adjustment to remove seasonal effects from actualwind speed datasets Wang et al [21] exploited a radial basisfunction (RBF) neural network for wind speed predictionand the effectiveness of this method was proved by a practicalcase Zhou et al [17] proposed a prediction method based ona support vector machine (SVM) for short-term wind speedprediction De Giorgi et al [19] adopted the ANNs to forecastwind speeds and compared them to the linear time-series-based model with the ANNs providing a robust approachfor wind prediction All of these methods have improved theprecision of wind speed predictions to some extent

However wind speed time series are highly noisy andunstable therefore using the primary wind speed seriesdirectly to establish prediction models is subject to largeerrors [22ndash24] To build an effective prediction model thefeatures of original wind speed datasets must be fully ana-lyzed and considered The ensemble empirical mode decom-position (EEMD) [25] is an advanced effective technologywhich makes up for the deficiency of EMD [26] and has cer-tain advantages over other typical decomposition approachessuch as the wavelet decomposition and the Fourier decom-position [27] With direct intuitive empirical and adaptive

data processing EEMD was especially devised for nonlinearand complicated signal sequences such as wind speed seriesFor example Hu et al [22] proposed a hybrid method basedon the EEMD to disassemble the original wind speed datasetsinto a series of independent IntrinsicMode Functions (IMFs)and use SVM to predict the values for IMFs in differentfrequencies Jiang et al [28] also proposed a hybrid modelfor high-speed rail demand forecasting based on EEMD inwhich the original series are decomposed into certain signalswith different frequencies and then the grey support vectormachine (GSVM) is employed for forecasting Zhou et al [29]additionally proposed a hybrid method based on EEMD andthe generalized regression neural network (GRNN) In thismethod the original data are decomposed into different IMFswith corresponding frequencies and the residue componentby EEMD and then each component is taken as an input toestablish GRNN forecasting model

Each of the aforementionedmodels only employs a singleANN model to predict all of the signal sequences decom-posed by EEMD nevertheless different signals have differentcharacteristics meaning that a simple individual model canno longer adapt to all properties of the data Moreoverprevious literature has not addressed which features are bestsuited for choosing the most appropriate approach Thus inour study we propose a hybrid model based on a modelselector that combines RBF GRNN and SVR to addresssignal data series with different characteristics to furtherimprove forecasting accuracy

In existing neural network training structures modelparameters are very vital factors affecting prediction preci-sion and different types of data require different parametersThe genetic algorithm (GA) and particle swarm optimization(PSO) algorithms are the most common approaches tooptimize the parameters of neural network structures Liuet al [30] used the genetic algorithm to determine the weightcoefficients of a combined model for wind speed forecastingZhao et al [31] developed a combined model for energyconsumption prediction based on model parameters opti-mization with the genetic algorithm Ren et al [32] appliedthe particle swarm optimization to set weight coefficientsof a forecasting model for 6-hour wind speed forecastingHowever these meta-heuristic algorithms have the draw-backs of being hard to understand and achieving the globaloptimal solution slowly The fruit fly optimization algorithm(FOA) [33] was a new optimization and evolutionary compu-tation technique which has distinct advantages in its simplecomputational process fewer parameters to be fine-tunedand stronger ability to search for global optimal solutionsand outperforms other metaheuristic algorithms [34 35] Inour study we introduce the FOA algorithm to automaticallydetermine the necessary parameters of the RBF GRNN andSVR models to achieve better performance

The rest of the paper is organized as follows Section 2briefly introduces related methods while Section 3 describesthe proposed hybrid approach in detail Section 4 describesthe dataset used for this study and discusses the forecastingresults of proposed model compared with other predictionmodels Section 5 concludes the work

Advances in Meteorology 3

2 Related Methodology

This section briefly introduces EEMD FOA and three classi-cal forecasting models RBF GRNN and SVR which will beused in our research

21 RBF The radial basis function (RBF) neural network isa type of feedforward network developed by Broomhead andLowe [36] This type of neural network is based on a super-vised algorithm and has been widely applied to interpolationregression prediction and classification [37ndash39] It has threelayers of architecture where there are no weights betweenthe input hidden layers and each hidden unit implements aradial-activated function The Gaussian activation functionis used in each neuron at the hidden layer which can beformulated as

ℎ119895 (119909) = exp(minussum119872119894=1 (119909119894 minus 120583119895)

2

21205792119895

) (1)

where119909119894 is the 119894th input sample120583119895 is themean value of the 119895thhidden unit presenting the center vector 120579119895 is the covarianceof the 119895th hidden unit denoting the width of the RBF kernelfunction and 119872 is the number of training samples

The network output layer is linear so that the 119896th outputis an affine function that can be expressed as

119910119896 =

119871

sum

119895=1

ℎ119895119908119895119896 + 120588119896 (2)

where 119908119895119896 is the weight between the 119896th output and 119895th hid-den unit 120588119896 is the biased weight of the 119896th output and 119871 isthe number of hidden nodes

22 GRNN The general regression neural network (GRNN)first proposed by Specht [40] is a very powerful computa-tional technique used to solve nonlinear approximation prob-lems based on nonlinear regression theory The advantagesof GRNNs include its good feasibility simple structure andfast convergence rate It consists of four layers and its basicprinciples are presented in Figure 1

23 Support Vector Regression (SVR) SVR is a version of anSVM for regression and was introduced by Lasala et al [41]In the model a regression function 119910 = (119909) is applied to aforecast based on an input set Attempts are made to mini-mize the generalization error that will impact generalizationperformance Figure 2 illustrates the basic rules of SVR andthe more detailed information can be referenced in [42]

24 EEMD The empirical mode decomposition (EMD)method as an adaptive data analysis technique has provento be effective in analyzing nonlinear and nonstationary timeseries such as wind speed series It decomposes complexsignals into IMFs that satisfy the following conditions

(1) In the whole data sequence the number of extremaand the number of zero crossings in the entire sampleddataset must either be equal or differ at most by one

(2)Themean value at any point of the envelope defined bythe local maxima and the envelope defined by the local min-ima is zero With the hypothesis of decomposition and the

i

i

i

p

p

p

S1

S2

O

i

p

S

O

Y =S1

S2

NeuronsInput

Pattern

Summation

Output

Input valueSynapseOutput value

S1 = sumj=1

yj middot Pj

S2 = sumj=1

Pj

Pj = exp[[minus(X minus Xj)T(X minus Xj)

21205902]]

wS1= yi

wS2= 1

Figure 1 A structure schematic chart of GRNN (where 119895 = 1 2

119899 119883 is the input variable of the network 119883119895 is a training vectorof the 119895th neuron in the pattern layer 120590 denotes the smoothingparameter (also called spread parameter)119910119895 is themeasured value ofthe output variable 119875119895 is the pattern Gaussian function 1199081198781 and 1199081198782are the network weights 1198781 and 1198782 are the signals from summationneurons and 119884 is the network output)

definition of the IMF above the EMD process of a raw dataseries 119909(119905) (119905 = 1 2 119879) can be formulated as

