A Stacked Autoencoder-Based Deep Neural Network for Achieving Gearbox Fault Diagnosis · 2019. 7....

Research ArticleA Stacked Autoencoder-Based Deep Neural Network forAchieving Gearbox Fault Diagnosis

Guifang Liu1 Huaiqian Bao 12 and Baokun Han1

1College of Mechanical and Electronic Engineering Shandong University of Science and Technology Qingdao 266590 China2AUCMA Company Limited Qingdao 266510 China

Correspondence should be addressed to Huaiqian Bao bhqian163com

Received 19 March 2018 Accepted 12 June 2018 Published 25 July 2018

Academic Editor Muddasser Alam

Copyright copy 2018 Guifang Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Machinery fault diagnosis is pretty vital in modern manufacturing industry since an early detection can avoid some dangeroussituations Among various diagnosis methods data-driven approaches are gaining popularity with the widespread development ofdata analysis techniques In this research an effective deep learning method known as stacked autoencoders (SAEs) is proposedto solve gearbox fault diagnosis The proposed method can directly extract salient features from frequency-domain signals andeliminate the exhausted use of handcrafted features Furthermore to reduce the overfitting problem in training process and improvethe performance for small training set dropout technique and ReLU activation function are introduced into SAEs Two gearboxdatasets are employed to conform the effectiveness of the proposed method the result indicates that the proposed method can notonly achieve significant improvement but also is superior to the raw SAEs and some other traditional methods

1 Introduction

As one of the most vital components of rotating machinerygearboxes are widely used in various industrial fields suchas vehicles and machine tools [1] Due to the complexitystructure of gearbox and various working conditions inter-ference gears always cause fault quite easily If the fault is notdetected in time it can result in the crash of entire systemand serious loss of property So it is challenging to conducteffective fault diagnosis system In modern industries data-driven systems have revolutionized manufacturing throughenabling computers to collect a massive amount of data frommonitored machines [2] At the same time machines havealso been more precise than ever before and machineryfault diagnosis has sufficiently embraced multifault diagnosisrevolution in condition monitoring system Contrasted withtop-down modeling proposed by the physics-based faultdiagnosis systems data-driven systems provide a bottom-up model to detect the occurrence of machinery faults [3]As is well-known the physics-based methods are unableto be updated online with measured data and also cannotdeal well with large-scale data On the other hand with the

fast-developing computer systems and sensors data-drivenbased fault diagnosis systems have drawn increasing publicattentions

The basic framework of data-driven system usually con-sists of four consecutive stages data acquisition featureextraction model training and model testing [4] Conven-tional data-driven methods are usually trying to design aright set of features and then put them into some shallowmachine learning models such as Naive Bayes (NB) [5]Support Vector Machines (SVM) [6] and logistic regres-sion [7] But these works usually focus on manual featureextraction (statistical features frequency and time-frequencyfeatures) that always need plenty of human labor and cannotupdate online [8] Meanwhile the selection of these featurescould not leave prior knowledge and feature engineeringSo it is really a tough problem for these methods to extractintrinsic features behind the raw time-series data As thehottest subfield of machine learning deep learning hasbeen regarded as a powerful solution for the intelligentfault diagnosis system to extract salient features throughmultilayer architecture such as artificial neural networks(ANN) [9 10] autoencoders [11 12] restricted Boltzmann

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 5105709 10 pageshttpsdoiorg10115520185105709

2 Mathematical Problems in Engineering

machine (RBM) [13 14] and convolutional neural networks(CNN) [15 16] Compared with traditional methods deeplearning methods do not need human labor and expertknowledge for feature extraction All the hyperparameters inmodel training and pattern classification modules are able tobe trained jointly Therefore deep learning can be employedto address machinery fault diagnosis in a very general way

As one of the widely used deep learning techniquesstacked autoencoders (SAEs) have attracted considerableattention in fault diagnosis It has been investigated as acommon component of DNN by Bengio et al [17] Jia et al[18] proposed a SAEs based DNNs for roller bearing andplanetary gearbox fault diagnosis with input as frequencyspectra after Fourier transform Guo et al [19] employedmultidomain statistical features of the raw vibration signalsas the input of SAEs which can be viewed as a kind of featurefusion Liu et al [20] fed the normalized spectrograms createdby STFT into SAEs for rolling bearing fault diagnosis In thework presented in [21] the nonlinear soft threshold approachand digital wavelet frame were used to process the measuredsignal and then fed into SAEs for rotating machinery diag-nosis Jia et al [22] constructed a local connection networkbased on normalized sparse autoencoder and L1 norm wasemployed to find sparse features

Inspired by the prior researches a new framework basedon SAEs is proposed to resolve the gearbox fault diagnosisFurthermore to overcome the deficiency of overfitting prob-lem in the training process and improve the performancefor small training set dropout technique [23] and ReLUactivation function are introduced into SAEs Rest of thepaper is organized as follows Section 2 briefly introduces thealgorithms of SAEs dropout and ReLU activation functionSection 3 is dedicated to detailing the content of the proposedmethod In Section 4 the multifault gearbox dataset isadopted to validate the effectiveness of the proposedmethodFurthermore the superiority of the proposed method isexhibited by comparing with the other traditional methodsFinally some conclusions are drawn in Section 5

