study on the sound quality of steady and unsteady exhaust...

Research ArticleStudy on the Sound Quality of Steady andUnsteady Exhaust Noise

Falin Zeng1 and Sunmin Sun 2

1Automobile Engineering Research Institute Jiangsu University Zhenjiang China2School of Automobile and Traffic Engineering Jiangsu University Zhenjiang China

Correspondence should be addressed to Sunmin Sun 731281380qqcom

Received 17 January 2018 Accepted 10 June 2018 Published 28 June 2018

Academic Editor Francesco Aymerich

Copyright copy 2018 Falin Zeng and Sunmin SunThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In order to predict and study the sound quality of automobile exhaust noise Zwicker steady-state and time-varying method wereapplied to calculate the psychoacoustic objective parameter values in terms of the exhaust noise of sample cars at uniform velocityand accelerated velocity Thereby a prediction model of GA-BP sound quality based on psychoacoustic objective parameters wasestablished At the same time wavelet analysis was used to decompose the accelerated signal in order to overcome the shortcomingssuch as Heisenberg uncertainty the RNR (regularization nonstationary regression technique) was applied to compute the WVDdistribution (RNR-WVD) therefrom obtaining the coefficient matrices of different-band signals after wavelet decomposition andthen A weighting was carried out on the coefficient matrices so as to establish a new sound quality parameter SQP-WRW (soundquality parameter base on wavelet and then proceed to RNR-WVD) as the input of GA-BP model and therefrom a sound qualityprediction model was established The results indicate that the model based on SQP-WRW has higher precision for predicting thesound quality of acceleration signal and it can better reflect the characteristics of acceleration signal and sound quality

1 Introduction

The research of automobile NVH has worked its way fromnoise control to the new stage emphasizing the design ofnoise and sound quality the traditional research of vehiclenoise aiming for sound pressure level can no longer satisfythe demand of the contemporary consumers

The sound quality of automobiles reflects the subjectivefeeling of people towards the noise the present researchon sound quality is mostly based on subjective evaluationtest which can accurately and directly reflect the quality ofvoice but it is time-consuming and labor-consuming On theground of that domestic and foreign scholars put forwardprediction models of automobile sound quality based onpsychoacoustics parameters Zhang et al [1] optimized thegenetic algorithm of support vectormachines and establishedthe prediction model of diesel engine sound quality basedon psychoacoustic objective parameters Based on the psy-choacoustic objective parameters Zuo Shuguang et al [2]proposed the multiple linear regressions neural network

and support vector machine 3 prediction models for vehicleinterior noise and carried out comparison study Bi Fengronget al [3] established the least squares support vector machinemodel on the basis of psychoacoustic objective parametersand EEMD signal features thereby conducting the researchof the acoustic quality of diesel engine radiated noise Leeet al [4] proposed the wavelet transform-based evaluationparameters of impact sound quality HFEC and the objectiveparameters with both roughness and volatility asmultivariatelinear regression model which were applied to predict theacoustic quality of suspension system components

To sum up the present research on the sound quality ofautomobile mainly stays in the prediction model based onpsychoacoustic objective parameters however the automo-bile noise mainly belongs to unsteady signal and the singleuse of the analysis of time domain or frequency domaincannot accurately reflect the characteristic of vehicle noiseWe should study and extract the signal features from timeand frequency domains while the sound quality predictionmodel based on advanced time frequency signal processing

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6205140 11 pageshttpsdoiorg10115520186205140

2 Mathematical Problems in Engineering

035

030

025

020

soun

d pr

essu

re (P

a)

015

010

005

0000 1000 2000 3000 4000 5000

frequency (Hz)

1000rmin2000rmin3000rmin

4000rmin5000rmin

Figure 1 Exhaust signal collection under steady-state condition ofsample car 1

(such as wavelets EMD and WVD) has not yet been widelyused [5]

The exhaust noise of vehicles is one of the most importantnoise sources the research on noise quality of which is ofcertain significance to noise pollution control Firstly thispaper obtained relative psychoacoustic objective parametersof steady-state and acceleration signals in Artermis based onZwicker steady-state and time-varying algorithm [6] and thenoise quality GA-BP prediction model based on psychoa-coustic parameters was established Later on the methodsof wavelet analysis and regularization unsteady regressionwere introduced to calculate the WVD distribution andthe characteristic parameters SQP-WRW of the accelerationexhaust signal were set up as the input of GA-BP model Theresult suggests that the latter can predict the sound qualityof nonstationary signal more accurately which can providea reference for the research of unsteady exhaust soundquality

2 Subjective Evaluation Modelof Exhaust Noise

Based on GB1496-79 Measuring Method for Noise of Power-Driven Vehicles this paper adopted LMS to test and collectthe steady-state exhaust noise signals as well as the acceler-ation noise signals of 10 domestic vehicles The signals withengine speed of 1000rpm 2000rpm 3000rpm 4000rpm and5000rpm were collected and signals in the entire process inwhich engine speed changes from 1000rpm to 5000rpm werecollected According to the research experience [7] loudnesssharpness roughness volatility kurtosis and A sound levelwere used to be the input parameters of the model Thesteady-state noise test results of sample car 1 is shown inFigure 1 it can be concluded that the sound pressure level

of noise generally increased with the increase of rotationalspeed

21 Subjective Evaluation Test Pair comparison method wasutilized in this subjective test 5s of steady-state signals wasintercepted and 15s of characteristic signals in accelerationwas extracted In order to eliminate the effect of time durationon the subjective evaluation the steady-state signal sampleswere treated with delayed time processing Samples werecompared in pair in which the sample with decent evaluationwill obtain 1 point and the ones with unsatisfying evaluationwill gain nothing so that each sample will get a definite valuerepresenting its sound quality which is more intuitive andconducive for the modelling later on