119909 (119905) =

119898

sum

119896=1

imf119898 (119905) + 119903119898 (119905) (3)

where 119909(119905) denotes any nonlinear and nonstationary signalimf119898(119905) is the 119898th IMF of the signal and 119903119898(119905) is the residualitem which can be a constant or the signal mean trend

However the EMD method is imperfect and the mode-mixing problem [43] is encountered frequently in practicalapplication Due to the mentioned drawback of EMD theadvent of the EEMD method was proposed by Wu andHuang [25] and the procedures of EEMD can be presentedas follows

Step (a) Add a white noise series to the original data

Step (b) Decompose the data with added white noise to IMFsthrough the EMD algorithm

Step (c) Repeat the abovementioned two steps but add whitenoise series at different scales each time

Step (d) Calculate the means of each IMF of the decomposi-tion to constitute the final IMFs

As a result the white noise series incorporated into theoriginal signal can provide a uniform reference scale tofacilitate the EMDprocess and consequently help extract thetrue IMFs The relationship between the ensemble numberthe error tolerance and the addednoise level can be described


Input space

Kernelmapping

Feature space

Regression

Primal space

x

Y Y

K(x)

120576120576

120576

120576

120576

120576

f(x) =Nsum

i=1

(120573lowasti minus 120573i)K(xi xj) + b

120582 gt 0K(xi xj) = exp (minus12058210038171003817100381710038171003817xi minus xj

100381710038171003817100381710038172)

Figure 2 A schematic diagram of SVR architecture

according to thewell-established statistical rule proved byWuand Huang

119873120576 =1205762

1205762119899

(4)

where 120576 is the amplitude of the added noise 120576119899 is the finalstandard deviation of error and 119873120576 is the value of ensemblemembers Generally it is suggested that an amplitude fixed at02 will result in an exact result In this study we set the valueof ensemble members to 100 and select the optimal standarddeviation of white noise series from 01 to 02 with a 119896-foldcross-validation method

25 Fruit Fly Optimization Algorithm (FOA) The fruit flyoptimization algorithm (FOA) imitated by the food-findingbehavior of the fruit fly is a new swarm intelligence algorithmthat was put forward by Pan in 2012 [33] It is an interactiveevolutionary computation method for finding global opti-mization and has been shown to perform better than tradi-tionalmetaheuristic algorithmsThe FOA succeeds in solvingoptimization challenges and has received significant attentionin multiple scientific and academic fields

The fruit fly a type of insect is superior to other speciesin visual and olfactory sensory abilities It can make themost of its instinctive advantages to find food even capableof smelling a food source from 40 km away The fruit flyrsquosmethod of searching for food starts by using the olfactoryorgan to smell food odors in the air and then flies towards thatlocationUpon getting closer to the food location it continuesto seek food and the companyrsquos flocking location using itskeen eyesight and then it flies to that position too Figure 3shows the iterative process of food searching of a fruit flyswarm

A rudimentary FOA algorithm is outlined as shown inAlgorithm 1

3 Combined Model

The combined model first applies the EEMD techniqueto decompose the original time series into a collection ofrelatively stationary subseries and themodel selection is used

Table 1 Four evaluation rules

Metric Equation Definition

MAE MAE =1

119873

119873

sum

119899=1

1003816100381610038161003816119910119899 minus 1198991003816100381610038161003816

The averageabsolute forecasterror of 119899 timesforecast results

RMSE RMSE = (1

119873

119873

sum

119899=1

(119910119899 minus 119899)2)

12 The rootmean-squareforecast error

IA IA = 1 minussum119879

119905=1 (119910119905 minus 119905)2

sum119879

119905=1 (1003816100381610038161003816119910 minus 119905

1003816100381610038161003816 +1003816100381610038161003816119910 minus 119910119905

1003816100381610038161003816)2

The index ofagreement

to select the optimal model above artificial neural networksbased on FOA optimization for predicting each subseriesThe prediction results are then aggregated to obtain the finalprediction values of wind speed series

31 Model Selection Through the process of EEMD distinctinformation scales in the original wind speed series can bedetermined and decomposed into a set of IMFs Additionallydifferent IMFs exhibit different frequency characteristics andthe instantaneous frequency of each IMF has its meaningat any point Moreover no clear theory exists to determinewhich characteristic is best suited for choosing the mostsuitable approachThus wemust describe some performancemetrics to comprehensivelymeasure the strengths of differentmodels To evaluate the forecast capacity of the proposedmodels three evaluation criteria are applied in model selec-tion They are the mean absolute error (MAE) root mean-square error (RMSE) and index of agreement (IA) as shownin Table 1

Here 119910119899 and 119899 denote the real and predicted values attime 119899 respectively 119873 is the sample size The IA is a dimen-sionless indicator that portrays the similarity between theobserved and forecasted tendencies The range of IA is from0 to 1 and for a ldquoperfectrdquo model the value of IA is close to 1while the MAE and RMSE are equivalent to 0


ObjectiveMaxmize smell concentrationOutputThe best smell concentration (Smellbest)ParametersIteration number (Maxgen) Population size (sizepop) Location range (LR) Random fly direction and distance zone of fruit fly(Smellbest)(1) lowastInitializationlowast(2) lowastSetMaxgen sizepoplowast(3) lowastInitialization swarm location LR and fly range FRlowast(4) Iter = 0(5) 119883 axis = rand (LR) 119884 axis = rand (LR)(6) lowastCalculate initial smell concentrationlowast(7) Smellbest = Function (119883 axis 119884 axis)(8) Repeat(9) While 119894 = 1 2 119872119886119909119892119890119899

(10) lowastOsphresis searching processlowast(11) lowastGiven the random direction and distance for food searching of any individual fruit flylowast(12) 119883119894 = 119883 axis + rand (FR) 119884119894 = 119884 axis + rand (FR)(13) lowastCalculate the distance of food source to the initialization locationlowast(14) 119863119894119904119905119894 = radic1198832119894 + 1198842119894 (15) lowastCalculate the smell concentration judgment valuelowast(16) 119878119894 = 1119863119894119904119905119894(17) lowastCalculate the smell concentrationlowast(18) 119878119898119890119897119897119894 = 119865119906119899119888119905119894119900119899(119878119894)

(19) lowastFind out the fruit fly with maximal smell concentration among the swarmlowast(20) [119887119890119904119905119878119898119890119897119897 119887119890119904119905119868119899119889119890119909] = max (119878119898119890119897119897)

(21) lowastVision searching processlowast(22) If bestSmell gt Smellbest then Smellbest = bestSmell(23) 119883 axis = 119883 (bestIndex) 119884 axis = 119884 (bestIndex)(24) Iter = Iter + 1(25) Until Iter = Maxgen