2 Theoretical Background

21 Stacked Autoencoders Autoencoder is a kind of unsuper-vised learning structure that owns three layers input layerhidden layer and output layer as shown in Figure 1 Theprocess of an autoencoder training consists of two partsencoder and decoder Encoder is used for mapping the inputdata into hidden representation and decoder is referred toreconstructing input data from the hidden representationGiven the unlabeled input dataset xnNn=1 where xn isin R

mtimes1hn represents the hidden encoder vector calculated from xnand xn is the decoder vector of the output layer Hence theencoding process is as follows

hn = f (W1xn + b1) (1)

where f is the encoding function W1 is the weight matrix ofthe encoder and b1 is the bias vector

The decoder process is defined as follows

xn = g (W2hn + b2) (2)

where g is the decoding function W2 is the weight matrix ofthe decoder and b2 is the bias vector

The parameter sets of the autoencoder are optimized tominimize the reconstruction error

120601 (Θ) = argmin1205791205791015840

1n

nsumi=1L (xi xi) (3)

where L represents a loss function L(x x) = x minus x2As shown in Figure 2 the structure of SAEs is stacking n

autoencoders into n hidden layers by an unsupervised layer-wise learning algorithm and then fine-tuned by a supervisedmethod So the SAEs based method can be divided into threesteps(1) Train the first autoencoder by input data and obtain

the learned feature vector(2)The feature vector of the former layer is used as the

input for the next layer and this procedure is repeated untilthe training completes(3) After all the hidden layers are trained backpropaga-

tion algorithm (BP) is used tominimize the cost function andupdate the weights with labeled training set to achieve fine-tuning

22 Dropout Dropout is an effective strategy that has beenproved to reduce overfitting in the training process of neuralnetworks The overfitting problem always happens when thetraining set is small which would result in a low accuracy onthe test set Dropout can randomly affect the neurons of thehidden layer to lose power in the training process as shownin Figure 3 but the weights of those neurons are preservedFurthermore the neurons can recover to work when the nextsample is input Technically dropout is able to be achieved bysetting the output date of some hidden neurons to 0 and thenthese neurons cannot be related to the forward propagationprocess Many researches have tested the effect of dropouton reducing the overfitting problem for the small trainingset [28] and this paper will also employ it to enhance thefeature extraction ability and classification accuracy of SAEsfor multifault gearbox fault diagnosis

23 ReLU For traditional activation functions (sigmoidand hyperbolic tangent functions) the gradients decreasequickly with training error propagating to forward layersTherectified linear units (ReLU) activation function has receivedextensive attention in recent years since its gradient will notdecrease with the independent variables increasing So thenetwork with ReLU does not suffer from gradient diffusionor vanishing The ReLU function is shown in (4) and thestructure is displayed in Figure 4

fr (x) = max (0 x) (4)

3 Proposed Framework

This section details the proposed intelligent fault diagnosismethod In the method SAEs are combined with dropoutto achieve multifault gearbox fault diagnosis The frameworkand illustration of the proposed method are displayed in Fig-ure 5 SAEs combinedwith dropoutmodel are applied to train

Mathematical Problems in Engineering 3

Input layer

Output layer

Encoder

Decoder

Hidden layer

Figure 1 Structure of autoencoder

Hidden layer 1

AE3

AE2

AE1

Hidden layer 2

Hidden layer 3

Classifier

Input layer

Stack

Fine-fun

Figure 2 Structure of stacked autoencoders

Figure 3 Dropout neural net model Left a standard neural net Right an example of a thinned net produced by applying dropout

theweightmatrix from frequency spectra of vibration signalsSpecifically the procedure can be described as follows(1) The spectra of vibration signals are composed the

training set Xi liMi=1 where M is the number of samplesXj isin RNtimes1 is the ith sample containing N Fourier coefficientsand li is the health label of Xi

(2) Build the DNNs by SAEs and then employ theunlabeled training set XiMi=1 to pretrain the DNNs layer-by-layer(3) Utilize BP algorithm to update the weights and fine-

turn the parameters of the SAEs with labeled training setXi liMi=1


0

1

2

3

10 2 3minus2 minus1minus3

Figure 4 Structure of ReLU function

Data acquisition

Classifier

Input layer

Hidden layer 1

Hidden layer 2

Dropout

FFT

BP

AE1

AE2

3

2

1

middot middot middot





Figure 5 Flowchart of the proposed method

(4)The testing set is adopted to validate the effectivenessof the proposed method