A total of 42 people participated in the subjective evalua-tion they are postgraduates majoring in vehicle-related fieldfrom a university and related workers in research institutesThere are 24males and 18 females aged roughly within 24ndash40According to sample coincidence degree and consistencycoefficient [8] the data of 4 reviewers were eliminated theaverage coincidence degree of the samples was 0783 andthe average consistency coefficient was 0928 Thereof theconsistency coefficients were computed by Kendall method[9] and the psychoacoustic objective parameters of thesamples and the results of the subjective tests are shown inTable 1 The normalization formula of satisfaction is showedas formula (2)

22 Correlation Analysis In order to study the relationshipbetween the subjective satisfaction degree of exhaust noiseand the psychoacoustic objective parameters a comparisonstudy was carried out between the subjective satisfactionscore and psychoacoustic objective parameters SPSS19 soft-ware was used to do the correlation analysis The resultsare shown in Table 2 Because the sample contains unsteadynoise it will produce extreme values with the change of timeTherefore we applied two-tailed Spearman rank correlationto carry on the correlation analysis wherein the spearmanrank correlation formula is as follows

119903 = 1 minus 6sum119899119894=1 (119880119894 minus 119881119894)2119899 (1198992 minus 1) (1)

In the formula119880119894 and119881119894 are the ranks of the two variablesthe role of which is to change the fixed-distance variableto nonfixed-distance thereby reducing the effect of extremevalues on the results 119899 is the sample number and 119903 is thespearman rank correlation coefficient

According to the results of correlation analysis it can beconcluded that the correlations between loudness sharpnessand satisfaction degree are relatively great The coefficientshave reached 0875 and 0682 respectively the influenceof these two parameters has a great weight on the noisesatisfaction and except for the positive correlations betweenroughness kurtosis and subjective satisfaction degreeother parameters have inverse correlations with satisfactiondegree

Mathematical Problems in Engineering 3

Table 1 Objective parameters and satisfaction values of samples

Sample number loudness sharpness Roughness fluctuation A sound pressure Kurtosis satisfaction Satisfaction normalizationstable1 2501 165 075 0290 629 004 6211 0582stable2 2531 091 034 0016 638 -006 8786 0859stable3 2969 196 089 001 642 -021 7847 0758stable4 3261 167 184 0005 645 013 6007 0560 stable49 2926 172 0144 014 6351 -011 6957 0662stable50 4568 164 026 012 6798 -052 2982 0235accele1 3929 175 115 011 6624 013 4162 0362accele2 4541 164 034 015 6688 -035 3063 0246accele3 3059 124 218 006 6321 -092 6286 0590 accele9 2771 188 072 011 6198 005 7177 0686accele10 4649 151 11 024 6788 -022 3497 0291

Table 2 Correlation coefficients between satisfaction and subjective parameters

Acoustic parameters loudness sharpness Roughness fluctuation KurtosisCorrelation coefficients -0875lowastlowast -0682lowast 0271lowast -0204 0159lowast

(Note lowastlowast indicates that when the bilateral confidence level is 001 the correlation is significant lowast indicates that when the bilateral confidence level is 005 thecorrelation is significant)

3 Establishment of GA-BP PredictionModel for Sound Quality

31 Establishment of Steady GA-BP Model In this paper BP(backpropagation) network was used to establish a com-plex nonlinear mapping relationship between psychoacous-tic parameters and subjective satisfaction degree and GA(genetic algorithms) was applied to optimize the weights andthresholds of neural networks This not only can solve theproblem that the nonlinear model of BP algorithm is easy tofall into local minimum but also can improve the efficiencyof the calculation and the accuracy of the model The modelestablished is shown in Figure 2The number of hidden layernodes was calculated according to the formula radic1198991 + 1198992 + 119886and the number of nodes was selected 7 according to thetraining results wherein 1198991 and 1198992 are the number of inputand output layer nodes respectively In order to improvethe accuracy of acoustic quality prediction model this paperused steady-state noises as the modelrsquos training samples 46steady-state samples were chosen as training samples andthe 4 remaining samples were used to validate the modelrsquosaccuracy

Tansig was chosen as the transfer function of the hiddenlayer and purelin was chosen as the transfer function ofthe output layer for the model Gradient descent algorithmtraingd was chosen as network learning algorithm the learn-ing efficiency 119894119903was set as 01 and the momentum coefficient119898119888 was set as 09 the common mean square error (MSE)was used as the network training object function the trainingtarget was set as 0001 the maximum number of generationswas 200 and the population size was 40 the generation gap(GGAP) was set as 085 the crossover rate was set as 07and the mutation rate was set as 001 The input and output

wloudness

sharpness

roughness

fluctuation

A pressure

kurtosis

Hidden 1

hidden 2

hidden 3

hidden 4

hidden 5

hidden 6

hidden 7

satisfaction

v

Figure 2 Structure of GA-BP prediction model

samples were all normalized before training The normalizedformula is as follows

119866 = 08 times (119909119894 minus 119909min)(119909max minus 119909min) + 01 (2)