Algorithm 1 FOA

The main processes of the proposed hybrid model aredemonstrated in Figure 4 The detailed steps of the hybridmodel are as follows

Step 1 (EEMD process) The raw data series are decomposedinto 7 different IMFs and a residue 119877 Because the first IMFwith high frequency is evoked by noise it is removed directlyand the rest are used for forecasting

Step 2 (model selection and optimization of model parame-ters) First select the appropriate parameter from the RBFGRNN and SVR models by the FOA Next the abovemen-tionedmodels are then selected bymodel selection to forecastIMFs and a residual R

Step 3 (ensemble forecast) Combine the forecasting resultsof each signal component to obtain the final result

4 Results and Analysis

In this section the process descriptions of RBF GRNN andSVR models optimized by the FOA are presented firstlyand then followed by the process descriptions of the modelselection Results conclude with the final forecasting results

of the hybrid model compared to other different forecastingmodels

41 Data Selection Shandong Province located in easternChina has abundant wind energy resources In our study thewind speed series from the wind farm in Weihai was usedto examine the performance of the combined model Figures5(a) and 5(b) present the statistical measures and visualgraphs of four wind speed datasets which show apparentdifferences between the four seasons Thus the originalwind speed data picked randomly corresponding to the fourseasons of the year are used to test whether the proposedmodels can be applied on different occasionsThewind speeddata were sampled at an interval of 15min so there are 96data records per day Data from 4 days providing a total of384 points of 15min data were selected for model trainingand the next 48 of the 15min data values were used to testthe effectiveness of the developed hybrid model (as shown inFigure 5(b))

42 The Performance Metric Forecasting accuracy is animportant criterion in the evaluation of forecasting modelsIn this paper three metric rules were applied to evaluate the


The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

Figure 3 The process of food-seeking of a fruit fly swarm

accuracy of forecasting models as shown in Table 1 In addi-tion two benchmark models and bias-variance frameworkare used to test the hybrid model

421 Persistence Model The persistence model as a simplestatistical model which has simple calculation and providesaccurate prediction in a very short time has been widelyused as benchmark model to evaluate the accuracy of moreadvanced forecasting model The persistence model can begiven by

119905+119896 = 119901119905 (5)

where is the forecasting value 119905 is a time index and 119896 is thelook-ahead time

422 Autoregressive Integrated Moving Average (ARIMA)ARIMA model is widely used because it can characterizenonlinear data A general ARIMAmodel is known asARIMA(119901 119889 119902) where 119901 is the order of the autoregressive part 119889 isthe number of differences from the original time series datatomake it stationary and 119902 is the order of themoving averageportion The general equation for ARIMA models is

119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)

where 119910119896 is the observed value at time 119896119891119898 is the119898th autore-gressive parameter 120590119899 is the 119899th moving average parameterand 120576119896 is the error at time 119896

423 Bias-Variance Framework To estimate the availabilityof the wind speed forecasting models bias-variance frame-work [44] was employed to evaluate accuracy and stability ofthe proposed hybrid model and single models Let 119909119905 minus 119905 be

FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction

IMF(n)IMF(i)IMF(2)IMF(1)

Modelselector

middot middot middot middot middot middot R(n)

Figure 4Theprocedures ofwind speed forecasting using the hybridmodel

the difference between observed value 119909119905 and predicted value119905 and the average difference over all points is

1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)

where 119905 is the 119905th data for performance evaluation and 119879

is all the forecasting data used for performance evaluationThe expectation of the total number of forecasting values is119864() = (1119879) sum

119879119905=1 119905 and the expectation of the actual value

is 119909 = (1119879) sum119879119905=1 119909119905 The bias-variance framework can be

decomposed as follows

119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)

where Bias2() indicates the prediction accuracy of theforecasting model and Var () demonstrates the stability

43 Process of Parameter Optimization Selecting the appro-priate parameter is very critical to improving the accuracyof model prediction thus the abovementioned FOA is usedto optimize the parameters of the RBF GRNN and SVR


Study site in Weihai

Statistical measures of original wind speed series in Weihai

Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer

Training set Testingset

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)

Figure 5 Specific location of the study sites and the statistical measures of original wind speed datasets in Weihai

Table 2 Experiment parameters of RBF

Experimental parameters Default valueThe learning velocity 005Training requirements precision 00001

models (as shown in Figure 6(a)) First in the RBF modelthe centers and widths [120583 120579] of the basic functions should besubstituted by the smell concentration judgment value (119878119894)of the FOA and other experiment parameters of RBF areshown inTable 2The smoothing parameter (120590) of theGRNNthe penalty parameter (119862) and loss function parameter (120576)of the SVR are also represented by (119878119894) of the FOA Afterthat the offspring is entered into the three models and thesmell concentration value is calculated again Then smellconcentration (Smell119894) replacing 119878119894 with the smell concen-tration judgment function (also called the fitness function)is calculated with the smaller value of fitness function thebetter results will be found Through the fruit flyrsquos randomfood searching using its sensitive sense of smell and flockingto the location of the highest smell concentration usingits vision the optimal parameters of the three models areobtained

To test the effect of the model parameters optimized bythe FOA the four seasons of wind speed data were selectedThe three criterions were employed to evaluate the perfor-mance of the three models optimized by the FOA Resultsof the comparison are shown in Table 3 and Figure 6(b)It can be clearly observed that the FOARBF FOAGRNNand FOASVR consistently have the least statistical error as

Table 3 Comparison between RBF GRNN and SVR and FOARBFFOAGRNN and FOASVR forecast for wind speed in four seasons

Error criteria Spring Summer Fall Winter

RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151

FOARBFMAE 07584 06693 07583 07340RMSE 09144 08072 10817 10174IA 08653 08837 09211 09016

GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339

FOAGRNNMAE 07371 06912 07296 07186RMSE 08881 08404 10394 09933IA 08738 08669 09245 09016

SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128

FOASVRMAE 07440 06319 06941 06798RMSE 08755 07812 09697 09799IA 08740 08914 09346 09097

indicated by theMAE RMSE and IA One can conclude thatthe FOA optimization can effectively improve the predictionperformance of the traditional neural network model


The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start

Initialize the location of fruit flyswarm population sizemaximum iteration number

Every fruit fly searchingfor the food by osphresis

CalculateSi and Disti

Find and keep the maximal smellconcentration value and updatethe best location

Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit

hmfruit fly byCalculate Smelli for every


21205902]]

K(x x1)

K(x x2)

K(x x3)

ℎj(x) = exp(minussumM

i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1

120576(f(xi) minus yi)

Smelli = Function(Si)

(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18

Summer Fall WinterSpring Summer Fall WinterSpringSummer Fall WinterSpring

(b)