4 Experiments

41 Case 1 Fault Diagnosis of a Multifault Gearbox

411 DataDescription Gear faults including distributed fault(worn) and localized faults (broken pit) as well as coupledfault in power train perhaps cause catastrophic accidentsTherefore an early recognition of the gear faults is criticalfor normal operation of a gearbox Our paper focuses oninvestigating the multifault gearbox In this section a muli-fault gearbox experimental dataset is employed to validatethe effectiveness of the proposed method [29] The vibrationsignals were collected on a specially designed bench whichconsisted of a one phase input and three-phase outputmotor (the nominal power is 075 kW and nominal rotationfrequency is 880 rpm) a gearbox the shaft supporting seatsa flexible coupling and a magnetic powder brake as showin Figure 6 The sensor is a piezoelectric accelerometer(DH131E) mounted on the flat surface of gearbox and thesampling frequency is 5120Hz The gearbox includes two

gears (pinion and wheel gear) and the gear parameters aredisplayed in Table 1 There are six health conditions underthree loads normal a single worn pinion a single pit ofwheel a single broken tooth of wheel coupled fault of brokenwheel and worn pinion and coupled fault of wheel pit andworn pinion For brevity the six fault types of gear arenamed as Type-1 Type-2 Type-3 Type-4 Type-5 and Type-6 respectively 100 data samples are collected from each faulttype under one load by an overlapped manner so a total of1800 samples are obtained from the designed bench and eachsample contains 1000 data points Considering the rotationfrequency of shaft is 880 rpm so each period of rotationcontains 350 data points For avoiding the influence of speedfluctuation each sample collects almost three periods ofrotation data (1000 data points) The frequency spectra arealso adopted as input data and each sample contains 500Fourier coefficients The major reason of using frequencyspectra is that the frequency spectra can show the distributionof constitutive components with discrete frequencies andmore clarity information about the state of rotatingmachines[18] Herewe randomly select 4 samples from the normal typeof gear and obtain their Fourier coefficients by FFT as shownin Figure 7 It is easy to find that the time-domain features of


Table 1 Gear parameters

Gear Teeth Module(mm) Pressure angle (deg) MaterialsPinion 55 2 20 S45CWheel 75 2 20 S45C

Shaft supporting seat Flexible couplings Gearbox Magnetic powder brake

Three-phase motor

Tooth-shaped belt

Figure 6 Bench of multifault gearbox

minus20

0

20

minus20

0

20

minus20

0

20

0

1

2

Sample 1

Sample 2

Sample 4

Sample 3

minus20

0

20

400 600 800 1000200Time points

400 600 800 1000200

400 600 800 1000200

400 600 800 10002000

1

2

0

1

2

0

1

2

200 300 400 500100Frequency coefficients

200 300 400 500100

200 300 400 500100

200 300 400 500100

Figure 7 Comparison of time-domain and frequency-domain coefficients

each sample are different but the frequency spectra featuresare becoming regularity with each other The structure of thedesigned DNNs is 500 200 100 and 6 respectively

412 Diagnosis Results The parameter of dropout rate 120572 ischanged from 0 to 07 with a step size of 01 and 15 trials arecarried out for the experiment in order to reduce the effectiveof randomness 10 of samples are randomly selected to trainthe model and the rest are used for testing The diagnosisaccuracies are shown in Figure 8 It is clearly seen that when 120572is 03 the diagnosis accuracy is the highest and the standard

deviation is the lowest so 03 is chosen as the dropout rate inthis experiment

To classify the six health conditions of the gears 10samples are employed to train the proposed model and therest are used for testing The learning rate is 001 and theiteration number is 100The training and testing accuracies of15 trials are displayed in Figure 9 and the average training andtesting accuracies are 100 and 9934 plusmn 025 respectivelywhich indicates that the proposed model can also distinguishthe six health conditions of gear with a high accuracy Toillustrate the process concretely the classification results of


90

92

94

96

98

100

Aver

age a

ccur

acy

()

01 02 03 04 05 06 070Dropout rate

Figure 8 Diagnosis results using different learning rates

Training accuracyTesting accuracy

99

992

994

996

998

100

Accu

racy

()

4 6 8 10 12 142Trial number

Figure 9 Diagnosis result using the proposed method

the 14th testing trial are drawn in Figure 10 It can be seen that3 of the testing samples are misclassified yielding the successrates 9944 Among them 1 sample of type-3 ismisclassifiedas type-4 2 samples of type-4 are misclassified as type-3and 1 sample of type-5 is misclassified as type-6 respectivelyTo further display the ability of the proposed method t-distributed stochastic neighbor embedding (t-SNE) [30] isemployed to visualize the learned featuresTherefore the 100-dimension feature vector is embedded into a 3-dimensionfeature vector The classification result is shown in Figure 11It is easy to find that the same types of samples are gatheredtogether and different types are separated excellently

For comparison several diagnosis methods are presentedand the diagnosis results are displayed in Table 2 Li etal [24] proposed a method combining 19 time-domainand frequency-domain features with self-organizing mapwhen their method was adopted to classify the six types ofthe gearbox dataset and achieved 9251 plusmn 423 testingaccuracy In [25] wavelet multifractal features and SVMmodel were used to represent the six gear fault types andfinally obtained 8765plusmn537 classification accuracy Lin etal [26] proposed a fault diagnosis method using multifractaldetrended fluctuation (MFDFA) and here achieved 9623 plusmn169 accuracy Lou et al [27] applied multiple domainfeatures and ensemble fuzzy ARTMAP neural networksto distinguish the health conditions and 9883 plusmn 042