The training results of the model are shown in Figure 3 Itcan be seen from the training results that with the increaseof the iterative times of the genetic algorithm the target valueof the population is decreasing that is the adaptability isincreasing and it tends to be stable in the 50th iterationAfter the optimization of the genetic algorithm the objectfunction value of the network training becomes smaller withthe increase of training times At the 100th iteration the targetvalue of the model tends to stabilize and the error reaches theset target The value of fitting check of training result(R2) is0994 the sample expectation and the training value almost


Table 3 Prediction results of accelerated signal satisfaction

sample sample sample sample sample sample sample sample sample samplecar1 car2 car3 car4 car5 car6 car7 car8 car9 car10

satisfaction 0362 0246 059 0467 0558 0621 049 0652 0686 0291Prediction value 0336 0234 0551 0442 0511 0552 0509 0610 0621 0313error () 72 51 67 54 85 111 -39 64 95 -75

0 50 100 150 200Number of iterations

0

05

1

15

2

Obj

ectiv

e fun

ctio

n va

lue

Objective value corresponding to the mean of the population


0

005

01

015

02

Obj

ectiv

e fun

ctio

n va

lue

The objective function value of the optimal solution

10

08

06

04

02

00

Soun

d qu

ality

satis

fact

ion

Expected outputNeural network output

0 10 20 30 40 50

Sample number

Comparison of GA-BP prediction value and subjective evaluation value

Figure 3 Training results of GA-BP model based on psychoacoustic parameters

perfectly coincide The psychoacoustic objective parametervalues of the remaining four steady noises were used as theinput of the training GA-BPmodel and the validation errorsrsquopercentages are 23 18 16 and 35 respectively andthe average verification error is only 23 which proves thatthe GA-BP network model has higher precision and cansatisfy the requirements of the sound quality research andprediction

The GA-BP model established was used to predict thesound quality of the acceleration noise of the 10 vehiclesamples and the predicted results are shown in Table 3 It can

be found that the prediction errors of the acceleration noisesignals of the 10 vehicles are basically greater than 5 and theerror RMS value is 713

32 Establishment of Unsteady GA-BP Model The soundquality prediction model based on steady-state sample train-ing is not ideal when it comes to predicting the sound qualityof the acceleration exhaust noise and in order to studywhether the training samples result in the difference in themodel established and lead to insufficient accuracy 8 groupsof the acceleration unsteady noise samples were used as the


08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

06860621

model 1sample9 error95sample error75

03130291

sample 9 sample 10

satisfaction value of subjective evaluationmodel prediction

0686064

model 2sample 9 error 67

sample 10 error 69

0291 0271

sample 9 sample 10

satisfactionvalue of subjective evaluationmodel predictive value

Figure 4 Prediction results of the two models

training samples of GA-BP model and the remaining twogroups were used in the prediction of the new model

The network structure of the model is still 6-7-1 thetraining parameters transfer functions network trainingmethods and genetic algorithm parameters are all consistentwith model 1 After the training of the model the objectiveparameter values of the predicting samples were introducedinto the predicting model and the comparison results of thetwo predictions are shown in Figure 4

From the comparison results it can be perceived thatthe application of GA-BP sound quality model trained byacceleration noise samples improved the precision comparedwith the previous model but the prediction accuracy was stillnot satisfying

4 Based on WVT-RNR-WVDSound Quality Model

41 Based onWVT-RNR-WVDSignal Analysis Wavelet anal-ysis as a nearly mature analysis method for signal time-frequency can effectively process acceleration signals butthe classical wavelet analysis is rooted in the superpositionof specific basis functions and it is difficult to approximatethe local signal characteristics of the small wave functionsderived by a single basis function on different levels Thismay result in the loss of nonstationary signal characteristics[10] In this regard we can introduce WVD (Wigner-Ville)which is a bilinear time frequency distribution with a highertime frequency resolution and a certain noise suppressioncapability to improve the accuracy of signal analysis How-ever the WVD spectral decomposition has the disadvantageof cross noise so the regularization unsteady-state regression(RNR) [11 12] was proposed in this paper to compute WVDspectral decomposition Based on the above methods a new

acoustic quality evaluation parameter SQP-WRW (soundquality parameter based on wavelet and then proceed) wasproposed to evaluate the sound quality of the accelerationexhaust noise the process chart is shown in Figure 5

411 Wavelet Transform Wavelet is a function with oscil-latory attenuation Given a small wave function 120595(t) thewavelet transform sequence function is a function family[13] transferred from a single primary image wavelet throughexpansion and translation as shown in the following form

120595119886119887 (119905) = |119886|minus12 120595(119905 minus 119887119886 ) (3)

wherein 119886 is an expansion factor reflecting the scale orwidth of the function and 119887 is a translation factor reflectingthe translation position of the function along the time axisΨab(t) is the function family obtained by the expansion andtranslation of wavelet function 120595(t) under the continuouschange of 119886 and b Given a square-integrable signal x(t) thenthe wavelet transform is as follows

119882119909 (119886 119887) = int 119909 (119905) |119886|minus12 120595(119905 minus 119887119886 )119889119905 = ⟨119909 120595 (119886 119887)⟩ (4)

Wx(ab) contains the information of x(t) and Ψab(t) sothe selection of the wavelet function is very important