Figure 6 The procedures of RBF GRNN and SVR optimized by FOA


0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT

t=1 (yt minus yt)2sumT

t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2

Figure 7 The process of the hybrid model

44The Process of Model Selection Given the complexity andchaos of the original wind speed series the tendency of windspeed is very difficult to directly predict by using the above-mentioned individual models As such the original windspeed datasets are decomposed into several IMFs and aresidue 119877(119899) by EEMD which make the raw datasets easierto simulateThe FOARBF FOAGRNN and FOASVRmodelsare used to forecast each IMF and the residue 119877(119899) as the

input nodes hidden nodes and output nodes of the threeneural networks are set to 4 9 and 1 respectivelyThe rollingoperation method was used in this paper and the windspeed data in four seasons were selected to test the proposedmodels

The selection process of the hybrid model is shown inFigure 7 and its results are shown in Tables 4ndash7 and it canbe clearly observed that each individual model exhibits the


Table 4 The forecasting results of model selection among theFOARBF FOAGRNN and FOASVR in spring

Components Error criteria FOARBF FOAGRNN FOASVR

IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614

Table 5 The forecasting results of model selection among theFOARBF FOAGRNN and FOASVR in summer


IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874

best performance at a specific IMF Nevertheless no singlemodel can perform best in all situations For example Table 4

Table 6 The forecasting results of model selection among theFOARBF FOAGRNN and FOASVR in autumn


IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875

Table 7 The forecasting results of model selection among theFOARBF FOAGRNN and FOASVR in winter


IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655

shows the forecasting results in springtime and reveals thatthe FOARBF provides the best results at the IMF5 and IMF7


Table 8 The typical results of the hybrid model and the results of the other models for the four seasons

Case Errors Persistence model ARIMA model EEMD-FOARBF EEMD-FOAGRNN EEMD-FOASVR Hybridmodel

SpringMAE 07741 07285 03675 05690 03692 00976RMSE 09023 08769 04714 07505 04783 01308IA 08638 08684 09647 09019 09617 09973

SummerMAE 07208 07111 04312 05280 03940 01032RMSE 08589 08615 05287 06472 04920 01280IA 08716 08682 09374 08965 09496 09964

FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987

WinterMAE 07833 07017 06117 06211 04171 00875RMSE 10450 09779 07548 07955 05301 01164IA 09098 09133 09399 09264 09749 09988

AverageMAE 07373 07323 05255 05345 03743 00999RMSE 09162 09336 06912 07064 04902 01301IA 09002 08956 09429 09245 09684 09978

The FOASVR however exhibits the lowest MAE and RMSEvalues among all individualmodels at IMF2 IMF3 and IMF6while the lowest value at IMF4 and 119877(119899) is achieved by theFOAGRNN The analysis of three other seasons can be seenin the Appendix

45 Forecasting Results and Comparative Analysis In theabovementioned process the six independent IMFs andone residual decomposed by EEMD are predicted by threedifferent models FOARBF FOAGRNN and FOASVR Theoptimal model corresponding to each IMF and 119877(119899) is thenselected through model selection In Step 3 each IMF ispredicted by the selected optimal methods and the finalresults are obtained by assembling the forecasting results ofeach IMF

451 Forecasting Comparison Results To evaluate the per-formance accuracy of the proposed hybrid model based onmodel selector three singlemodels and two benchmarkmod-els are employed to compare with the hybrid model Singlemodels include the FOARBF FOAGRNN and FOASVReach of which is used for forecasting all of the signals decom-posed by EEMD Two benchmarkmodels include persistencemodel and ARIMA model The comparison results for fore-casting ability are as shown in Table 8 Detailed analyses areelaborated as follows

(1) By comparing the hybrid model with the otherfive models the lowest MAE and RMSE values areachieved by hybrid model In particular the IA valuesof the hybridmodelwere improved by 1084 1140582 793 and 304 on four seasons comparedwith the persistence model ARIMA model EEMD-FOARBF EEMD-FOAGRNN and EEMD-FOASVR

(2) When compared to benchmark model the EEMD-FOARBF EEMD-FOAGRNN EEMD-FOASVR and

Table 9 Bias-variance test of seven models for the mean value infour seasons

Model Bias varianceBias Var

Hybrid model 0016168 0000178EEMD-FOASVR 0057193 0051961EEMD-FOAGRNN 0099827 0192708EEMD-FOARBF 0063177 0143495ARIMA 0117167 0244263Persistence model 0165100 0216753

the hybrid model show optimal forecasting resultsaccording to MAE RMSE and IA likely becauseEEMD technology is effective in improving the fore-casting accuracy as a data preprocess step

(3) When compared to the EEMD-FOARBF EEMD-FOAGRNN and EEMD-FOASVR the hybridmethod also shows better prediction results indi-cating that the hybrid method can take advantagesof each individual model to obtain more completeinformation

Above all the proposed hybrid model has been verifiedas an effective approach for improving the forecasting perfor-mance through the analysis of the prediction results

452 Tested with Bias-Variance Framework Table 9 showsthe results of the bias-variance test the values of bias indicatethe prediction accuracy of the forecasting model and valuesof variance demonstrate the stability The results reveal thefollowing

(1) The absolute values of the biases of the hybrid modelare less than those of the other models which indi-cates that the hybrid model has a higher accuracy in


wind speed forecastingThevariance results also showthat the hybrid model is more stable

(2) The results of bias and variance values of the EEMD-FOARBF EEMD-FOAGRNN EEMD-FOASVR andhybrid model are less than the persistence model andARIMA this reveals EEMD and FOA are effectiveapproaches for improving the accuracy and stabilityof forecasting models

Thus it is clear that the hybrid model has a higher accu-racy and stability in wind speed forecasting and it performsmuch better than individual models in forecasting

5 Conclusions

Reliable and precise wind speed forecasting is vital forwind power generation systems However wind speed showsnonlinearity and nonstationarity which pose great challengesto the task of predicting wind speed precisely Regardingthe currently available forecasting models the single modelapplied for forecasting wind speed has limited capacity andis not suitable for all situations The appropriate selectionapproach of the hybrid model can give full play to thestrengths of each of the individual models and make eachindividual model perform in its specific manner For thesereasons we proposed a hybrid model based on EEMDthat combines three commonly used neural networks opti-mized by the FOA The main contributions of this modelare summarized as follows (1) Due to the instability ofwind series EEMD technique is utilized as a preprocessingapproach to decompose the original time series into acollection of relatively stationary subseries for forecasting(2) To overcome the drawbacks of the unstable forecastingresults of the RBF GRNN and SVR the FOA optimizationis applied to improve the prediction performance of thetraditional forecasting model (3) Because the IMF signalswith different characteristics are hard to forecast by a singlemodel a model selection combining FOARBF FOAGRNNand FOASVR is proposed to further improve forecastingaccuracyThe experimental results indicate that the proposedhybrid model has minimum statistical error in terms ofMAE RMSE IA and bias variance and it proved that theproposed hybrid method performs better than single modelsand is superior to other hybrid models as well such as theEEMD-FOARBF EEMD-FOAGRNN and EEMD-FOASVRBased on the abovementioned analysis we conclude that theproposed hybrid model can not only take full advantage ofseveral single ANNs to improve prediction accuracy but alsoeasily implement the task in wind parks