50 100 150 200 250 300 350 400 450 5000Sample number

1

2

3

4

5

6

Hea

lth la

bel

Figure 10 Diagnosis result of the 14th trial

minus50

0

50minus50

050 Dimension 1

Dimension 2

Type-1Type-2Type-3

Type-4Type-5Type-6

minus50

0

50

Dim

ensio

n 3

Figure 11 Feature visualization map

accuracywas obtained Furthermore the raw stacked autoen-coders without dropout (Raw SAEs) are also adopted forcomparison and the testing accuracy is just 9316 plusmn378 which exhibits the effectiveness of dropout in featureextraction Compared with the methods above it shows thatthe proposed method can not only automatically distinguishthe six health conditions of gearbox but also achieve a higheraccuracy with a lower percentage of training samples

To further investigate the learned features in the proposedmodel another experiment is conducted as shown in Figures12 and 13 As a result two level features can be obtained fromtwo hidden layers of the DNNs which can be called learnedfeatures so 200- and 100-dimensional learned feature vectorsof each sample are obtained respectively For achieving agood view on the visualization all the learned feature vectorsof the same type test samples are gathered together [31]Figure 12 displays the learned 100-dimensional features ofgearbox dataset using the raw SAEs without dropout andFigure 13 shows the learned 100-dimension features using theproposed method It can be clearly seen that all the learnedfeature vectors of one health condition by the proposedmethod are almost the same trend with each other Bycontrast the feature vectors of each health condition by theraw SAEsmethod are mixed with each other and can not finda unit tendency And also the amplitudes of feature vectorsby the two methods are different the proposed method isable to learn more distinguished feature vectors that own


Table 2 Comparison of classification accuracy

Method Training samples Testing accuracy[24] 40 9251 plusmn 423[25] 75 8765 plusmn 537[26] NA 9623 plusmn 169[27] 50 9883 plusmn 042Raw SAEs 10 9316 plusmn 378Proposed 10 9934 plusmn 025

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Type-1

Type-2

Type-3

Type-4

Type-5

Type-6

00102

00102

00102

00102

00102

00102

20 30 40 50 60 70 80 90 10010Dimension number of learned features

20 30 40 50 60 70 80 90 10010

Figure 12 Learned features of gearbox dataset using the raw SAEs

10 20 30 40 50 60 70 80 90 1000

0102

10 20 30 40 50 60 70 80 90 1000

0102

10 20 30 40 50 60 70 80 90 1000

0102

10 20 30 40 50 60 70 80 90 1000

0102

10 20 30 40 50 60 70 80 90 1000

0102

00102

Type-1

Type-5

Type-4

Type-3

Type-2

Type-6


Figure 13 Learned features of gearbox dataset using the proposedmethod

larger amplitudes than the raw SAEs method Therefore theproposed method can effectively mine the main variations ina high order space from different fault signals than the rawSAEs method without dropout

42 Case 2 Fault Diagnosis of a Motorcycle Gearbox Tofurther validate the proposed method a motorcycle gearboxdataset [32] is taken as the second case analysis Figure 14displays the gearbox being referred to besides the gear-box there are an electrical motor with the rotation speed1420 rpm a data acquisition system a tachometer a triaxialaccelerometer and a load mechanismThe sample frequencywas 16384Hz There are four health types of gear as shownin Figures 14(b)ndash14(c) normal condition (NC) slightly worn(SW) medium worn (MW) and broken tooth (BT) InFigure 14(e) the gears which have 24 teeth and 29 teeth(tested gear) are a pair of driven and driving gears Thevibration signals of four gear health types are depicted inFigure 15 It can be easy to find that the NC and BT are easilydistinguished but the SW andMW are hardly discriminated50 samples of NC and 100 samples of SW MW and BT arecollected and each sample contains 1000 data points

Similarly 10 samples are employed to train the proposedmodel and the rest are used for testing and the parameter setis the same as Case 1The training and testing accuracies of 15trials are displayed in Figure 16 and the average training andtesting accuracies are 100 and 9926 plusmn 041 respectivelywhich also indicates that the proposed model can distinguishthe four health types of the motorcycle gearbox with a highaccuracyThen the classification results of the 3rd testing trialare displayed in Figure 17 Only 2 samples are misclassifiedie 1 sample of SW is misclassified as MW and 1 sampleof MW is misclassified as SW respectively Meanwhile thevisualization of the 2-dimensional feature vectors mappedby t-SNE is shown in Figure 18 The excellent classificationresult is also obtained which illustrates the robustness of theproposed method

5 Conclusions

An intelligent fault diagnosis method based on SAEs ispresented for gearbox fault diagnosis In order to reduceoverfitting problem and improve the performance of tradi-tional SAEs for small training set the dropout technique andReLU activation function are both adopted As illustratedin the experimental study the proposed method can extractuseful features from different fault gear types and achievea high diagnosis accuracy Comparison studies show thatthe proposed method outperforms the raw SAEs methodand some other traditional methods On the other hand the


Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)

Figure 14 (a) Experimental setup (b) worn teeth (c) broken teeth (d) accelerometer location (e) schematic of the gearbox

times 104

minus2000

200

Am

plitu

de

01 02 03 04 05 060Time (s)

0246

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(a)

times 104

minus200

0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

times 104

minus200

0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

minus500

0

500

Am

plitu

de

01 02 03 04 05 060Time (s)

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

02468

(d)

Figure 15 Vibration data and corresponding frequency spectra of the four different types of gear conditions (a) NC (b) SW (c) MW and(d) BT



98

985

99

995

100

Accu

racy

()



1

2

3

4

Hea

lth la

bel

50 100 150 200 250 3000Sample number


NCSW

MWBT

minus30

minus20

minus10

0

10

20

30

Dim

ensio

n 2

0 20 40minus40 minus20minus60Dimension 1


exhibition of the learned features illustrates that with thehelp of dropout technique and ReLU activation function theproposed method can capture salient features and obtain ahigher diagnosis result than the raw SAEs method Mean-while it can clearly describe the process on how DNNs dealwithmechanical signals which is worth further study in faultdiagnosis In future work a wide range of experiments willbe investigated to evaluate the robustness of the proposedmethod

Data Availability

The data used to support the findings of this study can befound in the online versions at httpsdoiorg101006mssp20001338 and httpdxdoiorg101016jymssp201606012

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by National Natural Science Foun-dation of China (Grant no 51675315) and Shandong Provincekey research and development projects (2017GGX40120)

References

[1] X Jiang S Li and QWang ldquoA study on defect identification ofplanetary gearbox under large speed oscillationrdquoMathematicalProblems in Engineering vol 2016 Article ID 5289698 18 pages2016

[2] S Yin X Li H Gao and O Kaynak ldquoData-based techniquesfocused on modern industry an overviewrdquo IEEE Transactionson Industrial Electronics vol 62 no 1 pp 657ndash667 2015

[3] J Gao LWuHWang andYGuan ldquoDevelopment of amethodfor selection of effective singular values in bearing fault signalde-noisingrdquo Applied Sciences vol 6 no 5 p 154 2016

[4] R Zhao R Yan J Wang and K Mao ldquoLearning to monitormachine health with convolutional Bi-directional LSTM net-worksrdquo Sensors vol 17 no 2 article no 273 2017

[5] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diagnosisofmonoblock centrifugal pump using wavelet analysisrdquoAppliedSoft Computing vol 12 no 8 pp 2023ndash2029 2012

[6] A Widodo and B Yang ldquoSupport vector machine in machinecondition monitoring and fault diagnosisrdquo Mechanical Systemsand Signal Processing vol 21 no 6 pp 2560ndash2574 2007

[7] J Yan and J Lee ldquoDegradation assessment and fault modes clas-sification using logistic regressionrdquo Journal of ManufacturingScience and Engineering vol 127 no 4 pp 912ndash914 2005

[8] Z Feng M Liang and F Chu ldquoRecent advances in time-frequency analysis methods for machinery fault diagnosis areview with application examplesrdquo Mechanical Systems andSignal Processing vol 38 no 1 pp 165ndash205 2013

[9] B A Paya and I I Esat ldquoArtificial neural networks based faultdiagnostics of rotatingmachinery using wavelet transforms as apreprocessorrdquoMechanical Systems and Signal Processing vol 11no 5 pp 751ndash765 1997

[10] K Patan and J Korbicz Artificial Neural Networks in FaultDiagnosis pp 333-379 Springer Berlin Germany 2004

[11] C Lu Z YWangW LQin and JMa ldquoFault diagnosis of rotarymachinery components using a stacked denoising autoencoder-based health state identificationrdquo Signal Processing vol 130 pp377ndash388 2017

[12] NKVermaVKGuptaM Sharma andRK Sevakula ldquoIntel-ligent condition based monitoring of rotating machines usingsparse auto-encodersrdquo in Proceedings of the 2013 IEEE Inter-national Conference on Prognostics and Health Management(PHM rsquo13) pp 1ndash7 IEEE Gaithersburg MD USA June 2013


[13] P Tamilselvan and PWang ldquoFailure diagnosis using deep belieflearning based health state classificationrdquoReliability Engineeringamp System Safety vol 115 no 7 pp 124ndash135 2013

[14] M Gan C Wang and C Zhu ldquoConstruction of hierarchicaldiagnosis network based on deep learning and its application inthe fault pattern recognition of rolling element bearingsrdquoMech-anical Systems and Signal Processing vol 72 no 2 pp 92ndash1042016

[15] O Janssens V Slavkovikj B Vervisch et al ldquoConvolutionalneural network based fault detection for rotating machineryrdquoJournal of Sound and Vibration vol 377 pp 331ndash345 2016

