Research ArticleA Novel Deep Sparse Filtering Method for Intelligent FaultDiagnosis by Acoustic Signal Processing

Guowei Zhang Jinrui Wang Baokun Han Sixiang Jia Xiaoyu Wang and Jingtao He

College of Mechanical and Electronic Engineering Shandong University of Science and Technology Qingdao China

Correspondence should be addressed to Baokun Han bk_han163com

Received 2 April 2020 Revised 18 June 2020 Accepted 11 July 2020 Published 26 July 2020

Academic Editor Changqing Shen

Copyright copy 2020Guowei Zhang et al-is 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

Increased attention has been paid to research on intelligent fault diagnosis under acoustic signals However the signal-to-noiseratio of acoustic signals is much lower than vibration signals which increases the difficulty of signal denoising and featureextraction To solve the above defect a novel batch-normalized deep sparse filtering (DSF) method is proposed to diagnose thefault through the acoustic signals of rotating machinery In the first stage the collected acoustic signals are prenormalized toeliminate the adverse effects of singular samples and then the normalized signal is transformed into frequency-domain signalthrough fast Fourier transform (FFT) In the second stage the learned features are obtained by training batch-normalized DSFwith frequency-domain signals and then the features are fine-tuned by backpropagation (BP) algorithm In the third stagesoftmax regression is used as a classifier for heath condition recognition based on the fine-tuned features Bearing and planetarygear datasets are used to validate the diagnostic performance of the proposed method -e results show that the proposed DSFmodel can extract more powerful features and less computing time than other traditional methods

1 Introduction

Rotating machinery is widely used in automobile enginewind power equipment and water turbine generatorequipment A slight mechanical fault may directly affect theoperation of machines and cause severe accident -us it isimportant to ensure the high stability operation of machines[1] Fault diagnosis technology has been proven to be aneffective method to monitor the operating state of equip-ment in recent years [2ndash4] How to extract useful featuresfrom massive mechanical data to precisely diagnose thehealth condition of machines has always been a hot researchtopic [5ndash7]

As an effective fault diagnosis method of rotating ma-chinery increased attention has been paid to research onacoustic signal processing Given that the acoustic signals areeasier to obtain and less costly than vibration signals [8]therefore it has become a trend to apply acoustic signal tofault diagnosis [9] However the signal-to-noise ratio ofacoustic signals is low which increases the difficulty of signaldenoising and feature extraction Traditional fault diagnosis

is usually based on the signal processing methods such asshort time Fourier transform (STFT) [10] wavelet transform(WT) [11] and empirical mode decomposition (EMD) [12]which overcomes the difficulty of processing acoustic signalsand achieves certain results However all of the methodsmentioned above require empirical knowledge and are time-consuming

Unsupervised learning may hold potential to overcomethe aforementioned weakness in traditional intelligent faultdiagnosis method -e basic idea behind unsupervisedfeature learning is that training artificial intelligence tech-niques can be viewed as learning a nonlinear function whichtransforms the raw data from the original space into afeature space Hence unsupervised feature learning is rec-ommended -e purpose of unsupervised feature learning isto adaptively learn effective features from unlabeled datarather than from artificial engineering feature representation[13] Meanwhile unsupervised feature learning has beenwidely applied in the speech recognition [14] face recog-nition [15] image classification [16] and other fields Sparsefiltering (SF) [17] is an unsupervised two-layer neural

HindawiShock and VibrationVolume 2020 Article ID 8837047 11 pageshttpsdoiorg10115520208837047

network which can use its own population sparsity lifesparsity and high dispersion to learn deep discriminativefeatures automatically So far SF has been successfully ap-plied to many scenarios and its usefulness repeatedlyconfirmed Meanwhile how the implicit hypothesis andconstraints of sparse filtering make it suitable for somescenes is confirmed by [18] Lei et al [19] first constructivelyemployed SF to bearing fault diagnosis by adopting a two-stage learning method which greatly reduced human laborand made intelligent fault diagnosis much easier to handlebig data Yang et al [20] introduced L2-norm regularizationto enhance the generalization ability of SF and achievedbetter classification performance Qian et al [21] introducedL1-norm regularization into the cost function of SF andreplaced the soft-absolute activation function with logarithmfunction to prevent overfitting more efficiently Wang et al[22] proposed a framework based on sparse filtering whichcan adaptively extract features from frequency-domainsignals

Although SF can automatically extract useful featuresfrom vibration signals its feature extraction ability remainspoor in processing acoustic signals So we set up the batch-normalized deep sparse filtering (DSF) model to filter theacoustic signal twice to remove the redundant informationbetter and then the weights are fine-tuned by back prop-agation (BP) algorithm -erefore a novel DSF model isproposed to deal with the acoustic signal in this paper -emain contributions of this paper are summarized as follows

(1) Batch normalization is introduced into DSF modelwhich can reparametrize the hidden layer of DSFimprove the training speed and accelerate theconvergence speed

(2) A two-layer batch-normalized DSF is established tofilter the acoustic signal twice and then the weightsare adjusted by BP algorithm to get more robustfeatures -e experimental results of gearbox andbearing datasets show that DSF has higher accuracyand faster computing time than other SF models

-e rest of this paper is organized as follows In Section2 DSF in deep learning is introduced In Sections 3 and 4 adeep sparse filtering framework is established and planetarygear and bearing datasets are investigated using the differentSF models respectively -e conclusion is presented inSection 5

2 Theoretical Background

21 Sparse Filtering Traditional unsupervised featurelearning methods [23] need to adjust multiple parameters toachieve better performance which is an arduous task-erefore Ngiam et al [17] proposed a method with onlyone parameter called SF to solve this weakness As a simpleand efficient unsupervised learning method SF only focuseson the sparse distribution of data features -e structure ofSF is shown in Figure 1 Its input and output are collecteddataset and the learned features respectively

First acoustic signals are collected from each healthcondition and combined into training set xi1113864 1113865

K

i1 where xi

RLtimes1 is a sample containing L data points and K is thesample number Second weight matrix W isin RLtimesPis obtainedby xi1113864 1113865

K

i1 training with SF model Finally the SF modelcan learn the corresponding feature set f i

1113966 1113967K

i1 by weightmatrixW wherefi isin RPtimes1 denotes the feature vector withP

learned features -e features of each sample can be cal-culated as

fij W

Tj x

i (1)

where fij corresponds to the jth feature of the ith sample

Features fij make up a feature matrix each row of the feature

matrix is normalized through its L2 norm

1113957f fj

fj

2

(2)

-en each column is normalized by its L2 norm and thefeatures are mapped into the unit L2-ball

1113954fi

1113957f

i

1113957fi

2

(3)

Finally the optimization features can be obtained by L1penalty the cost function of SF is given as

minimizeW

1113944

K

i1

1113954fi

1 1113944

K

i1

1113957fi

1113957fi

2

1

(4)