Based on the experience the Daubechies (dbN) waveletswith orthogonality compactness and approximate symmetrywas selected to analyze the acceleration signals Firstly thefrequency below 20hz of signals was filtered by Pasteurizedhigh-pass filter so as to eliminate the influence of infrasoundand then high-frequency denoising process was carried outto the filtered noise signals based on Shannon CriterionFigure 6 shows the contrast spectrum before and after pro-cessing


Accelerated exhaust signal

Wavelet decomposition

Signal preprocessing

analytic wavelet 1

analytic wavelet 2

analytic wavelet 3

RNR-WVD calculating and A-weighting

Model training with the calculating values

Sound quality prediction model of accelerated noise built

middot middot middot

Figure 5 The calculation flow process chart of the parameter

frequency (Hz)

20HZ high pass filter

Sound pressure (Pa)

Figure 6 Filter processing spectrum diagram


0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10

Figure 7 Wavelet decomposition results of sample car 2 acceleration signal

From the frequency spectrum of the acceleration signalsit can be observed that its energy is basically concentratedin low-frequency range below 500Hz but the sharpness wascalculated based on Zwicker which focuses on the proportionof medium-high-frequency components in the entire signalsRoughness and fluctuation reflect the feelings of the humanear on themodulation frequency and amplitude of the soundKurtosis reflects the signal abrupt or flat degree accordingto Table 2 the roughness fluctuation and kurtosis are lessrelated to subjective satisfaction However the unsteady-stateacceleration signal is very volatile and unordered so theseparameters calculated based onZwicker could not express thefluctuation and steepness of the unstable signal accurately

Carrying out the wavelet transform to the processednoise signals based on the Daubechies in MATLAB is thenfollowed by reconstructing the obtained wavelet transformcoefficients by wrcoef function Thereby the result of waveletdecomposition can be obtained as shown in Figure 7We cansee that the original signal is decomposed into 8-layer detailwavelet di (i=18) and approximate wavelet a8 by wavelettransform Through the wavelet transform the original sig-nal was processed with multiscale decomposition and therelationship between the original signal and decompositionwavelets can be expressed in the following formula119878 = 1198891 + 1198892 + 1198893 + 1198894 + 1198895 + 1198896 + 1198897 + 1198898 + 1198868 (5)

412 WVD Distribution and Regularization Theories WVDis proposed byWigner in the study of quantum mechanics in1932 which was later applied by Ville in signal analysis WVDis a quadratic distribution which can meet many mathemat-ical properties expected by time frequency analysis and its

transformation form is relatively simple which belongs to thetime frequency analysis of strict sense [14] Given a signal x(t)its Wigner-Ville distribution is defined as

119882119881119863119909 (119905 119891) = int+infinminusinfin

119911 (119905 + 1205912) 119911lowast (119905 minus 1205912) 119890minus1198952120587119891120591119889120591 (6)

wherein z(t) is the analytic signal in the time domain theanalytic signal z(t) is defined as119911 (119905) = 119909 (119905) + 119895119867 [119909 (119905)] (7)

wherein x(t) is the real signal 119905 is the time 120591 is thedelayed time 119891 is the frequency 119911lowast is the transpose of z andH[x(t)] is the Hilbert transformation [15] of the real signalx(t) From the above formula it can be found that productterm appears in the WVD distribution which leads to crossinterference in the analysis ofmultifrequency signals and thiscross interference will affect the readability of the signals

In order to eliminate the cross interference caused bythe WVD distribution regularization regression techniquewas introduced to compute WVD the core of which is theshaping regularization theory firstly the theory of shapingregularization is briefly expounded

Regularization technique is a practical mathematicalmethod which aims to strengthen the limit of estimatedmodel so as to solve the problem of ill-posed inverseproblem The most commonly used regularization methodis Tikhonov regularization [16] Fomel [17] proposes shapingregularization theory by considering the function of shapingoperatorThemethod can be used to select the regularizationoperator in a simple way such as Gaussian smooth operatorand band-pass filter operator Subsequently Fomel extends


the theory of shaping regularization to nonlinear inverseproblem thereby establishing the theoretical basis of shapingregularization in inverse problem One assumes that thevector 119889 represents data119898 represents model parameters andthe relationship between the data and the model is defined byforward-modelling operator 119871 which can be expressed as119889 = 119871119898 (8)

With the least square method the optimization problemcan be solved as follows

min 119889 minus 1198711198982 (9)

wherein -2 indicates the norm of 1198972 The aim of leastsquares optimization method is to estimate the optimalsolution 119898 under the condition of known data 119889 Whenthe condition number of the operator 119871 is large the directsolution of the inverse problem to calculate 119898 is unstableconsidering Tikhonov regularization method to be used tostrengthen the constraint of the model119898 there are

min 119889 minus 1198711198982min 1205761198631198982 (10)

In the formula 119863 is the regularization term of Tikhonovand then the optimization problem of the above formula hasthe following theoretical solution

= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)

Smooth operator was taken into account in the shapingregularization in general smooth operator can be regardedas themapping of the constraintmodel in an acceptable spacewhich is called shaping by Fomel [18] The shaping operatorcan be written as

119904 = (119868 + 1205762119863119879119863)minus1 (12)

wherein 119904 is shaping operator from which we can derivethat

1205762119863119879119863 = 119904minus1 minus 119868 (13)