[16] X Guo L Chen and C Shen ldquoHierarchical adaptive deep con-volution neural network and its application to bearing faultdiagnosisrdquoMeasurement vol 93 pp 490ndash502 2016

[17] Y Bengio and Y Lecun ldquoScaling learning algorithms towardsAIrdquo Large-Scale Kernel Machines pp 321ndash359 2007

[18] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural networksa promising tool for fault characteristic mining and intelligentdiagnosis of rotating machinery with massive datardquoMechanicalSystems and Signal Processing vol 72-73 pp 303ndash315 2016

[19] L Guo H Gao H Huang X He and S Li ldquoMultifeaturesfusion and nonlinear dimension reduction for intelligent bear-ing condition monitoringrdquo Shock and Vibration vol 2016Article ID 4632562 10 pages 2016

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

[21] J Tan W Lu J An and X Wan ldquoFault diagnosis method studyin roller bearing based on wavelet transform and stacked auto-encoderrdquo inProceedings of the 27thChinese Control andDecisionConference CCDC 2015 pp 4608ndash4613 IEEE May 2015

[22] F Jia Y Lei L Guo J Lin and S Xing ldquoA neural networkconstructed by deep learning technique and its application tointelligent fault diagnosis of machinesrdquo Neurocomputing vol272 pp 619ndash628 2018

[23] G Hinton N Srivastava A Krizhevsky I Sutskever and RSalakhutdinov ldquoImproving neural networks by preventing co-adaptation of feature detectorsrdquo 2012 httpsarxivorgabs12070580

[24] W Li S Zhang and G He ldquoSemisupervised distance-pre-serving self-organizing map for machine-defect detection andclassificationrdquo IEEE Transactions on Instrumentation and Mea-surement vol 62 no 5 pp 869ndash879 2013

[25] WDu J Tao Y Li andC Liu ldquoWavelet leadersmultifractal fea-tures based fault diagnosis of rotating mechanismrdquoMechanicalSystems and Signal Processing vol 43 no 1-2 pp 57ndash75 2014

[26] J S Lin and Q Chen ldquoFault diagnosis of rolling bearings basedonmultifractal detrended fluctuation analysis andMahalanobisdistance criterionrdquo Mechanical Systems and Signal Processingvol 38 no 2 pp 515ndash533 2013

[27] X Lou andK Loparo ldquoBearing fault diagnosis based onwavelettransform and fuzzy inferencerdquo Mechanical Systems and SignalProcessing vol 18 no 5 pp 1077ndash1095 2004

[28] S Wang and C Manning ldquoFast dropout trainingrdquo in Pro-ceedings of the International Conference on Machine LearningJMLRorg p 118 2013

[29] X Jiang S Li and Y Wang ldquoA novel method for self-adaptivefeature extraction using scaling crossover characteristics ofsignals and combining with LS-SVM for multi-fault diagnosisof gearboxrdquo Journal of Vibroengineering vol 17 no 4 pp 1861ndash1878 2015

[30] J Wang S Li X Jiang and C Cheng ldquoAn automatic featureextraction method and its application in fault diagnosisrdquo Jour-nal of Vibroengineering vol 19 no 4 pp 2521ndash2533 2017

[31] J Wang X Jiang S Li and Y Xin ldquoA novel feature represen-tation method based on deep neural networks for gear faultdiagnosisrdquo in Proceedings of the 2017 Prognostics and SystemHealth Management Conference (PHM-Harbin) pp 1ndash6 IEEEHarbin China July 2017

[32] X Jiang S Li and Y Wang ldquoStudy on nature of crossover phe-nomena with application to gearbox fault diagnosisrdquoMechani-cal Systems and Signal Processing vol 83 pp 272ndash295 2017

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machine (RBM) [13 14] and convolutional neural networks(CNN) [15 16] Compared with traditional methods deeplearning methods do not need human labor and expertknowledge for feature extraction All the hyperparameters inmodel training and pattern classification modules are able tobe trained jointly Therefore deep learning can be employedto address machinery fault diagnosis in a very general way

As one of the widely used deep learning techniquesstacked autoencoders (SAEs) have attracted considerableattention in fault diagnosis It has been investigated as acommon component of DNN by Bengio et al [17] Jia et al[18] proposed a SAEs based DNNs for roller bearing andplanetary gearbox fault diagnosis with input as frequencyspectra after Fourier transform Guo et al [19] employedmultidomain statistical features of the raw vibration signalsas the input of SAEs which can be viewed as a kind of featurefusion Liu et al [20] fed the normalized spectrograms createdby STFT into SAEs for rolling bearing fault diagnosis In thework presented in [21] the nonlinear soft threshold approachand digital wavelet frame were used to process the measuredsignal and then fed into SAEs for rotating machinery diag-nosis Jia et al [22] constructed a local connection networkbased on normalized sparse autoencoder and L1 norm wasemployed to find sparse features