22 Deep Sparse Filtering -e standard SF model is a simpletwo-layer neural network In this paper DSF model isdesigned by layer-by-layer unsupervised learning Specifi-cally the output features of the first SF are used as the inputof the second SF to extract the feature layer by layer and thenthe weights are reversely fine-tuned using the BP algorithmIn addition we use a rectified linear unit function (ReLU)[24] as activation function -e output features of nthhidden layer can be calculated as

hn ReLU WTn x nminus11113872 1113873 (5)

where Wn represents the weight matrix between nth hiddenlayer and (nminus1)th hidden layer Each SF layer is trained bysolving the minimization problem as

minimizeW

1113944

k

i1

1113954hn

1 1113944

k

i1

1113957hn

1113957hn

2

1

(6)

where k is the number of training samples in nth layerAt the same time the batch normalization is introduced

to optimize the DSF Batch normalization can reparametrizealmost deep networks in an elegant way -e procedure isable to be used in every activation layer without parameteradjustment For a layer with n-dimensional inputx (x1 middot middot middot xk) to improve the training and reduce theinternal covariate shift two necessary simplifications aretaken by batch normalization

Firstly each scalar feature is normalized independentlyby making its own zero mean and unit variance

2 Shock and Vibration

x

i xi minus E[xi]

Var[xi]

radic (7)

where E[xi] is the mean of each unit andVar[xi]

radicdenotes

the standard deviationHowever the simply normalization of each input in a

layer still can change the representation of the layer So twoparameters ci and βi are employed for each activation xiwhich aim to scale and shift the normalized value

fi cix

i + βi (8)

ci and βi are learned along with the raw model pa-rameters and restore the representation power of the net-work Note that the raw activations can be recovered bysetting ci

Var[xi]

radicand βi E[xi] In this case the steady

distribution of activation values can be guaranteed duringeach training

Here we apply the batch normalization immediatelybefore the activation layers of SF So equation (5) is replacedwith

hn f(BNWx) (9)

-erefore BN transform introduces normalized acti-vations into the network and ensures the layers can continuelearning on input distributions that reduce the influence ofinternal covariate shift so that an easy starting condition canbe constructed for training and further accelerating thetraining

-e number of layers can be selected according todifferent task requirements It is generally believed thatincreasing the number of hidden layers can reduce thenetwork error and improve the accuracy but it alsocomplicates the network thus increasing the networktraining time and the tendency of overfitting So it isactually a trade-off choice in application of the proposedmethod In this paper we choose two layers of DSF toextract the feature of acoustic signal which can not onlyensure less computation but also extract deeper featuresFigure 2 shows the schematic of DSF -e acoustic signaldatasets are used to train the first SF layer and subse-quently the second SF layer Firstly the output batch-normalized features of the first SF layer are used as theinput features of the second SF layer and then thesoftmax regression is connected to the last layer of DSF asthe classification layer Finally BP algorithm is used forthe reverse weight fine-tuning

3 Intelligent Fault Diagnosis FrameworkBased on DSF

-e proposed fault diagnosis method mainly consists ofthree stages as shown in Figure 3 In the first stage thecollected time-domain acoustic signals are pre-normalizedto eliminate the adverse effects of singular samples-en thenormalized time-domain signal is transformed into fre-quency-domain signal through FFT In the second stage theweight matrix W is obtained by training batch-normalizedDSF with frequency-domain signals and then theW is fine-tuned by BP algorithm Finally the optimized W is used tolearn the deep discriminative features from the originalfrequency-domain signals In the third stage softmax re-gression is used as a classifier for heath condition recog-nition through the learned features

(1) Training data collection the acoustic time-domainsignals collected from rotating machinery underdifferent health conditions are divided into K

samples to form the training dataset xi yi1113864 1113865K

i1 wherexi isin RNtimes1 denotes each sample containing N time-domain points and yi denotes the health conditionlabel of the ith sample

(2) Training data processing training set is rewritten as amatrix form X isin RNtimesK Before training the DSFmodel each column of training set X is first nor-malized by its l2-norm as follows

1113957xj

xj

xj 2 (10)

-en prenormalization training dataset xin1113864 1113865

K

i1 istransformed into training dataset ti1113864 1113865

K

i1 by FFTwhere ti isin RNintimes1 denotes each sample containingNin Fourier coefficients Nin represents the inputdimension of DSF and Nout is the output dimension-e training set ti1113864 1113865

K

i1 can be further written as amatrix S isin RNintimesK for simplicity

(3) DSFmodel training firstly the obtained S is inputtedto the batch-normalized DSF model for the trainingof weight matrix W -en the BP algorithm iscombined with the corresponding sample labels tofine-tune the W of DSF

(4) Model testing remaining samples are used as testingsamples to test the accuracy of the trained DSFmodel

4 Experiments

41 Case Study 1 Rolling Bearing Fault Diagnosis

411 Data Description In this section the acoustic signalsof bearing are collected from the specially designed testbench to validate the diagnosis performance of proposedDSF method As shown in Figure 4(a) the test bench in-cludes a motor three shaft couplings a bearing seat agearbox and a brake As shown in Figure 4(b) the collecteddataset includes 9 health conditions normal condition (NC)

Input layer

Weight matrix

Output layer

Figure 1 SF structure

Shock and Vibration 3

outer race fault 02mm (OF02) outer race fault 04mm(OF04) inner race fault 02mm (IF02) inner race fault04mm (IF04) roller fault 02mm (RF02) roller fault04mm (RF04) roller fault 02mm and outer race fault02mm (ROF02) and roller fault 04mm and outer racefault 04mm (ROF04) -e sampling frequency of theacoustic sensor is 128 kHz and the rotating speed is 1300 rmin 200 samples are collected from each health conditionand a total of 1800 samples are obtained Each sample

contains 2400 time-domain points and 1200 frequency-domain points are obtained by FFT

One sample is randomly selected from each healthcondition to show the acoustic signal details -e time-domain and corresponding frequency-domain waveforms ofthe samples are shown in Figure 5 It can be seen that it isarduous to distinguish different health conditions artificiallyand the huge amount of data also increases the difficulty offeature extraction -erefore the DSF model is proposed to

Acoustic signal

Layer 1Sparse filtering features

Rectified linear unit function as activation function

Layer 1 Sparse filtering

Layer 2Sparse filtering features

Rectified linear unit function as activation function

Sofmax classification

Layer 2 Sparse filtering

Backpropagation

BN

BN

Backpropagation

Figure 2 Schematic of DSF

FFT

Softmax regression

SF1

SF2

Fine-tune

Training samples

Normalization

Batch-normalized

Figure 3 Intelligent fault diagnosis framework based on DSF

4 Shock and Vibration

automatically extract the feature of acoustic signal andconduct precise fault classification

412 Results and Analysis -e frequency-domain signal isused as the input of DSF model and the output dimensionsof the two SF layers are set to 800 and 400 respectively -enumber of outputs of softmax classification is 9 -ereforethe structure of the DSF model is 1200-800-400-9 Subse-quently we investigate the effect of iteration numberRandomly select 5 samples for training and the diagnosticaccuracies using different iteration number are displayed inFigure 6 Since the increasing of the accuracies is not obviousafter number of iterations exceeds 40 we choose 40 as theiteration number of DSF Meanwhile the iteration numberof the BP algorithm is 50 and the batch size is 30 In order toshow the superiority of DSF model standard SF [19] L1regularized sparse filtering (L1-SF) [21] and L2 regularizedsparse filtering (L2-SF) [20] are used as comparisonmethods -e output dimension of the three comparisonmethods is set as 1200 the number of iterations is 100 andthe regularization parameter is 1E-5 20 trails are conductedfor each experiment to reduce the influence of randomness-e computing platform is a PC with an I5-4210M CPU and8GB RAM