Introducing the above formula into formula (11) we canobtain the theoretical solution under shaping regularization

= (119871119879119871 + 119904minus1 minus 119868)minus1 119871119879119889= [119868 + 119904 (119871119879119871 minus 119868)]minus1 119904119871119879119889 (14)

Set the discrete WVD distribution as

119882119881119863119889 (119899 119896) = 119873minus1sum119898=0

2119911 (119899 + 119898) 119911lowast (119899 minus 119898) 119890minus119895(4120587119899119896119873) (15)

Its cross-correlation function 119877(119899119898) is defined as

119877 (119899119898) = 2119911 (119899 + 119898) 119911lowast (119899 minus 119898) |119898| le 1205790 |119898| ge 120579 (16)

wherein 120579 = min119899119873 minus 119899 and the inverse transforma-tion of WVD can be deduced as follows

119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)

The least squares optimal solution of the formula above is

min1003817100381710038171003817100381710038171003817100381710038171003817119877 (119899119898) minus 119873minus1sum

119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)

The correlation functions R(nm) and WVDd(nk) inthe above formula are complex and real respectively theabove optimization problem is an ill-posed problem inmathematics because the unknown quantity ismore than theconstraint equation and therefore the shaping regularizationalgorithm is introduced to solve this problem

In this paper the Gaussian smooth operator withadjustable size was used as the shaping operator What needsto be emphasized is that although WVD expressions aremathematical real functions the WVDd(nk) are complexafter using RNR iterations Therefore the absolute valuesof WVDd(nk) were taken as time frequency distributioncharacteristic quantity of WVD Figure 8 shows the analyticwavelet d8 analysis results of sample car 2 byWVD and RNR-WVDThe results show that there are a lot of ldquoburrrdquo in WVDanalysis which is mainly due to the cross noise caused byWVD decomposition algorithm Through contrasting con-tour graphs it can be clearly observed that the interferenceof cross noises can be effectively overcome by RNR-WVDmethod which is introduced with smooth operator And thiscan bring the signal a better smoothness and clearer timefrequency resolution Some false characteristic interferencein the signal analysis was also eliminated and this can makethe signal characteristic extraction more accurate

42 Establishment of Sound Quality Model Based on SQP-WRW Based on the above analysis a new sound qualityparameter SQP-WRW was established by using waveletanalysis and RNR-WVD method and it was taken as inputparameter to establish sound quality prediction model Anda comparison study was carried out with the GA-BP modelbased on psychoacoustic parameter of the acceleration sig-nals The main establishment steps of SQP-WRW model areas follows

Step 1 Wavelet Decomposition After filtering and denoisingthe collected acceleration exhaust signals the wavelet trans-form was used to decompose the processed signals and 9analytic wavelets were obtained which are an approximatesignal and 8 detail signals

Step 2 RNR-WVD Transform Processing the analyticwavelets obtained by wavelet decomposition based onRNR-WVD and then k matrices RWkmn (k=9) with m rowsand n columns were obtained in which K is the number ofthe decomposition wavelets

Step 3 (weighting) In order to simulate the acoustic filteringcharacteristic of human ear the matrices RWkmn were


Table 4 SQP-WRW values of accelerated samples

a8 d8 d7 d6 d5 d4 d3 d2 d1Sample car 1 10955 1401 1597 2229 7708 7941 54154 375346 118379Sample car 2 9321 1323 1341 4501 8224 9911 43891 410778 222820Sample car 3 5832 1034 1122 1239 4003 4177 31222 273798 118682Sample car 4 7767 673 1621 3422 5681 10118 33753 426380 271852Sample car 5 1170 1069 1323 2579 3929 9249 50988 259973 123762Sample car 6 12172 1557 1774 2477 8564 8823 60171 417051 131598Sample car 7 9697 1322 1534 3023 4105 11702 82416 452357 292415Sample car 8 8385 1176 1392 4001 7311 8879 39014 365137 198062Sample car 9 6053 962 1191 2321 3536 8324 45889 243972 111383Sample car 10 7934 1082 1255 2473 3359 9574 67423 369291 239250

Figure 8 WVD and RNR-WVD analysis results of signal d8 of sample car 2

treated with A weighting and the weighting coefficientmatrices 119877119882119896119898119899 can be obtained

Step 4 (SQP-WRWcalculation) Calculating the accelerationnoise quality parameters SQP-WRW based on WVT andRNR-WVD the formula is as follows119878119876119875 minus119882119877119882119896

= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)

wherein K is set within 1ndash9 which is the number ofanalytic wavelets RMS[] is used to obtain the valid valueof each coefficient matrix the SQP-WRW values of eachacceleration sample are shown in Table 4

Unsteady-state signal is different from steady-state signalIts distribution parameter and distribution rule will change

dramatically with time The SQP-WRWparameter presentedin this paper can reflect the signal intensity disorder degreeand jitter degree in time and frequency domain A coefficientmatrix will be obtained after the RNR-WVD processionwhich records the characteristics of the signal Taking one-dimensional time and one-dimensional frequency as anexample but the actual coefficient matrix is m rows andn columns the schematic diagram is shown in Figure 9Different curve has different max and min value differentdistribution rule and parameters and different SQP-WRWfollowed The parameter can almost describe the character-istics of nonstationary signals