Inspired by the prior researches a new framework basedon SAEs is proposed to resolve the gearbox fault diagnosisFurthermore to overcome the deficiency of overfitting prob-lem in the training process and improve the performancefor small training set dropout technique [23] and ReLUactivation function are introduced into SAEs Rest of thepaper is organized as follows Section 2 briefly introduces thealgorithms of SAEs dropout and ReLU activation functionSection 3 is dedicated to detailing the content of the proposedmethod In Section 4 the multifault gearbox dataset isadopted to validate the effectiveness of the proposedmethodFurthermore the superiority of the proposed method isexhibited by comparing with the other traditional methodsFinally some conclusions are drawn in Section 5

2 Theoretical Background

21 Stacked Autoencoders Autoencoder is a kind of unsuper-vised learning structure that owns three layers input layerhidden layer and output layer as shown in Figure 1 Theprocess of an autoencoder training consists of two partsencoder and decoder Encoder is used for mapping the inputdata into hidden representation and decoder is referred toreconstructing input data from the hidden representationGiven the unlabeled input dataset xnNn=1 where xn isin R

mtimes1hn represents the hidden encoder vector calculated from xnand xn is the decoder vector of the output layer Hence theencoding process is as follows

hn = f (W1xn + b1) (1)

where f is the encoding function W1 is the weight matrix ofthe encoder and b1 is the bias vector

The decoder process is defined as follows

xn = g (W2hn + b2) (2)

where g is the decoding function W2 is the weight matrix ofthe decoder and b2 is the bias vector

The parameter sets of the autoencoder are optimized tominimize the reconstruction error

120601 (Θ) = argmin1205791205791015840

1n

nsumi=1L (xi xi) (3)

where L represents a loss function L(x x) = x minus x2As shown in Figure 2 the structure of SAEs is stacking n

autoencoders into n hidden layers by an unsupervised layer-wise learning algorithm and then fine-tuned by a supervisedmethod So the SAEs based method can be divided into threesteps(1) Train the first autoencoder by input data and obtain

the learned feature vector(2)The feature vector of the former layer is used as the

input for the next layer and this procedure is repeated untilthe training completes(3) After all the hidden layers are trained backpropaga-

tion algorithm (BP) is used tominimize the cost function andupdate the weights with labeled training set to achieve fine-tuning

22 Dropout Dropout is an effective strategy that has beenproved to reduce overfitting in the training process of neuralnetworks The overfitting problem always happens when thetraining set is small which would result in a low accuracy onthe test set Dropout can randomly affect the neurons of thehidden layer to lose power in the training process as shownin Figure 3 but the weights of those neurons are preservedFurthermore the neurons can recover to work when the nextsample is input Technically dropout is able to be achieved bysetting the output date of some hidden neurons to 0 and thenthese neurons cannot be related to the forward propagationprocess Many researches have tested the effect of dropouton reducing the overfitting problem for the small trainingset [28] and this paper will also employ it to enhance thefeature extraction ability and classification accuracy of SAEsfor multifault gearbox fault diagnosis

23 ReLU For traditional activation functions (sigmoidand hyperbolic tangent functions) the gradients decreasequickly with training error propagating to forward layersTherectified linear units (ReLU) activation function has receivedextensive attention in recent years since its gradient will notdecrease with the independent variables increasing So thenetwork with ReLU does not suffer from gradient diffusionor vanishing The ReLU function is shown in (4) and thestructure is displayed in Figure 4

fr (x) = max (0 x) (4)

3 Proposed Framework

This section details the proposed intelligent fault diagnosismethod In the method SAEs are combined with dropoutto achieve multifault gearbox fault diagnosis The frameworkand illustration of the proposed method are displayed in Fig-ure 5 SAEs combinedwith dropoutmodel are applied to train


Input layer

Output layer

Encoder

Decoder

Hidden layer


Hidden layer 1

AE3

AE2

AE1

Hidden layer 2

Hidden layer 3

Classifier

Input layer

Stack

Fine-fun








0

1

2

3



Data acquisition

Classifier

Input layer

Hidden layer 1

Hidden layer 2

Dropout

FFT

BP

AE1

AE2

3

2

1








4 Experiments








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20 30 40 50 60 70 80 90 10010


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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

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200

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de

01 02 03 04 05 060Time (s)

0246

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(a)

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200

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01 02 03 04 05 060Time (s)

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1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

times 104

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0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

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0

500

Am

plitu

de

01 02 03 04 05 060Time (s)

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

02468

(d)




98

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99

995

100

Accu

racy

()



1

2

3

4

Hea

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bel

50 100 150 200 250 3000Sample number


NCSW

MWBT

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0

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30

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Acknowledgments


References









































Journal of












Journal of







Volume 2018






Volume 2018









Input layer

Output layer

Encoder

Decoder

Hidden layer


Hidden layer 1

AE3

AE2

AE1

Hidden layer 2

Hidden layer 3

Classifier

Input layer

Stack

Fine-fun








0

1

2

3



Data acquisition

Classifier

Input layer

Hidden layer 1

Hidden layer 2

Dropout

FFT

BP

AE1

AE2

3

2

1








4 Experiments








Three-phase motor

Tooth-shaped belt


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20

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0

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Sample 1

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0

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0

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200 300 400 500100

200 300 400 500100

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90

92

94

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100

Aver

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()