-e diagnosis results of different numbers of trainingsamples using the proposed DSF model are shown in Fig-ure 7 It is obvious that the accuracy and computing timeincrease with the rise of the training sample number It canbe seen from the figure that the DSF model with only 5 ofthe training samples can achieve average testing accuracy of9815plusmn 033 indicating that the proposed method candiagnose 9 health conditions in the absence of trainingsamples When the number of samples increases to 10 the

average test accuracy reaches 9992plusmn 0027 and theaverage computing time is 149s -erefore in the followingexperiments 10 of the samples were used for training

-e diagnosis results of the four methods are shown inFigure 8 It is certain that the DSF model has the highestaverage testing accuracy (9993) and the lowest standarddeviation (0027) among all the methods It can be seenfrom the figure that the average accuracy of the standard SFis 8905plusmn 139 which is the worst among the methods-e testing accuracies of L1-SF and L2-SF are9045plusmn 109 and 9163plusmn 077 respectively which areslightly higher than those of SF It is worth mentioning thatthe proposed DSF model computing time is 149s Bycontrast the average computing time of SF L1-SF and L2-SF is about 100s -is finding indicates that the DSF methodcan better overcome the difficulty of extracting the acousticsignal features and achieve the highest accuracy and leastcomputing time among the four methods in terms of di-agnosing bearing fault types

In order to better present the superiority of DSF here wemake a detailed comparison between our method and otherseveral classical methods by using the same bearing datasetas summarized in Table 1 In Method 1 ensemble empiricalmode decomposition (EMMD) [25] was employed to extractfeatures and then the features were classified by an optimizedSVM It achieved 9667 testing accuracy on the bearingdataset In Method 2 Jia et al [26] constructed SAE baseddeep network utilizing frequency spectra as inputs to di-agnosis and 9968 testing accuracy is obtained In Method3 the frequency spectra are also used as inputs of BackPropagation Neural Networks (BPNN) and the diagnosisaccuracy is 7374 In Method 4 Xie et al [27] proposedfeature extraction algorithm based on empirical mode de-composition (EMD) and convolutional neural network

Motor BrakeBearing seatRotorSha

coupling

Acoustic sensorGearbox

(a)

OF IFRF

(b)

Figure 4 (a) Bearing fault test rig and (b) three fault bearings

Shock and Vibration 5

(CNN) techniques and obtained 9975 testing accuracy InMethod 5 the proposed method achieves the best testingaccuracy of 9993 when classifying ten different faultconditions which outperforms all compared approaches

To show the details of the diagnostic results of the fourmethods the confusion matrixes on the bearing dataset arepresented in Figure 9 It can be seen from Figures 9(a) and9(b) that the classification results of SF and L1-SF are un-satisfactory -e concurrent faults such as ROF02 andROF04 are not well distinguished and the single faults suchas RF04 and OF04 are not perfectly distinguished-e faultclassification performance of L2-SF is slightly better thanthat of SF and L1-SF as shown in Figure 9(c) but it cannotdistinguish different health conditions with high accuracywhich means that concurrent faults increase the difficulty offault classification As shown in Figure 9(d) the proposed

DSF model can distinguish not only single faults but alsoconcurrent faults perfectly which shows that the proposedmethod can better extract the deep features of acousticsignal

42 Case Study 2 Planetary Gear Fault Diagnosis

421 Data Description -e gear fault signals are measuredfrom the gearbox of the test bench as shown in Figure 4(a)-e collected dataset contains one normal condition (NC)and four kinds of mechanical faults including sun wheelcrack (WC) sun wheel pit (WP) pinion crack (PC) andpinion pit (PP) as shown in Figure 10 -e gear speed is2600 rmin and the sampling frequency is 1024 kHz 300samples were collected for each health condition and each

005

00

ndash005

005

00

ndash005

005

00

ndash005

005

00

ndash005

02

00

ndash02

02

00

ndash02

01

00

ndash01

01

00

ndash01

01

00

ndash01

10

5

0

1510

50

10

5

0

10

5

0

10

5

0

10

5

0

5

0

10

5

0

1510

50

NC

IF0

2IF

04

ROF0

2O

F02

OF0

4RO

F04

RF0

2RF

04

0 500 1000 1500 2000Time-domain sampling points

0 200 400 600 800 1000 1200Spectrum characteristic dimension

Figure 5 Time- and frequency-domain waveforms of bearing signals under the nine health conditions

6 Shock and Vibration

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

x

i xi minus E[xi]

Var[xi]

radic (7)

where E[xi] is the mean of each unit andVar[xi]

radicdenotes

the standard deviationHowever the simply normalization of each input in a

layer still can change the representation of the layer So twoparameters ci and βi are employed for each activation xiwhich aim to scale and shift the normalized value

fi cix

i + βi (8)

ci and βi are learned along with the raw model pa-rameters and restore the representation power of the net-work Note that the raw activations can be recovered bysetting ci

Var[xi]

radicand βi E[xi] In this case the steady

distribution of activation values can be guaranteed duringeach training

Here we apply the batch normalization immediatelybefore the activation layers of SF So equation (5) is replacedwith

hn f(BNWx) (9)

-erefore BN transform introduces normalized acti-vations into the network and ensures the layers can continuelearning on input distributions that reduce the influence ofinternal covariate shift so that an easy starting condition canbe constructed for training and further accelerating thetraining

-e number of layers can be selected according todifferent task requirements It is generally believed thatincreasing the number of hidden layers can reduce thenetwork error and improve the accuracy but it alsocomplicates the network thus increasing the networktraining time and the tendency of overfitting So it isactually a trade-off choice in application of the proposedmethod In this paper we choose two layers of DSF toextract the feature of acoustic signal which can not onlyensure less computation but also extract deeper featuresFigure 2 shows the schematic of DSF -e acoustic signaldatasets are used to train the first SF layer and subse-quently the second SF layer Firstly the output batch-normalized features of the first SF layer are used as theinput features of the second SF layer and then thesoftmax regression is connected to the last layer of DSF asthe classification layer Finally BP algorithm is used forthe reverse weight fine-tuning

3 Intelligent Fault Diagnosis FrameworkBased on DSF

-e proposed fault diagnosis method mainly consists ofthree stages as shown in Figure 3 In the first stage thecollected time-domain acoustic signals are pre-normalizedto eliminate the adverse effects of singular samples-en thenormalized time-domain signal is transformed into fre-quency-domain signal through FFT In the second stage theweight matrix W is obtained by training batch-normalizedDSF with frequency-domain signals and then theW is fine-tuned by BP algorithm Finally the optimized W is used tolearn the deep discriminative features from the originalfrequency-domain signals In the third stage softmax re-gression is used as a classifier for heath condition recog-nition through the learned features