Appendix

To further prove that the proposed hybrid model can selectthe best model for different cases the forecasting results inother seasons can be seen in Tables 4ndash6 For example Table 4shows the experimental results from three single modelsin the summer Among all the single models when theFOARBF was applied the value of IA was higher than thoseof the other methods at IMF2 and IMF6 At IMF4 IMF7and 119877(119899) the FOAGRNN provides the optimal results At

other signals the results from the FOASVR are the bestTable 5 shows the results in autumn Among all the modelsat IMF2 IMF3 IMF4 and IM6 the FOASVR performs thebest while the FOAGRNN performs better than the othersat IMF7 and 119877(119899) Meanwhile the FOARBF provides theoptimal results at other signals The forecasting results ofthree single models in winter are presented in Table 6 AtIMF6 IMF7 and 119877(119899) the most accurate results belong tothe FOAGRNN When the FOASVR is used the results aremore accurate from IMF2 to IMF4 Results show that theFOARBF only performs desirably at IMF5 From Tables 3ndash6we find that FOASVR always performs well at high frequencysignals FOAGRNN works well at low frequency signalsand FOARBF usually provides optimal results at middlefrequency signals Consequently no single model providesthe best results for all of the signals but each model has itsstrengths at special IMFs Therefore the best-suited model ischosen based on different conditions

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research was supported by the National Natural Sci-ence Foundation Project (41225018) and Arid MeteorologyResearch Fund (IAM201305)

References

[1] A Kumar K Kumar N Kaushik S Sharma and S MishraldquoRenewable energy in India current status and future poten-tialsrdquo Renewable and Sustainable Energy Reviews vol 14 no 8pp 2434ndash2442 2010

[2] ldquoEnergyOutlook 2035rdquo 2015 httpwwwbpcomcontentdambppdfenergy-economicsenergy-outlook-2016bp-energy-out-look-2016pdf

[3] S Ahmed M T Islam M A Karim and N M KarimldquoExploitation of renewable energy for sustainable developmentand overcoming power crisis in BangladeshrdquoRenewable Energyvol 72 pp 223ndash235 2014

[4] CNREC China Wind Solar and Bioenergy Roadmap 2050Short Version 2014 httpwwwcnrecorgcnenglishpub-lication2014-12-25-457html

[5] China Renewable Energy Technology Catalogue 2014 httpwwwcnrecorgcnenglishpublication2014-12-29-461html

[6] A B Awan and Z A Khan ldquoRecent progress in renewable en-ergymdashremedy of energy crisis in Pakistanrdquo Renewable and Sus-tainable Energy Reviews vol 33 pp 236ndash253 2014

[7] S Salcedo-Sanz A Pastor-Sanchez J Del Ser L Prieto andZ W Geem ldquoA Coral Reefs Optimization algorithm withHarmony Search operators for accurate wind speed predictionrdquoRenewable Energy vol 75 pp 93ndash101 2015

[8] G Giebel R Brownsword G Kariniotakis M Denhard andC Draxl ldquoThe state-of-the-art in short-term prediction of windpower A literature overviewrdquo Tech Rep 6470de79-5287-45a9-8e4f-b629919aff7aPaperp5443 ANEMOSplus 2011

[9] G Giebel and L Landberg ldquoState-of-the-Art on Methods andSoftware Tools for Short-Term Prediction of Wind Energy


Productionrdquo Energy 2010 httpswwwresearchgatenetpubli-cation47549887 State-of-the-art Methods and software toolsfor short-term prediction of wind energy production

[10] G Kariniotakis P Pinson N Siebert G Giebel and RBarthelmie ldquoThe state of the art in short-term prediction ofwind power-from an offshore perspectiverdquo in Proceedings of theFrench SeaTechWeekConference pp 20ndash21 Brest France 2004

[11] D Version The State-of-the-Art in Short-Term Prediction ofWind Power 2011

[12] S Qin F Liu J Wang and Y Song ldquoInterval forecasts of anovelty hybrid model for wind speedsrdquo Energy Reports vol 1pp 8ndash16 2015

[13] J L Torres A Garcıa M De Blas and A De Francisco ldquoFore-cast of hourly average wind speed with ARMA models inNavarre (Spain)rdquo Solar Energy vol 79 no 1 pp 65ndash77 2005

[14] J Wang S Qin Q Zhou and H Jiang ldquoMedium-term windspeeds forecasting utilizing hybrid models for three differentsites in Xinjiang Chinardquo Renewable Energy vol 76 pp 91ndash1012015

[15] A Y Alanis L J Ricalde and E N Sanchez ldquoHigh OrderNeural Networks for wind speed time series predictionrdquo in Pro-ceedings of the International Joint Conference onNeuralNetworks(IJCNN rsquo09) pp 76ndash80 IEEE Atlanta Ga USA June 2009

[16] S A Pourmousavi Kani and M M Ardehali ldquoVery short-termwind speed prediction a new artificial neural network-Markovchain modelrdquo Energy Conversion and Management vol 52 no1 pp 738ndash745 2011

[17] J Zhou J Shi and G Li ldquoFine tuning support vector machinesfor short-term wind speed forecastingrdquo Energy Conversion andManagement vol 52 no 4 pp 1990ndash1998 2011

[18] G Li and J Shi ldquoOn comparing three artificial neural networksfor wind speed forecastingrdquo Applied Energy vol 87 no 7 pp2313ndash2320 2010

[19] M G De Giorgi A Ficarella and M G Russo ldquoShort-termwind forecasting using artificial neural networks (ANNs)rdquo inEnergy Sustain pp 197ndash208 2009

[20] Z-H Guo J Wu H-Y Lu and J-Z Wang ldquoA case studyon a hybrid wind speed forecasting method using BP neuralnetworkrdquo Knowledge-Based Systems vol 24 no 7 pp 1048ndash1056 2011

[21] J Wang W Zhang J Wang T Han and L Kong ldquoA novelhybrid approach for wind speed predictionrdquo Information Sci-ences vol 273 pp 304ndash318 2014

[22] J Hu J Wang and G Zeng ldquoA hybrid forecasting approachapplied to wind speed time seriesrdquo Renewable Energy vol 60pp 185ndash194 2013

[23] J Wang W Zhang Y Li J Wang and Z Dang ldquoForecastingwind speed using empirical mode decomposition and Elmanneural networkrdquo Applied Soft Computing vol 23 pp 452ndash4592014