Step 5 (modelling) Normalizing the SQP-WRWK (k=129) the results of which were taken as the inputs of the GA-BP model and a 9-10-1 sound quality prediction model wasestablishedThe algorithmparameters and the objective func-tion were consistent with the model based on psychoacousticparameters The 1-8 acceleration signals were used as the


Table 5 Comparison of prediction results of three models

Model satisfaction prediction value Actualsatisfaction

|error|Steady

training-model 1Accele

training-model 2SQP-WRW

training-model 3 model1 model2 model3

Accele signal 9 0621 0640 0664 0686 95 67 32Accele signal 10 0313 0271 0301 0291 75 69 34Mean error 85 68 33Predictivecorrelationcoefficient

0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1

Figure 9 SQP-WRW characteristics

training samples of model and the left samples were takenas the test data After training the mean square error of theprediction values and the target values is 00006 as shown inFigure 10 and the value of correlation coefficient (R2 ) reached0996 after the model training

Table 5 shows a comparison of the prediction results ofthe three built models from which it can be found thatthe model trained by the parameter SQP-WRW values ismore accurate in predicting the sound quality of accelerationexhaust noise signals and it can be concluded that theparameter SQP-WRW built in this paper can be used toextract the characteristics of the unsteady noise signal andit is suitable to be used as the training parameter of theprediction model of sound quality

5 Conclusions

(1) Based on Zwicker steady-state and unsteady-state algo-rithm the psychoacoustic objective parameters of steady-state exhaust noise and acceleration exhaust noise werecalculated and the GA-BP sound quality prediction modelswere established by steady-state and unsteady-state samplesrespectively which were applied to predict the unsteadyacceleration exhaust noise

(2) By combining WVT and RNR-WVD methods thecoefficient matrices featuring the information of time fre-quency signal characteristics in different frequency range

07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue

R-square0996EquationPlotWeightInterceptSlopeResidual Sum of Squares

R-Square(COD)Adj R-Square

y = a + blowastxB

No Weightingcell[Book1]FitLinecell[Book1]FitLine

568649E-4099787

099575

099505

Prediction value

Pearsons r

Figure 10 Correlation between predicted and target values of themodel

can be obtained and the obtained coefficient matrices wereprocessed with A weighting thereby obtaining a new soundquality parameter SQP-WRW which was used as GA-BPinput to train the sound quality model And a comparisonstudy was conducted with the prediction model based onthe psychoacoustic objective parameters The results suggestthat the model trained by SQP-WRW has higher precisionin terms of the sound quality prediction of the unsteadysignal and the parameter SQP-WRW built in this paper canbe used to extract the characteristics of the unsteady noisesignal and it is suitable to be used as the training parameterof the prediction model of sound quality which can providecertain reference for the future research on the sound qualityof unsteady noise signal

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper


References

[1] H Liu J Zhang P Guo F Bi H Yu and G Ni ldquoSound qualityprediction for engine-radiated noiserdquo Mechanical Systems andSignal Processing vol 56 pp 277ndash287 2015

[2] X Shen M S Zuo G and L Lin I ldquoInteriror sound qualityforecast for veheicles based on support vectormachinerdquo Journalof Vibration amp Shock 2010

[3] F Bi L Li J Zhang and T Ma ldquoSound quality predictionfor diesel engine radiated noise based on EEMD-HT andLSSVMrdquo Tianjin Daxue Xuebao (Ziran Kexue yu GongchengJishu Ban)Journal of Tianjin University Science and Technologyvol 50 no 1 pp 28ndash34 2017

[4] S-K Lee H-W Kim and E-W Na ldquoImprovement of impactnoise in a passenger car utilizing soundmetric based on wavelettransformrdquo Journal of Sound and Vibration vol 329 no 17 pp3606ndash3619 2010

[5] U K Chandrika and J H Kim ldquoDevelopment of an algorithmfor automatic detection and rating of squeak and rattle eventsrdquoJournal of Sound and Vibration vol 329 no 21 pp 4567ndash45772010

[6] C Liu Y He and H Yu ldquoLoudness characteristics for vehicleinterior time-varying noise under braking conditionrdquo ChineseJournal of Automotive Engineering [CJAE] 2013

[7] S-K Lee ldquoObjective evaluation of interior sound quality inpassenger cars during accelerationrdquo Journal of Sound andVibration vol 310 no 1-2 pp 149ndash168 2008

[8] S Amman N Otto and C Jones ldquoSound quality analysis ofvehicle windshield wiper systemsrdquo in Proceedings of the Noise ampVibration Conference amp Exposition 1993

[9] M Hussain J Golles A Ronacher and H SchiffbankerldquoStatistical evaluation of an annoyance index for engine noiserecordingsrdquo in Proceedings of the Noise amp Vibration Conferenceamp Exposition vol 100 pp 527ndash532 1991

[10] P Jiang Q Shi W Chen et al ldquoA research on the constructionof city road driving cycle based onwavelet analysisrdquoAutomotiveEngineering vol 33 no 1 pp 69-70 2011

[11] X Wu and T Liu ldquoSpectral decomposition of seismic datawith reassigned smoothed pseudo Wigner-Ville distributionrdquoJournal of Applied Geophysics vol 68 no 3 pp 386ndash393 2009

[12] H Bai F Yingxiong U and I Weifu L ldquoOptimal rate for leastsquaress regularized regression with Markov chain samplesrdquoJournal of Hubei University 2016