(1) Training data collection the acoustic time-domainsignals collected from rotating machinery underdifferent health conditions are divided into K

samples to form the training dataset xi yi1113864 1113865K

i1 wherexi isin RNtimes1 denotes each sample containing N time-domain points and yi denotes the health conditionlabel of the ith sample

(2) Training data processing training set is rewritten as amatrix form X isin RNtimesK Before training the DSFmodel each column of training set X is first nor-malized by its l2-norm as follows

1113957xj

xj

xj 2 (10)

-en prenormalization training dataset xin1113864 1113865

K

i1 istransformed into training dataset ti1113864 1113865

K

i1 by FFTwhere ti isin RNintimes1 denotes each sample containingNin Fourier coefficients Nin represents the inputdimension of DSF and Nout is the output dimension-e training set ti1113864 1113865

K

i1 can be further written as amatrix S isin RNintimesK for simplicity

(3) DSFmodel training firstly the obtained S is inputtedto the batch-normalized DSF model for the trainingof weight matrix W -en the BP algorithm iscombined with the corresponding sample labels tofine-tune the W of DSF

(4) Model testing remaining samples are used as testingsamples to test the accuracy of the trained DSFmodel

4 Experiments

41 Case Study 1 Rolling Bearing Fault Diagnosis

411 Data Description In this section the acoustic signalsof bearing are collected from the specially designed testbench to validate the diagnosis performance of proposedDSF method As shown in Figure 4(a) the test bench in-cludes a motor three shaft couplings a bearing seat agearbox and a brake As shown in Figure 4(b) the collecteddataset includes 9 health conditions normal condition (NC)

Input layer

Weight matrix

Output layer

Figure 1 SF structure

Shock and Vibration 3

outer race fault 02mm (OF02) outer race fault 04mm(OF04) inner race fault 02mm (IF02) inner race fault04mm (IF04) roller fault 02mm (RF02) roller fault04mm (RF04) roller fault 02mm and outer race fault02mm (ROF02) and roller fault 04mm and outer racefault 04mm (ROF04) -e sampling frequency of theacoustic sensor is 128 kHz and the rotating speed is 1300 rmin 200 samples are collected from each health conditionand a total of 1800 samples are obtained Each sample

contains 2400 time-domain points and 1200 frequency-domain points are obtained by FFT

One sample is randomly selected from each healthcondition to show the acoustic signal details -e time-domain and corresponding frequency-domain waveforms ofthe samples are shown in Figure 5 It can be seen that it isarduous to distinguish different health conditions artificiallyand the huge amount of data also increases the difficulty offeature extraction -erefore the DSF model is proposed to

Acoustic signal

Layer 1Sparse filtering features

Rectified linear unit function as activation function

Layer 1 Sparse filtering

Layer 2Sparse filtering features

Rectified linear unit function as activation function

Sofmax classification

Layer 2 Sparse filtering

Backpropagation

BN

BN

Backpropagation

Figure 2 Schematic of DSF

FFT

Softmax regression

SF1

SF2

Fine-tune

Training samples

Normalization

Batch-normalized

Figure 3 Intelligent fault diagnosis framework based on DSF

4 Shock and Vibration

automatically extract the feature of acoustic signal andconduct precise fault classification

412 Results and Analysis -e frequency-domain signal isused as the input of DSF model and the output dimensionsof the two SF layers are set to 800 and 400 respectively -enumber of outputs of softmax classification is 9 -ereforethe structure of the DSF model is 1200-800-400-9 Subse-quently we investigate the effect of iteration numberRandomly select 5 samples for training and the diagnosticaccuracies using different iteration number are displayed inFigure 6 Since the increasing of the accuracies is not obviousafter number of iterations exceeds 40 we choose 40 as theiteration number of DSF Meanwhile the iteration numberof the BP algorithm is 50 and the batch size is 30 In order toshow the superiority of DSF model standard SF [19] L1regularized sparse filtering (L1-SF) [21] and L2 regularizedsparse filtering (L2-SF) [20] are used as comparisonmethods -e output dimension of the three comparisonmethods is set as 1200 the number of iterations is 100 andthe regularization parameter is 1E-5 20 trails are conductedfor each experiment to reduce the influence of randomness-e computing platform is a PC with an I5-4210M CPU and8GB RAM

-e diagnosis results of different numbers of trainingsamples using the proposed DSF model are shown in Fig-ure 7 It is obvious that the accuracy and computing timeincrease with the rise of the training sample number It canbe seen from the figure that the DSF model with only 5 ofthe training samples can achieve average testing accuracy of9815plusmn 033 indicating that the proposed method candiagnose 9 health conditions in the absence of trainingsamples When the number of samples increases to 10 the

average test accuracy reaches 9992plusmn 0027 and theaverage computing time is 149s -erefore in the followingexperiments 10 of the samples were used for training

-e diagnosis results of the four methods are shown inFigure 8 It is certain that the DSF model has the highestaverage testing accuracy (9993) and the lowest standarddeviation (0027) among all the methods It can be seenfrom the figure that the average accuracy of the standard SFis 8905plusmn 139 which is the worst among the methods-e testing accuracies of L1-SF and L2-SF are9045plusmn 109 and 9163plusmn 077 respectively which areslightly higher than those of SF It is worth mentioning thatthe proposed DSF model computing time is 149s Bycontrast the average computing time of SF L1-SF and L2-SF is about 100s -is finding indicates that the DSF methodcan better overcome the difficulty of extracting the acousticsignal features and achieve the highest accuracy and leastcomputing time among the four methods in terms of di-agnosing bearing fault types

In order to better present the superiority of DSF here wemake a detailed comparison between our method and otherseveral classical methods by using the same bearing datasetas summarized in Table 1 In Method 1 ensemble empiricalmode decomposition (EMMD) [25] was employed to extractfeatures and then the features were classified by an optimizedSVM It achieved 9667 testing accuracy on the bearingdataset In Method 2 Jia et al [26] constructed SAE baseddeep network utilizing frequency spectra as inputs to di-agnosis and 9968 testing accuracy is obtained In Method3 the frequency spectra are also used as inputs of BackPropagation Neural Networks (BPNN) and the diagnosisaccuracy is 7374 In Method 4 Xie et al [27] proposedfeature extraction algorithm based on empirical mode de-composition (EMD) and convolutional neural network

Motor BrakeBearing seatRotorSha

coupling

Acoustic sensorGearbox

(a)

OF IFRF

(b)

Figure 4 (a) Bearing fault test rig and (b) three fault bearings

Shock and Vibration 5

(CNN) techniques and obtained 9975 testing accuracy InMethod 5 the proposed method achieves the best testingaccuracy of 9993 when classifying ten different faultconditions which outperforms all compared approaches

To show the details of the diagnostic results of the fourmethods the confusion matrixes on the bearing dataset arepresented in Figure 9 It can be seen from Figures 9(a) and9(b) that the classification results of SF and L1-SF are un-satisfactory -e concurrent faults such as ROF02 andROF04 are not well distinguished and the single faults suchas RF04 and OF04 are not perfectly distinguished-e faultclassification performance of L2-SF is slightly better thanthat of SF and L1-SF as shown in Figure 9(c) but it cannotdistinguish different health conditions with high accuracywhich means that concurrent faults increase the difficulty offault classification As shown in Figure 9(d) the proposed