[24] W Zhang J Wang J Wang Z Zhao and M Tian ldquoShort-termwind speed forecasting based on a hybrid modelrdquo Applied SoftComputing Journal vol 13 no 7 pp 3225ndash3233 2013

[25] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 6281ndash6284 2009

[26] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London Series A Mathematical and Physical Sciencesvol 454 no 1971 pp 903ndash995 1998

[27] E Haven X Liu and L Shen ldquoDe-noising option prices withthe wavelet methodrdquo European Journal of Operational Researchvol 222 no 1 pp 104ndash112 2012

[28] X Jiang L Zhang and M X Chen ldquoShort-term forecasting ofhigh-speed rail demand a hybrid approach combining ensem-ble empirical mode decomposition and gray support vectormachine with real-world applications in Chinardquo TransportationResearch Part C Emerging Technologies vol 44 pp 110ndash1272014

[29] Q Zhou H Jiang J Wang and J Zhou ldquoA hybrid model forPM25 forecasting based on ensemble empirical mode decom-position and a general regression neural networkrdquo Science of theTotal Environment vol 496 pp 264ndash274 2014

[30] D Liu D Niu H Wang and L Fan ldquoShort-term windspeed forecasting using wavelet transform and support vectormachines optimized by genetic algorithmrdquo Renewable Energyvol 62 pp 592ndash597 2014

[31] H Zhao R Liu Z Zhao and C Fan ldquoAnalysis of energy con-sumption prediction model based on genetic algorithm andwavelet neural networkrdquo in Proceedings of the 3rd InternationalWorkshop on Intelligent Systems and Applications (ISA rsquo11) pp1ndash4 IEEE Wuhan China 2011

[32] C Ren N An J Wang L Li B Hu and D Shang ldquoOptimalparameters selection for BP neural network based on particleswarm optimization A Case Study ofWind Speed ForecastingrdquoKnowledge-Based Systems vol 56 pp 226ndash239 2014

[33] W Pan ldquoA new fruit fly optimization algorithm taking thefinancial distress model as an examplerdquo Knowledge-Based Sys-tems vol 26 pp 69ndash74 2012

[34] H-Z Li S Guo C-J Li and J-Q Sun ldquoA hybrid annual powerload forecasting model based on generalized regression neuralnetwork with fruit fly optimization algorithmrdquo Knowledge-Based Systems vol 37 pp 378ndash387 2013

[35] Y Cong J Wang and X Li ldquoTraffic flow forecasting by a leastsquares support vector machine with a fruit fly optimizationalgorithmrdquo Procedia Engineering vol 137 pp 59ndash68 2016

[36] D S Broomhead and D Lowe ldquoRadial basis functions multi-variable functional interpolation and adaptive networksrdquoTech Rep 2 1988 httpswwwresearchgatenetpublication233783084 Radial basis functions multi-variable functionalinterpolation and adaptive networks

[37] H B Celikoglu ldquoApplication of radial basis function and gener-alized regression neural networks in non-linear utility functionspecification for travel mode choice modellingrdquo Mathematicaland Computer Modelling vol 44 no 7-8 pp 640ndash658 2006

[38] S Chen X Hong C J Harris and L Hanzo ldquoFully complex-valued radial basis function networks orthogonal least squaresregression and classificationrdquo Neurocomputing vol 71 no 16ndash18 pp 3421ndash3433 2008

[39] Z J Tamboli and S R Khot ldquoEstimated analysis of radial basisfunction neural network for induction motor fault detectionrdquoInternational Journal of Engineering and Advanced Technologyvol 2 pp 41ndash43 2013

[40] D F Specht ldquoA general regression neural networkrdquo IEEETransactions onNeural Networks vol 2 no 6 pp 568ndash576 1991

[41] JM Lasala RMehran JWMoses et al ldquoEvidence basedman-agement of patients undergoing PCI Conclusionrdquo Catheteriza-tion and Cardiovascular Interventions vol 75 supplement 1 ppS43ndashS45 2010

[42] W-C Hong Y Dong W Y Zhang L-Y Chen and B K Pan-igrahi ldquoCyclic electric load forecasting by seasonal SVR with


chaotic genetic algorithmrdquo International Journal of ElectricalPower and Energy Systems vol 44 no 1 pp 604ndash614 2013

[43] T Wang M Zhang Q Yu and H Zhang ldquoComparing theapplications of EMD and EEMD on time-frequency analysis ofseismic signalrdquo Journal of Applied Geophysics vol 83 pp 29ndash342012

[44] L Xiao W Shao T Liang and C Wang ldquoA combined modelbased on multiple seasonal patterns and modified firefly algo-rithm for electrical load forecastingrdquo Applied Energy vol 167pp 135ndash153 2016

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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environmentally friendly as such wind energy will be ableto satisfy the growing demand for electricity

Wind energy has great influence on power grid securitypower system operation and market economics due to itsintermittent nature especially in areas with high wind powerpenetrationThus the analysis and assessment ofwind energyare a meaningful but markedly difficult task for researchBecause wind power generation hinges on wind speedobtaining accurate wind speeds is important To improvethe precision of wind speed predictions numerous methodshave been proposed and developed in recent decades Thesemethods can be divided into three general types physicalmodels conventional statistical models and artificial intelli-gence models [8ndash11] Physical models use weather predictiondata such as temperature pressure orography obstacles andsurface roughness for the best forecasting accuracy but arepoor at short-term wind speed simulation Conventional sta-tistical models in contrast draw on vast historical data basedonmathematical models usually involving conventional timeseries analysis such as ARMA ARIMA or seasonal ARIMAmodels [12 13] and achieve more accurate short-term windspeed predictions than physical models However conven-tional statistical models are imperfect The fluctuating andintermittent characteristics of wind speed sequences requiremore complicated functions to capture the nonlinear rela-tionships rather than assuming a linear correlation structure[14] Given the development of statistical models along withthe advent of artificial intelligence techniques artificial intel-ligence models including artificial neural networks (ANNs)and other mixed methods have been proposed and are usedin the field of wind speed forecasting [15ndash20] For instancebecause of the chaotic nature of wind time series Alaniset al [15] proposed a higher order neural network (HONN)based on an extendedKalman filter formodel training whichprovides accurate one-step-ahead predictions Guo et al [20]proposed a hybrid wind speed forecastingmethod employinga backpropagation (BP) neural network and seasonal expo-nential adjustment to remove seasonal effects from actualwind speed datasets Wang et al [21] exploited a radial basisfunction (RBF) neural network for wind speed predictionand the effectiveness of this method was proved by a practicalcase Zhou et al [17] proposed a prediction method based ona support vector machine (SVM) for short-term wind speedprediction De Giorgi et al [19] adopted the ANNs to forecastwind speeds and compared them to the linear time-series-based model with the ANNs providing a robust approachfor wind prediction All of these methods have improved theprecision of wind speed predictions to some extent