[13] Y He C Liu Z Xu and Z Zhang ldquoCombined waveletdenoising for vehicle braking noise signal based on both softthreshold and genetic algorithm-based adaptive thresholdrdquoQiche GongchengAutomotive Engineering vol 36 no 6 pp703ndash708 2014

[14] H Wang T Qiu and Z Chen Non Stationary Random SignalAnalysis and Processing vol 2 NationalDefense Industry PressBeijing China 2008

[15] X Wang and Q Cao W ldquoThe Hilbert transform and itscharactersrdquo Journal of Hubei University 2008

[16] Z Zhang S Chen and Z Xu ldquoIterative regularization methodin generalized inverse beamformingrdquo Journal of Sound Vibra-tion p 396 2017

[17] S Fomel ldquoAdaptive multiple subtraction using regularizednonstationary regressionrdquo Geophysics vol 74 no 1 pp V25ndashV33 2009

[18] S Fomel ldquoShaping regularization in geophysical-estimationproblemsrdquo Geophysics vol 72 no 2 pp R29ndashR36 2007

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Submit your manuscripts atwwwhindawicom


035

030

025

020

soun

d pr

essu

re (P

a)

015

010

005

0000 1000 2000 3000 4000 5000

frequency (Hz)

1000rmin2000rmin3000rmin

4000rmin5000rmin

Figure 1 Exhaust signal collection under steady-state condition ofsample car 1

(such as wavelets EMD and WVD) has not yet been widelyused [5]

The exhaust noise of vehicles is one of the most importantnoise sources the research on noise quality of which is ofcertain significance to noise pollution control Firstly thispaper obtained relative psychoacoustic objective parametersof steady-state and acceleration signals in Artermis based onZwicker steady-state and time-varying algorithm [6] and thenoise quality GA-BP prediction model based on psychoa-coustic parameters was established Later on the methodsof wavelet analysis and regularization unsteady regressionwere introduced to calculate the WVD distribution andthe characteristic parameters SQP-WRW of the accelerationexhaust signal were set up as the input of GA-BP model Theresult suggests that the latter can predict the sound qualityof nonstationary signal more accurately which can providea reference for the research of unsteady exhaust soundquality

2 Subjective Evaluation Modelof Exhaust Noise

Based on GB1496-79 Measuring Method for Noise of Power-Driven Vehicles this paper adopted LMS to test and collectthe steady-state exhaust noise signals as well as the acceler-ation noise signals of 10 domestic vehicles The signals withengine speed of 1000rpm 2000rpm 3000rpm 4000rpm and5000rpm were collected and signals in the entire process inwhich engine speed changes from 1000rpm to 5000rpm werecollected According to the research experience [7] loudnesssharpness roughness volatility kurtosis and A sound levelwere used to be the input parameters of the model Thesteady-state noise test results of sample car 1 is shown inFigure 1 it can be concluded that the sound pressure level

of noise generally increased with the increase of rotationalspeed

21 Subjective Evaluation Test Pair comparison method wasutilized in this subjective test 5s of steady-state signals wasintercepted and 15s of characteristic signals in accelerationwas extracted In order to eliminate the effect of time durationon the subjective evaluation the steady-state signal sampleswere treated with delayed time processing Samples werecompared in pair in which the sample with decent evaluationwill obtain 1 point and the ones with unsatisfying evaluationwill gain nothing so that each sample will get a definite valuerepresenting its sound quality which is more intuitive andconducive for the modelling later on

A total of 42 people participated in the subjective evalua-tion they are postgraduates majoring in vehicle-related fieldfrom a university and related workers in research institutesThere are 24males and 18 females aged roughly within 24ndash40According to sample coincidence degree and consistencycoefficient [8] the data of 4 reviewers were eliminated theaverage coincidence degree of the samples was 0783 andthe average consistency coefficient was 0928 Thereof theconsistency coefficients were computed by Kendall method[9] and the psychoacoustic objective parameters of thesamples and the results of the subjective tests are shown inTable 1 The normalization formula of satisfaction is showedas formula (2)

22 Correlation Analysis In order to study the relationshipbetween the subjective satisfaction degree of exhaust noiseand the psychoacoustic objective parameters a comparisonstudy was carried out between the subjective satisfactionscore and psychoacoustic objective parameters SPSS19 soft-ware was used to do the correlation analysis The resultsare shown in Table 2 Because the sample contains unsteadynoise it will produce extreme values with the change of timeTherefore we applied two-tailed Spearman rank correlationto carry on the correlation analysis wherein the spearmanrank correlation formula is as follows

119903 = 1 minus 6sum119899119894=1 (119880119894 minus 119881119894)2119899 (1198992 minus 1) (1)

In the formula119880119894 and119881119894 are the ranks of the two variablesthe role of which is to change the fixed-distance variableto nonfixed-distance thereby reducing the effect of extremevalues on the results 119899 is the sample number and 119903 is thespearman rank correlation coefficient