DSF model can distinguish not only single faults but alsoconcurrent faults perfectly which shows that the proposedmethod can better extract the deep features of acousticsignal

42 Case Study 2 Planetary Gear Fault Diagnosis

421 Data Description -e gear fault signals are measuredfrom the gearbox of the test bench as shown in Figure 4(a)-e collected dataset contains one normal condition (NC)and four kinds of mechanical faults including sun wheelcrack (WC) sun wheel pit (WP) pinion crack (PC) andpinion pit (PP) as shown in Figure 10 -e gear speed is2600 rmin and the sampling frequency is 1024 kHz 300samples were collected for each health condition and each

005

00

ndash005

005

00

ndash005

005

00

ndash005

005

00

ndash005

02

00

ndash02

02

00

ndash02

01

00

ndash01

01

00

ndash01

01

00

ndash01

10

5

0

1510

50

10

5

0

10

5

0

10

5

0

10

5

0

5

0

10

5

0

1510

50

NC

IF0

2IF

04

ROF0

2O

F02

OF0

4RO

F04

RF0

2RF

04

0 500 1000 1500 2000Time-domain sampling points

0 200 400 600 800 1000 1200Spectrum characteristic dimension

Figure 5 Time- and frequency-domain waveforms of bearing signals under the nine health conditions

6 Shock and Vibration

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

outer race fault 02mm (OF02) outer race fault 04mm(OF04) inner race fault 02mm (IF02) inner race fault04mm (IF04) roller fault 02mm (RF02) roller fault04mm (RF04) roller fault 02mm and outer race fault02mm (ROF02) and roller fault 04mm and outer racefault 04mm (ROF04) -e sampling frequency of theacoustic sensor is 128 kHz and the rotating speed is 1300 rmin 200 samples are collected from each health conditionand a total of 1800 samples are obtained Each sample

contains 2400 time-domain points and 1200 frequency-domain points are obtained by FFT

One sample is randomly selected from each healthcondition to show the acoustic signal details -e time-domain and corresponding frequency-domain waveforms ofthe samples are shown in Figure 5 It can be seen that it isarduous to distinguish different health conditions artificiallyand the huge amount of data also increases the difficulty offeature extraction -erefore the DSF model is proposed to

Acoustic signal

Layer 1Sparse filtering features

Rectified linear unit function as activation function

Layer 1 Sparse filtering

Layer 2Sparse filtering features

Rectified linear unit function as activation function

Sofmax classification

Layer 2 Sparse filtering

Backpropagation

BN

BN

Backpropagation

Figure 2 Schematic of DSF

FFT

Softmax regression

SF1

SF2

Fine-tune

Training samples

Normalization

Batch-normalized

Figure 3 Intelligent fault diagnosis framework based on DSF

4 Shock and Vibration

automatically extract the feature of acoustic signal andconduct precise fault classification

412 Results and Analysis -e frequency-domain signal isused as the input of DSF model and the output dimensionsof the two SF layers are set to 800 and 400 respectively -enumber of outputs of softmax classification is 9 -ereforethe structure of the DSF model is 1200-800-400-9 Subse-quently we investigate the effect of iteration numberRandomly select 5 samples for training and the diagnosticaccuracies using different iteration number are displayed inFigure 6 Since the increasing of the accuracies is not obviousafter number of iterations exceeds 40 we choose 40 as theiteration number of DSF Meanwhile the iteration numberof the BP algorithm is 50 and the batch size is 30 In order toshow the superiority of DSF model standard SF [19] L1regularized sparse filtering (L1-SF) [21] and L2 regularizedsparse filtering (L2-SF) [20] are used as comparisonmethods -e output dimension of the three comparisonmethods is set as 1200 the number of iterations is 100 andthe regularization parameter is 1E-5 20 trails are conductedfor each experiment to reduce the influence of randomness-e computing platform is a PC with an I5-4210M CPU and8GB RAM

-e diagnosis results of different numbers of trainingsamples using the proposed DSF model are shown in Fig-ure 7 It is obvious that the accuracy and computing timeincrease with the rise of the training sample number It canbe seen from the figure that the DSF model with only 5 ofthe training samples can achieve average testing accuracy of9815plusmn 033 indicating that the proposed method candiagnose 9 health conditions in the absence of trainingsamples When the number of samples increases to 10 the

average test accuracy reaches 9992plusmn 0027 and theaverage computing time is 149s -erefore in the followingexperiments 10 of the samples were used for training

-e diagnosis results of the four methods are shown inFigure 8 It is certain that the DSF model has the highestaverage testing accuracy (9993) and the lowest standarddeviation (0027) among all the methods It can be seenfrom the figure that the average accuracy of the standard SFis 8905plusmn 139 which is the worst among the methods-e testing accuracies of L1-SF and L2-SF are9045plusmn 109 and 9163plusmn 077 respectively which areslightly higher than those of SF It is worth mentioning thatthe proposed DSF model computing time is 149s Bycontrast the average computing time of SF L1-SF and L2-SF is about 100s -is finding indicates that the DSF methodcan better overcome the difficulty of extracting the acousticsignal features and achieve the highest accuracy and leastcomputing time among the four methods in terms of di-agnosing bearing fault types

In order to better present the superiority of DSF here wemake a detailed comparison between our method and otherseveral classical methods by using the same bearing datasetas summarized in Table 1 In Method 1 ensemble empiricalmode decomposition (EMMD) [25] was employed to extractfeatures and then the features were classified by an optimizedSVM It achieved 9667 testing accuracy on the bearingdataset In Method 2 Jia et al [26] constructed SAE baseddeep network utilizing frequency spectra as inputs to di-agnosis and 9968 testing accuracy is obtained In Method3 the frequency spectra are also used as inputs of BackPropagation Neural Networks (BPNN) and the diagnosisaccuracy is 7374 In Method 4 Xie et al [27] proposedfeature extraction algorithm based on empirical mode de-composition (EMD) and convolutional neural network

Motor BrakeBearing seatRotorSha

coupling

Acoustic sensorGearbox

(a)

OF IFRF

(b)

Figure 4 (a) Bearing fault test rig and (b) three fault bearings

Shock and Vibration 5

(CNN) techniques and obtained 9975 testing accuracy InMethod 5 the proposed method achieves the best testingaccuracy of 9993 when classifying ten different faultconditions which outperforms all compared approaches

To show the details of the diagnostic results of the fourmethods the confusion matrixes on the bearing dataset arepresented in Figure 9 It can be seen from Figures 9(a) and9(b) that the classification results of SF and L1-SF are un-satisfactory -e concurrent faults such as ROF02 andROF04 are not well distinguished and the single faults suchas RF04 and OF04 are not perfectly distinguished-e faultclassification performance of L2-SF is slightly better thanthat of SF and L1-SF as shown in Figure 9(c) but it cannotdistinguish different health conditions with high accuracywhich means that concurrent faults increase the difficulty offault classification As shown in Figure 9(d) the proposed

DSF model can distinguish not only single faults but alsoconcurrent faults perfectly which shows that the proposedmethod can better extract the deep features of acousticsignal