However wind speed time series are highly noisy andunstable therefore using the primary wind speed seriesdirectly to establish prediction models is subject to largeerrors [22ndash24] To build an effective prediction model thefeatures of original wind speed datasets must be fully ana-lyzed and considered The ensemble empirical mode decom-position (EEMD) [25] is an advanced effective technologywhich makes up for the deficiency of EMD [26] and has cer-tain advantages over other typical decomposition approachessuch as the wavelet decomposition and the Fourier decom-position [27] With direct intuitive empirical and adaptive

data processing EEMD was especially devised for nonlinearand complicated signal sequences such as wind speed seriesFor example Hu et al [22] proposed a hybrid method basedon the EEMD to disassemble the original wind speed datasetsinto a series of independent IntrinsicMode Functions (IMFs)and use SVM to predict the values for IMFs in differentfrequencies Jiang et al [28] also proposed a hybrid modelfor high-speed rail demand forecasting based on EEMD inwhich the original series are decomposed into certain signalswith different frequencies and then the grey support vectormachine (GSVM) is employed for forecasting Zhou et al [29]additionally proposed a hybrid method based on EEMD andthe generalized regression neural network (GRNN) In thismethod the original data are decomposed into different IMFswith corresponding frequencies and the residue componentby EEMD and then each component is taken as an input toestablish GRNN forecasting model

Each of the aforementionedmodels only employs a singleANN model to predict all of the signal sequences decom-posed by EEMD nevertheless different signals have differentcharacteristics meaning that a simple individual model canno longer adapt to all properties of the data Moreoverprevious literature has not addressed which features are bestsuited for choosing the most appropriate approach Thus inour study we propose a hybrid model based on a modelselector that combines RBF GRNN and SVR to addresssignal data series with different characteristics to furtherimprove forecasting accuracy

In existing neural network training structures modelparameters are very vital factors affecting prediction preci-sion and different types of data require different parametersThe genetic algorithm (GA) and particle swarm optimization(PSO) algorithms are the most common approaches tooptimize the parameters of neural network structures Liuet al [30] used the genetic algorithm to determine the weightcoefficients of a combined model for wind speed forecastingZhao et al [31] developed a combined model for energyconsumption prediction based on model parameters opti-mization with the genetic algorithm Ren et al [32] appliedthe particle swarm optimization to set weight coefficientsof a forecasting model for 6-hour wind speed forecastingHowever these meta-heuristic algorithms have the draw-backs of being hard to understand and achieving the globaloptimal solution slowly The fruit fly optimization algorithm(FOA) [33] was a new optimization and evolutionary compu-tation technique which has distinct advantages in its simplecomputational process fewer parameters to be fine-tunedand stronger ability to search for global optimal solutionsand outperforms other metaheuristic algorithms [34 35] Inour study we introduce the FOA algorithm to automaticallydetermine the necessary parameters of the RBF GRNN andSVR models to achieve better performance

The rest of the paper is organized as follows Section 2briefly introduces related methods while Section 3 describesthe proposed hybrid approach in detail Section 4 describesthe dataset used for this study and discusses the forecastingresults of proposed model compared with other predictionmodels Section 5 concludes the work






2

21205792119895

) (1)



119910119896 =

119871

sum

119895=1

ℎ119895119908119895119896 + 120588119896 (2)







i

i

i

p

p

p

S1

S2

O

i

p

S

O

Y =S1

S2

NeuronsInput

Pattern

Summation

Output


S1 = sumj=1

yj middot Pj

S2 = sumj=1

Pj


21205902]]

wS1= yi

wS2= 1




119909 (119905) =

119898

sum

119896=1

imf119898 (119905) + 119903119898 (119905) (3)









Input space

Kernelmapping

Feature space

Regression

Primal space

x

Y Y

K(x)

120576120576

120576

120576

120576

120576

f(x) =Nsum

i=1



100381710038171003817100381710038172)



119873120576 =1205762

1205762119899

(4)





3 Combined Model




MAE MAE =1

119873

119873

sum

119899=1

1003816100381610038161003816119910119899 minus 1198991003816100381610038161003816


RMSE RMSE = (1

119873

119873

sum

119899=1

(119910119899 minus 119899)2)



119905=1 (119910119905 minus 119905)2

sum119879

119905=1 (1003816100381610038161003816119910 minus 119905

1003816100381610038161003816 +1003816100381610038161003816119910 minus 119910119905

1003816100381610038161003816)2










Algorithm 1 FOA











The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1




119905+119896 = 119901119905 (5)



119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)



FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction


Modelselector




1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)






119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)






Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






2

21205792119895

) (1)



119910119896 =

119871

sum

119895=1

ℎ119895119908119895119896 + 120588119896 (2)







i

i

i

p

p

p

S1

S2

O

i

p

S

O

Y =S1

S2

NeuronsInput

Pattern

Summation

Output


S1 = sumj=1

yj middot Pj

S2 = sumj=1

Pj


21205902]]

wS1= yi

wS2= 1




119909 (119905) =

119898

sum

119896=1

imf119898 (119905) + 119903119898 (119905) (3)









Input space

Kernelmapping

Feature space

Regression

Primal space

x

Y Y

K(x)

120576120576

120576

120576

120576

120576

f(x) =Nsum

i=1



100381710038171003817100381710038172)



119873120576 =1205762

1205762119899

(4)





3 Combined Model




MAE MAE =1

119873

119873

sum

119899=1

1003816100381610038161003816119910119899 minus 1198991003816100381610038161003816


RMSE RMSE = (1

119873

119873

sum

119899=1

(119910119899 minus 119899)2)



119905=1 (119910119905 minus 119905)2

sum119879

119905=1 (1003816100381610038161003816119910 minus 119905

1003816100381610038161003816 +1003816100381610038161003816119910 minus 119910119905

1003816100381610038161003816)2










Algorithm 1 FOA











The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1




119905+119896 = 119901119905 (5)



119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)



FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction


Modelselector




1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)






119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)






Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


Input space

Kernelmapping

Feature space

Regression

Primal space

x

Y Y

K(x)

120576120576

120576

120576

120576

120576

f(x) =Nsum

i=1



100381710038171003817100381710038172)



119873120576 =1205762

1205762119899

(4)





3 Combined Model




MAE MAE =1

119873

119873

sum

119899=1

1003816100381610038161003816119910119899 minus 1198991003816100381610038161003816


RMSE RMSE = (1

119873

119873

sum

119899=1

(119910119899 minus 119899)2)



119905=1 (119910119905 minus 119905)2

sum119879

119905=1 (1003816100381610038161003816119910 minus 119905

1003816100381610038161003816 +1003816100381610038161003816119910 minus 119910119905

1003816100381610038161003816)2










Algorithm 1 FOA











The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1




119905+119896 = 119901119905 (5)



119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)



FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction


Modelselector




1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)






119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)






Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






Algorithm 1 FOA











The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1




119905+119896 = 119901119905 (5)



119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)



FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction


Modelselector




1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)






119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)






Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1

(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1




119905+119896 = 119901119905 (5)



119910119896 =

119901

sum

119898=1

119891119898119910119896minus119898 +

119902

sum

119899=1

120590119899119890119896minus119898 + 120576119896 (6)



FOARBF

FOASVR

FOAGRNN

The original data

EEMDStep 1

Step 3

Step 2 Remove

Forecastingresults

Modereconstruction


Modelselector




1

119879

119879

sum

119905=1

(119909119905 minus 119905) =1

119879

119879

sum

119905=1

119909119905 minus1

119879

119879

sum

119905=1

119905 (7)






119864 ( minus 119909)2

= 119864 ( minus 119864 () + 119864 () minus 119909)2

= 119864 ( minus 119864 ())2

+ (119864 () minus 119909)2

= Var () + Bias2 ()

(8)






Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




Spring

WinterFallSummer

1880

134013801428

Maximum (ms)052

040140062

Minimum (ms)336

210216307

Std dev (ms)792

592603701

Mean (ms)

(a)

Win

d sp

eed

Spring

Winter

Fall

Summer


50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d

50 100 150 200 250 300 350 4000Time (15 min)

01020

(ms

)W

ind

spee

d50 100 150 200 250 300 350 4000

Time (15 min)

01020

(ms

)

(b)








RBFMAE 12798 09270 11633 09849RMSE 14989 11825 16560 14428IA 078923 06460 07761 08151


GRNNMAE 08321 09842 13096 13101RMSE 10964 12857 15960 17048IA 07684 06164 06470 05339


SVRMAE 10776 10346 13319 26280RMSE 12551 13142 18932 42264IA 08033 07448 07526 05128




The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


The best fruit fly

Food

Fly group

Iterativeevolution

(X1 Y1)

Dist1(X2 Y2)

Dist2

(X3 Y3)

Dist3

(Xi Yi)

S1 = 1Dist1

x1

x2

x3

x1

x2

x3

p

p

p

S1

S2

O

X1

X2

X3

ℎ1

ℎ2

ℎ3

sum

sum

120590

C

120576

120583

120579

RBF

SVR

GRNN

Start





Maxiteration

EndFr

uit fl

y op

timiz

atio

nal

gorit



21205902]]

K(x x1)

K(x x2)

K(x x3)


i=1 (xi minus 120583j)2

21205792j

)

f(x) = min 1

2W2 + C

1

k

ksumi=1



(a)

RMSE RMSE RMSE

GRNNFOAGRNN

SVRFOASVR

RBFFOARBF

0

03

06

09

12

15

18

005

115

225

335

445

0

03

06

09

12

15

18


(b)



0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in


0

55 6

R(n)

02

minus0

2

IMF7

0

04

minus0

4

IMF6

0

03

minus0

3

IMF5

0

04

minus0

4IMF4

01

minus1

IMF3

01

minus1

IMF2

01

minus1

IMF1

EEMD

Combinedmodel

FOARBF

FOASVR

FOAGRNN

MAE =1

T

Tsumt=1

1003816100381610038161003816yt minus yt1003816100381610038161003816

RMSE = ( 1

T

Tsumt=1

(yt minus yt)2)12

IA = 1 minussumT


t=1 (1003816100381610038161003816y minus yt1003816100381610038161003816 +

1003816100381610038161003816y minus yt1003816100381610038161003816)2








IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in




IMF2MAE 01679 01330 00769RMSE 01935 01653 00945IA 09013 09307 09808

IMF3MAE 00879 00762 00452RMSE 01089 00947 00599IA 09872 09900 09963

IMF4MAE 01297 00603 00766RMSE 01604 00717 00878IA 09321 09867 09751

IMF5MAE 00422 01298 01514RMSE 00595 01602 01727IA 09992 09949 09932

IMF6MAE 04546 02836 00052RMSE 06196 03994 00103IA 07801 09034 10000

IMF7MAE 00429 01394 01276RMSE 00433 01399 01354IA 09976 09754 09794

119877(119899)

MAE 02081 00025 00178RMSE 02081 00026 00304IA 04322 09998 09614



IMF2MAE 00617 01521 00807RMSE 00756 01857 01161IA 09883 09206 09718

IMF3MAE 01470 00874 00670RMSE 01919 01021 00772IA 09296 09825 09904

IMF4MAE 02023 00419 00681RMSE 02355 00513 00759IA 09387 09978 09952

IMF5MAE 00571 00397 00228RMSE 00656 00491 00256IA 09670 09824 09949

IMF6MAE 00136 04352 00904RMSE 00148 04580 01027IA 09977 03439 08650

IMF7MAE 00024 00022 00024RMSE 00025 00026 00027IA 09871 09864 09849

119877(119899)

MAE 00501 00366 00672RMSE 00595 00376 00701IA 09026 09682 08874




IMF2MAE 01206 02141 00884RMSE 01647 02888 01049IA 09640 08839 09874

IMF3MAE 00755 00662 00435RMSE 00984 00838 00535IA 09798 09849 09940

IMF4MAE 02501 00549 00247RMSE 02873 00639 00305IA 09396 09974 09994

IMF5MAE 00488 01090 00722RMSE 00553 01252 00777IA 09996 09977 09991

IMF6MAE 00745 00677 00275RMSE 00999 00685 00279IA 09761 09909 09985

IMF7MAE 00217 00194 00273RMSE 00244 00196 00273IA 09852 09889 09773

119877(119899)

MAE 01185 00756 00055RMSE 01281 00803 00068IA 02589 04183 09875



IMF2MAE 01980 01564 00736RMSE 02516 01936 00954IA 08183 08868 09802

IMF3MAE 01191 00475 00286RMSE 01494 00617 00351IA 09481 09907 09972

IMF4MAE 01802 00631 00173RMSE 02120 00775 00212IA 09224 09921 09994

IMF5MAE 00399 00661 00928RMSE 00491 00722 01013IA 09982 09958 09921

IMF6MAE 01175 00144 01348RMSE 01207 00162 01424IA 09902 09998 09853

IMF7MAE 03543 00066 00571RMSE 04067 00066 00889IA 04432 09998 09394

119877(119899)

MAE 00775 00024 00086RMSE 00810 00025 00101IA 03960 09982 09655







FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in






FallMAE 06708 07879 06917 04197 03169 01113RMSE 08585 10181 10098 06322 04604 01453IA 09554 09326 09294 09732 09874 09987




















5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in





5 Conclusions


Appendix



Competing Interests


Acknowledgments


References


























































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

















































Volume 2014

Mining


Journal of



Geophysics







Journal of




Advances in











Geology Advances in

research article a hybrid model based on ensemble...

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