According to the results of correlation analysis it can beconcluded that the correlations between loudness sharpnessand satisfaction degree are relatively great The coefficientshave reached 0875 and 0682 respectively the influenceof these two parameters has a great weight on the noisesatisfaction and except for the positive correlations betweenroughness kurtosis and subjective satisfaction degreeother parameters have inverse correlations with satisfactiondegree










wloudness

sharpness

roughness

fluctuation

A pressure

kurtosis

Hidden 1

hidden 2

hidden 3

hidden 4

hidden 5

hidden 6

hidden 7

satisfaction

v










0

05

1

15

2

Obj

ectiv

e fun

ctio

n va

lue



0

005

01

015

02

Obj

ectiv

e fun

ctio

n va

lue


10

08

06

04

02

00

Soun

d qu

ality

satis

fact

ion


0 10 20 30 40 50

Sample number








08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

06860621


03130291

sample 9 sample 10


0686064


sample 10 error 69

0291 0271

sample 9 sample 10










120595119886119887 (119905) = |119886|minus12 120595(119905 minus 119887119886 ) (3)


119882119909 (119886 119887) = int 119909 (119905) |119886|minus12 120595(119905 minus 119887119886 )119889119905 = ⟨119909 120595 (119886 119887)⟩ (4)







analytic wavelet 1

analytic wavelet 2

analytic wavelet 3






frequency (Hz)


Sound pressure (Pa)



0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018

















wloudness

sharpness

roughness

fluctuation

A pressure

kurtosis

Hidden 1

hidden 2

hidden 3

hidden 4

hidden 5

hidden 6

hidden 7

satisfaction

v










0

05

1

15

2

Obj

ectiv

e fun

ctio

n va

lue



0

005

01

015

02

Obj

ectiv

e fun

ctio

n va

lue


10

08

06

04

02

00

Soun

d qu

ality

satis

fact

ion


0 10 20 30 40 50

Sample number








08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

06860621


03130291

sample 9 sample 10


0686064


sample 10 error 69

0291 0271

sample 9 sample 10










120595119886119887 (119905) = |119886|minus12 120595(119905 minus 119887119886 ) (3)


119882119909 (119886 119887) = int 119909 (119905) |119886|minus12 120595(119905 minus 119887119886 )119889119905 = ⟨119909 120595 (119886 119887)⟩ (4)







analytic wavelet 1

analytic wavelet 2

analytic wavelet 3






frequency (Hz)


Sound pressure (Pa)



0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018













0

05

1

15

2

Obj

ectiv

e fun

ctio

n va

lue



0

005

01

015

02

Obj

ectiv

e fun

ctio

n va

lue


10

08

06

04

02

00

Soun

d qu

ality

satis

fact

ion


0 10 20 30 40 50

Sample number








08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

06860621


03130291

sample 9 sample 10


0686064


sample 10 error 69

0291 0271

sample 9 sample 10










120595119886119887 (119905) = |119886|minus12 120595(119905 minus 119887119886 ) (3)


119882119909 (119886 119887) = int 119909 (119905) |119886|minus12 120595(119905 minus 119887119886 )119889119905 = ⟨119909 120595 (119886 119887)⟩ (4)







analytic wavelet 1

analytic wavelet 2

analytic wavelet 3






frequency (Hz)


Sound pressure (Pa)



0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018









08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

08

07

06

05

Satis

fact

ion

valu

e

04

03

02

01

00

06860621


03130291

sample 9 sample 10


0686064


sample 10 error 69

0291 0271

sample 9 sample 10










120595119886119887 (119905) = |119886|minus12 120595(119905 minus 119887119886 ) (3)


119882119909 (119886 119887) = int 119909 (119905) |119886|minus12 120595(119905 minus 119887119886 )119889119905 = ⟨119909 120595 (119886 119887)⟩ (4)







analytic wavelet 1

analytic wavelet 2

analytic wavelet 3






frequency (Hz)


Sound pressure (Pa)



0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018












analytic wavelet 1

analytic wavelet 2

analytic wavelet 3






frequency (Hz)


Sound pressure (Pa)



0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018









0 5000 10000 15000minus20

0

20

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus05

0

05

0 5000 10000 15000minus1

0

1

0 5000 10000 15000minus2

0

2

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus5

0

5

0 5000 10000 15000minus10

0

10

0 5000 10000 15000minus10

0

10















min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018











min 119889 minus 1198711198982 (9)


min 119889 minus 1198711198982min 1205761198631198982 (10)


= (119871119879119871 + 1205762119863119879119863)minus1 119871119879119889 (11)


119904 = (119868 + 1205762119863119879119863)minus1 (12)


1205762119863119879119863 = 119904minus1 minus 119868 (13)




119882119881119863119889 (119899 119896) = 119873minus1sum119898=0





119877 (119899119898) = 119873minus1sum119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873) (17)



119896=0

119882119881119863119889 (119899 119896) 119890minus119895(4120587119898119896119873)10038171003817100381710038171003817100381710038171003817100381710038172 (18)













= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018














= radic 119898sum119894=1

119899sum119895=1

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816119877119882119898119899 (119894 119895)1003816100381610038161003816 minus 119877119872119878 [119877119882119898119899]119877119872119878 [119877119882119898119899]

10038161003816100381610038161003816100381610038161003816100381610038161003816(19)








|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018











|error|Steady





0988 0991 0996

t

sumi=0

|s1|

RMS[s1]minus 1

t

sumi=0

|s2|

RMS[s2]minus 1




5 Conclusions



07

07

06

06

05

05

04

04

03

0302

02

Eval

uatio

n va

lue



y = a + blowastxB


568649E-4099787

099575

099505

Prediction value

Pearsons r



Data Availability





References


























Journal of












Journal of







Volume 2018






Volume 2018









References


























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








study on the sound quality of steady and unsteady exhaust...

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