42 Case Study 2 Planetary Gear Fault Diagnosis

421 Data Description -e gear fault signals are measuredfrom the gearbox of the test bench as shown in Figure 4(a)-e collected dataset contains one normal condition (NC)and four kinds of mechanical faults including sun wheelcrack (WC) sun wheel pit (WP) pinion crack (PC) andpinion pit (PP) as shown in Figure 10 -e gear speed is2600 rmin and the sampling frequency is 1024 kHz 300samples were collected for each health condition and each

005

00

ndash005

005

00

ndash005

005

00

ndash005

005

00

ndash005

02

00

ndash02

02

00

ndash02

01

00

ndash01

01

00

ndash01

01

00

ndash01

10

5

0

1510

50

10

5

0

10

5

0

10

5

0

10

5

0

5

0

10

5

0

1510

50

NC

IF0

2IF

04

ROF0

2O

F02

OF0

4RO

F04

RF0

2RF

04

0 500 1000 1500 2000Time-domain sampling points

0 200 400 600 800 1000 1200Spectrum characteristic dimension

Figure 5 Time- and frequency-domain waveforms of bearing signals under the nine health conditions

6 Shock and Vibration

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

automatically extract the feature of acoustic signal andconduct precise fault classification

412 Results and Analysis -e frequency-domain signal isused as the input of DSF model and the output dimensionsof the two SF layers are set to 800 and 400 respectively -enumber of outputs of softmax classification is 9 -ereforethe structure of the DSF model is 1200-800-400-9 Subse-quently we investigate the effect of iteration numberRandomly select 5 samples for training and the diagnosticaccuracies using different iteration number are displayed inFigure 6 Since the increasing of the accuracies is not obviousafter number of iterations exceeds 40 we choose 40 as theiteration number of DSF Meanwhile the iteration numberof the BP algorithm is 50 and the batch size is 30 In order toshow the superiority of DSF model standard SF [19] L1regularized sparse filtering (L1-SF) [21] and L2 regularizedsparse filtering (L2-SF) [20] are used as comparisonmethods -e output dimension of the three comparisonmethods is set as 1200 the number of iterations is 100 andthe regularization parameter is 1E-5 20 trails are conductedfor each experiment to reduce the influence of randomness-e computing platform is a PC with an I5-4210M CPU and8GB RAM

-e diagnosis results of different numbers of trainingsamples using the proposed DSF model are shown in Fig-ure 7 It is obvious that the accuracy and computing timeincrease with the rise of the training sample number It canbe seen from the figure that the DSF model with only 5 ofthe training samples can achieve average testing accuracy of9815plusmn 033 indicating that the proposed method candiagnose 9 health conditions in the absence of trainingsamples When the number of samples increases to 10 the

average test accuracy reaches 9992plusmn 0027 and theaverage computing time is 149s -erefore in the followingexperiments 10 of the samples were used for training

-e diagnosis results of the four methods are shown inFigure 8 It is certain that the DSF model has the highestaverage testing accuracy (9993) and the lowest standarddeviation (0027) among all the methods It can be seenfrom the figure that the average accuracy of the standard SFis 8905plusmn 139 which is the worst among the methods-e testing accuracies of L1-SF and L2-SF are9045plusmn 109 and 9163plusmn 077 respectively which areslightly higher than those of SF It is worth mentioning thatthe proposed DSF model computing time is 149s Bycontrast the average computing time of SF L1-SF and L2-SF is about 100s -is finding indicates that the DSF methodcan better overcome the difficulty of extracting the acousticsignal features and achieve the highest accuracy and leastcomputing time among the four methods in terms of di-agnosing bearing fault types

In order to better present the superiority of DSF here wemake a detailed comparison between our method and otherseveral classical methods by using the same bearing datasetas summarized in Table 1 In Method 1 ensemble empiricalmode decomposition (EMMD) [25] was employed to extractfeatures and then the features were classified by an optimizedSVM It achieved 9667 testing accuracy on the bearingdataset In Method 2 Jia et al [26] constructed SAE baseddeep network utilizing frequency spectra as inputs to di-agnosis and 9968 testing accuracy is obtained In Method3 the frequency spectra are also used as inputs of BackPropagation Neural Networks (BPNN) and the diagnosisaccuracy is 7374 In Method 4 Xie et al [27] proposedfeature extraction algorithm based on empirical mode de-composition (EMD) and convolutional neural network

Motor BrakeBearing seatRotorSha

coupling

Acoustic sensorGearbox

(a)

OF IFRF

(b)

Figure 4 (a) Bearing fault test rig and (b) three fault bearings

Shock and Vibration 5

(CNN) techniques and obtained 9975 testing accuracy InMethod 5 the proposed method achieves the best testingaccuracy of 9993 when classifying ten different faultconditions which outperforms all compared approaches

To show the details of the diagnostic results of the fourmethods the confusion matrixes on the bearing dataset arepresented in Figure 9 It can be seen from Figures 9(a) and9(b) that the classification results of SF and L1-SF are un-satisfactory -e concurrent faults such as ROF02 andROF04 are not well distinguished and the single faults suchas RF04 and OF04 are not perfectly distinguished-e faultclassification performance of L2-SF is slightly better thanthat of SF and L1-SF as shown in Figure 9(c) but it cannotdistinguish different health conditions with high accuracywhich means that concurrent faults increase the difficulty offault classification As shown in Figure 9(d) the proposed

DSF model can distinguish not only single faults but alsoconcurrent faults perfectly which shows that the proposedmethod can better extract the deep features of acousticsignal

42 Case Study 2 Planetary Gear Fault Diagnosis

421 Data Description -e gear fault signals are measuredfrom the gearbox of the test bench as shown in Figure 4(a)-e collected dataset contains one normal condition (NC)and four kinds of mechanical faults including sun wheelcrack (WC) sun wheel pit (WP) pinion crack (PC) andpinion pit (PP) as shown in Figure 10 -e gear speed is2600 rmin and the sampling frequency is 1024 kHz 300samples were collected for each health condition and each

005

00

ndash005

005

00

ndash005

005

00

ndash005

005

00

ndash005

02

00

ndash02

02

00

ndash02

01

00

ndash01

01

00

ndash01

01

00

ndash01

10

5

0

1510

50

10

5

0

10

5

0

10

5

0

10

5

0

5

0

10

5

0

1510

50

NC

IF0

2IF

04

ROF0

2O

F02

OF0

4RO

F04

RF0

2RF

04

0 500 1000 1500 2000Time-domain sampling points

0 200 400 600 800 1000 1200Spectrum characteristic dimension

Figure 5 Time- and frequency-domain waveforms of bearing signals under the nine health conditions

6 Shock and Vibration

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

(CNN) techniques and obtained 9975 testing accuracy InMethod 5 the proposed method achieves the best testingaccuracy of 9993 when classifying ten different faultconditions which outperforms all compared approaches