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992

994

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998

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racy

()





50 100 150 200 250 300 350 400 450 5000Sample number

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10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Type-1

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20 30 40 50 60 70 80 90 10010


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0102

10 20 30 40 50 60 70 80 90 1000

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10 20 30 40 50 60 70 80 90 1000

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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

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200

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plitu

de

01 02 03 04 05 060Time (s)

0246

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(a)

times 104

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200

Am

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de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

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1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

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0

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01 02 03 04 05 060Time (s)

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02468

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Acknowledgments


References









































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Journal of







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Volume 2018









0

1

2

3



Data acquisition

Classifier

Input layer

Hidden layer 1

Hidden layer 2

Dropout

FFT

BP

AE1

AE2

3

2

1








4 Experiments








Three-phase motor

Tooth-shaped belt


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20

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0

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2


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92

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100

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age a

ccur

acy

()

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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

minus2000

200

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plitu

de

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0246

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(a)

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200

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(b)

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1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

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Am

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01 02 03 04 05 060Time (s)

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02468

(d)




98

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99

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100

Accu

racy

()



1

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Hea

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bel

50 100 150 200 250 3000Sample number


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ensio

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Data Availability




Acknowledgments


References









































Journal of












Journal of







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Volume 2018












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()

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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

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(a)

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1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

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plitu

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02468

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98

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99

995

100

Accu

racy

()



1

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3

4

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bel

50 100 150 200 250 3000Sample number


NCSW

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0

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ensio

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Acknowledgments


References









































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Journal of







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Volume 2018









90

92

94

96

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100

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age a

ccur

acy

()

01 02 03 04 05 06 070Dropout rate



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992

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998

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Accu

racy

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50 100 150 200 250 300 350 400 450 5000Sample number

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10 20 30 40 50 60 70 80 90 100

Type-1

Type-2

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20 30 40 50 60 70 80 90 10010


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10 20 30 40 50 60 70 80 90 1000

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Type-4

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Type-2

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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

minus2000

200

Am

plitu

de

01 02 03 04 05 060Time (s)

0246

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(a)

times 104

minus200

0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

times 104

minus200

0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

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0

500

Am

plitu

de

01 02 03 04 05 060Time (s)

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

02468

(d)




98

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99

995

100

Accu

racy

()



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bel

50 100 150 200 250 3000Sample number


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ensio

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Acknowledgments


References









































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Journal of







Volume 2018






Volume 2018











10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

10 20 30 40 50 60 70 80 90 100

Type-1

Type-2

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00102


20 30 40 50 60 70 80 90 10010


10 20 30 40 50 60 70 80 90 1000

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10 20 30 40 50 60 70 80 90 1000

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5 Conclusions



Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

minus2000

200

Am

plitu

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(a)

times 104

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0

200

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plitu

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01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

times 104

minus200

0

200

Am

plitu

de

01 02 03 04 05 060Time (s)

02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

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500

Am

plitu

de

01 02 03 04 05 060Time (s)

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

02468

(d)




98

985

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995

100

Accu

racy

()



1

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Hea

lth la

bel

50 100 150 200 250 3000Sample number


NCSW

MWBT

minus30

minus20

minus10

0

10

20

30

Dim

ensio

n 2




Data Availability




Acknowledgments


References









































Journal of












Journal of







Volume 2018






Volume 2018









Load Gearbox

Motor

ShockAbsorber

Tachometer

DataAcquisition

System

(a)

(b) (c)

X

ZY

(d)

Tested gear

Output

Input

24 teeth

29 teeth

(e)


times 104

minus2000

200

Am

plitu

de

01 02 03 04 05 060Time (s)

0246

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(a)

times 104

minus200

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plitu

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02468

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(b)

times 104

minus200

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200

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plitu

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01 02 03 04 05 060Time (s)

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1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

(c)

times 104

minus500

0

500

Am

plitu

de

01 02 03 04 05 060Time (s)

1000 2000 3000 4000 5000 6000 7000 80000Frequency (Hz)

02468

(d)




98

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Accu

racy

()



1

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Hea

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bel

50 100 150 200 250 3000Sample number


NCSW

MWBT

minus30

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ensio

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Data Availability




Acknowledgments


References









































Journal of












Journal of







Volume 2018






Volume 2018










98

985

99

995

100

Accu

racy

()



1

2

3

4

Hea

lth la

bel

50 100 150 200 250 3000Sample number


NCSW

MWBT

minus30

minus20

minus10

0

10

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Dim

ensio

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Data Availability




Acknowledgments


References









































Journal of












Journal of







Volume 2018






Volume 2018




































Journal of












Journal of







Volume 2018






Volume 2018








A Stacked Autoencoder-Based Deep Neural Network for Achieving Gearbox Fault Diagnosis · 2019. 7....

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Transcript of A Stacked Autoencoder-Based Deep Neural Network for Achieving Gearbox Fault Diagnosis · 2019. 7....