To show the details of the diagnostic results of the fourmethods the confusion matrixes on the bearing dataset arepresented in Figure 9 It can be seen from Figures 9(a) and9(b) that the classification results of SF and L1-SF are un-satisfactory -e concurrent faults such as ROF02 andROF04 are not well distinguished and the single faults suchas RF04 and OF04 are not perfectly distinguished-e faultclassification performance of L2-SF is slightly better thanthat of SF and L1-SF as shown in Figure 9(c) but it cannotdistinguish different health conditions with high accuracywhich means that concurrent faults increase the difficulty offault classification As shown in Figure 9(d) the proposed

DSF model can distinguish not only single faults but alsoconcurrent faults perfectly which shows that the proposedmethod can better extract the deep features of acousticsignal

42 Case Study 2 Planetary Gear Fault Diagnosis

421 Data Description -e gear fault signals are measuredfrom the gearbox of the test bench as shown in Figure 4(a)-e collected dataset contains one normal condition (NC)and four kinds of mechanical faults including sun wheelcrack (WC) sun wheel pit (WP) pinion crack (PC) andpinion pit (PP) as shown in Figure 10 -e gear speed is2600 rmin and the sampling frequency is 1024 kHz 300samples were collected for each health condition and each

005

00

ndash005

005

00

ndash005

005

00

ndash005

005

00

ndash005

02

00

ndash02

02

00

ndash02

01

00

ndash01

01

00

ndash01

01

00

ndash01

10

5

0

1510

50

10

5

0

10

5

0

10

5

0

10

5

0

5

0

10

5

0

1510

50

NC

IF0

2IF

04

ROF0

2O

F02

OF0

4RO

F04

RF0

2RF

04

0 500 1000 1500 2000Time-domain sampling points

0 200 400 600 800 1000 1200Spectrum characteristic dimension

Figure 5 Time- and frequency-domain waveforms of bearing signals under the nine health conditions

6 Shock and Vibration

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

sample contains 1600 data points Each sample gets 800frequency-domain points through FFT as the input of themodel

422 Results and Analysis 10 of gear samples wererandomly selected to train DSF model After testing we set600 and 100 as the output dimension of the two SF layers

Ave

rage

accu

racy

()

20 30 40 50 60 7010e iteration numbers of DSF

70

75

80

85

90

95

100

Figure 6 Average accuracy of different iteration number of DSF model

Ave

rage

tim

e (s)

Ave

rage

accu

racy

()

2 5 10 15 20 251Percentage of samples for training

0

5

10

15

20

25

30

35

40

50556065707580859095

100

Testing accuracyAverage time

Figure 7 -e diagnosis results of the DSF method using different percentage of training samples

SF L1-SF L2-SF DSF

Ave

rage

accu

racy

()

0102030405060708090

100

0

20

40

60

80

100

120

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 8 Comparison of the average diagnostic accuracies of four SF models

Shock and Vibration 7

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

Table 1 Performance comparison between the proposed DSF method and some classical method

Method Description Training samples () Testing accuracy ()1 EMMD features + SVM 25 97042 SAE+DNN 50 99683 BPNN+ frequency 50 73744 EMD features +CNN 75 99755 DSF 10 9993

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04Predicted labels

159 21166 2 7 5

173 4 1 24 1 130 9 6 5 7 18

174 1 51 160 3 16

1 2 156 1 201 1 15 156 7

1 179

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0

00 0 0 0 0 0

0 0 0 0 00 0 0 00 0 0 00 0 0 0 0 0 0

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(a)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

168 1 10 1169 1 5 5

150 23 6 11 131 36 7 1 4

1801 179

10 9 160 17 11 7 149 6

10 1 169

0 0 0 0 00 0 0 0 00 0 0 0 0

0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0 0

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

(b)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

Predicted labels

174 6174 3 1 2

172 7 12 143 31 2 2

180179 1

22 7 148 36 2 18 152 25 1 3 171

0 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0

0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 00 0 0 0 0

(c)

NC IF02 IF04 ROF02 OF02 OF04 ROF04 RF02 RF04

True

labe

ls

Predicted labels

NCIF02IF04ROF02OF02OF04ROF04RF02RF04

180180

180180

180180

1 179180

180

0 0 00 00 0 0

0 0 00 0 0 0 0 0

0

0 0 0 0 00 0 0 0 0 0

0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0

0 00 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0

(d)

Figure 9 Confusion matrixes for bearing dataset (a) SF (b) L1-SF (c) L2-SF and (d) DSF

(a) (b)

(c) (d)

Figure 10 Four kinds of gear fault feature diagrams

8 Shock and Vibration

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

-e numbers of iterations of the two SF layers are all 20 andthe output dimension of softmax is 5 -e iteration numberof the BP algorithm is 50 and the batch size is 20-e outputdimension of the three comparison methods is set as 800and other parameters set are the same as Case 1

Each experiment is repeated 20 times to reduce theeffects of randomness -e gear fault diagnosis results of thefour methods are shown in Figure 11 Specifically thetraining accuracy of the four methods is 100 -e per-formance of SF model is the most unsatisfactory and thetesting accuracy is 8782plusmn 091 -e testing accuracies ofL1-SF and L2-SF are 88 and 90 respectively By contrastthe proposed DSF model achieved the highest testing ac-curacy of 9911plusmn 011 Meanwhile the average com-puting time of DSF model is 958 s and the computing timeof three comparison methods is about 5 times that of DSFmodel In conclusion the proposed DSFmethod can achievethe highest accuracy and robustness in acoustic signal faultdiagnosis

-e average accuracies of the five health conditions areshown in Figure 12 It can be determined that the four

methods can precisely diagnose the health condition of PCHowever the three comparison methods have lower testingaccuracies for health conditions NC PP WC and WP Incontrast DSF model can overcome this shortcoming andaccurately diagnose the five health conditions

To confirm the performance of the proposed DSFmodel the t-distributed stochastic neighbor embedding(t-SNE) is applied to obtain the first two dimensions oflearned features and the results are shown in Figure 13 Itcan be seen from Figure 13(a) that the features of thesame health condition are well clustered However tenpoints of WC were misclassified to PP and five points ofNC were misclassified to WC which explains the phe-nomenon that this method obtains low diagnosis accu-racy for the health conditions of PP and WC InFigures 13(b) and 13(c) the interval between NC WCand NC is not obvious there are also more points that aremisclassified It is worth noting that each feature clusterof the DSF method is separated and only four points ofWC were mistakenly assigned to NC and three points ofWP were mistakenly assigned to PC which means that

SF L1-SF L2-SF DSFA

vera

ge ac

cura

cy (

)50556065707580859095

100

0

10

20

30

40

50

60

Ave

rage

tim

e (s)

Testing accuracyTraining accuracyAverage time

Figure 11 Comparison of the average diagnostic accuracies of four SF models

Ave

rage

accu

racy

()

80828486889092949698

100

PC PP WC WPNCHealth condition

DSFL2-SF

L1-SFSF

Figure 12 Comparison of average diagnosis accuracies of each health condition

Shock and Vibration 9

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

the extracted features of DSF model are morerecognizable

5 Conclusion

In this paper a batch-normalized DSF model is proposed toprocess acoustic signals for fault diagnosis Two SF modelsare stacked to extract the deep features of acoustic signalsand the optimal weight is obtained by fine-tuning process ofBP algorithm-e experiment results of bearing and gearboxdataset show that the DSF model can also achieve high testaccuracy in the case of insufficient training samplesMeanwhile compared with other SFmodels DSF can get the

highest accuracy and the least computing time which showsthat the proposed method is more efficient in featureextraction

Data Availability

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

Conflicts of Interest

-e authors declare no conflicts of interest regarding thispublication

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(a)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(b)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(c)

80

60

40

20

0

ndash20

ndash40

ndash60

ndash80806040200ndash20ndash40ndash60ndash80

NCPCPP

WCWP

(d)

Figure 13 First two dimensions of learned features of the four methods (a) SF (b) L1-SF (c) L2-SF and (d) DSF

10 Shock and Vibration

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11

Acknowledgments

-is work was supported by China Postdoctoral ScienceFoundation (2019M662399) and the Project of ShandongProvince Higher Educational Young Innovative Talent In-troduction and Cultivation Team (Performance Enhance-ment of Deep Coal Mining Equipment)

References

[1] C K Tan P Irving and D Mba ldquoA comparative experi-mental study on the diagnostic and prognostic capabilities ofacoustics emission vibration and spectrometric oil analysisfor spur gearsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 208ndash233 2007

[2] C Shen Y Qi and J Wang ldquoAn automatic and robustfeatures learning method for rotating machinery fault diag-nosis based on contractive autoencoderrdquo Engineering Ap-plications of Artificial Intelligence vol 76 pp 170ndash184 2018

[3] H Liu L Li and J Ma ldquoRolling bearing fault diagnosis basedon STFT-deep learning and sound signalsrdquo Shock and Vi-bration vol 2016 Article ID 6127479 12 pages 2016

[4] J Wang S Li B Han et al ldquoConstruction of a batch-nor-malized autoencoder network and its application in me-chanical intelligent fault diagnosisrdquoMeasurement Science andTechnology vol 30 no 1 p 15106 2019

[5] X Jiang C Shen J Shi and Z Zhu ldquoInitial center frequency-guided VMD for fault diagnosis of rotating machinesrdquoJournal of Sound and Vibration vol 435 pp 36ndash55 2018

[6] S A Khan and J M Kim ldquoAutomated bearing fault diagnosisusing 2D analysis of vibration acceleration signals undervariable speed conditionsrdquo Shock and Vibration vol 2016Article ID 8729572 11 pages 2016

[7] X Jiang and J Shi ldquoNon-dominated Solution Set Based onTime-Frequency Infograms for Local Damage Detection ofRotating Machinesrdquo Isa Transactions New York NY USA2019

[8] K Shibata A Takahashi and T Shirai ldquoFault diagnosis ofrotating machinery through visualisation of sound signalsrdquoMechanical Systems and Signal Processing vol 14 no 2pp 229ndash241 2000

[9] F Elasha M Greaves D Mba and D Fang ldquoA comparativestudy of the effectiveness of vibration and acoustic emission indiagnosing a defective bearing in a planetry gearboxrdquo AppliedAcoustics vol 115 no 2 pp 181ndash195 2017

[10] H Zhang S Lu Q He and F Kong ldquoMulti-bearing defectdetection with trackside acoustic signal based on a pseudotime-frequency analysis and Dopplerlet filterrdquo MechanicalSystems and Signal Processing vol 71 pp 176ndash200 2016

[11] Z Gao J Lin X Wang and X Xu ldquoBearing fault detectionbased on empirical wavelet transform and correlated kurtosisby acoustic emissionrdquo Materials vol 10 no 6 p 571 2017

[12] X Zhang Y Wang and K Wang ldquoRail crack detection basedon the adaptive noise cancellation method of emd at highspeedrdquo in Proceedings of 2017 IEEE International Instru-mentation and Measurement Technology Conference IEEETurin Italy May 2017

[13] A Coates A Ng and H Lee ldquoAn analysis of single-layernetworks in unsupervised feature learningrdquo in Proceedings ofthe Fourteenth International Conference on Artificial Intelli-gence and Statistics pp 215ndash223 Sicily Italy June 2011

[14] K Noda Y Yamaguchi K Nakadai H G Okuno andT Ogata ldquoAudio-visual speech recognition using deep

learningrdquo Applied Intelligence vol 42 no 4 pp 722ndash7372015

[15] X Zhu Z H Liu F H YangShi G Qi and S Z Li ldquoLarge-scale bisample learning on ID versus spot face recognitionrdquoInternational Journal of Computer Vision vol 127 no 6-7pp 684ndash700 2019

[16] L Yi B J Liu K M YangSun and S Abbas ldquoA deep multi-modal CNN for multi-instance multi-label image classifica-tionrdquo IEEE Transactions on Image Processing vol 27 no 12pp 6025ndash6038 2018

[17] J Sun Z Chen S A Bhaskar P W Koh and A Y NgldquoSparse filteringrdquo in Advances in Neural InformationProcessing Systems pp 1125ndash1133 2011

[18] F M Zennaro and K Chen ldquoTowards understanding sparsefiltering a theoretical perspectiverdquo Neural Networks vol 98pp 154ndash177 2018

[19] Y Lei F Jia J Lin S Xing and S X Ding ldquoAn intelligentfault diagnosis method using unsupervised feature learningtowards mechanical big datardquo IEEE Transactions on IndustrialElectronics vol 63 no 5 pp 3137ndash3147 2016

[20] Z Yang L Jin D Tao S Zhang and X Zhang ldquoSingle-layerunsupervised feature learning with l2 regularized sparse fil-teringrdquo in Proceedings ofIEEE China Summit amp InternationalConference on Signal and Information Processing pp 475ndash479Xirsquoan China July 2014

[21] W Qian S Li J Wang Z An and X Jiang ldquoAn intelligentfault diagnosis method of rotating machinery using L1-reg-ularized sparse filteringrdquo Journal of Vibroengineering vol 20no 8 pp 2839ndash2854 2018

[22] J Wang S Li Y Xin and Z An ldquoGear fault intelligentdiagnosis based on frequency-domain feature extractionrdquoJournal of Vibration Engineering amp Technologies vol 7 no 2pp 159ndash166 2019

[23] C Hou F Nie and X Li ldquoJoint embedding learning andsparse regression a framework for unsupervised feature se-lectionrdquo IEEE Transactions on Systems Man and Cyberneticsvol 44 no 6 pp 793ndash804 2014

[24] V Nair and G E Hinton ldquoRectified linear units improverestricted boltzmann machines vinod nairrdquo in Proceedings ofthe 27th International Conference on Machine Learningpp 807ndash814 Haifa Israel June 2010

[25] X Zhang and J Zhou ldquoMulti-fault diagnosis for rolling el-ement bearings based on ensemble empirical mode decom-position and optimized support vector machinesrdquoMechanicalSystems and Signal Processing vol 41 no 1-2 pp 127ndash1402013

[26] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 73pp 303ndash315 2016

[27] Y Xie and T Zhang ldquoFault diagnosis for rotating machinerybased on convolutional neural network and empirical modedecompositionrdquo Shock and Vibration vol 2017 Article ID3084197 12 pages 2017

Shock and Vibration 11