Research ArticleA Novel Method for Diagnosis of Bearing Fault UsingHierarchical Multitasks Convolutional Neural Networks

Yong-Zhi Liu 1 Yi-Sheng Zou 1 Yu-Liang Jiang1 Hui Yu 2 and Guo-Fu Ding1

1School of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China2School of Creative Technologies University of Portsmouth Portsmouth PO1 2DJ UK

Correspondence should be addressed to Yi-Sheng Zou zysappleswjtueducn

Received 3 June 2020 Revised 14 October 2020 Accepted 24 October 2020 Published 4 November 2020

Academic Editor M Z Naser

Copyright copy 2020 Yong-Zhi Liu 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

Intelligent mechanical fault diagnosis has developed very fast in recent years due to the advancement and application of deeplearning technologies us there are many deep learning network models that have been explored in fault classification anddiagnosis However there are still limitations in research on the relationship between fault location fault type and fault severityIn this paper a novel method for diagnosis of bearing fault using hierarchical multitask convolution neural networks (HMCNNs)is proposed taking into account the mentioned relationships e HMCNNmodel includes a main task and multiple subtasks Inthe HMCNNmodel a weighted probability is used to reduce the classification error propagation amongmultitasks to improve thefault diagnosis accuracy e validity of the proposed method is verified on bearing datasets Experimental results show that theproposed method is very effective and superior to the existing methods

1 Introduction

Rolling bearings as the key parts of mechanical equip-ment are widely used in rail transit equipment con-struction machinery precision machine toolsinstrumentation and other fields According to statisticsabout 40 of rotating machinery faults are caused bybearing faults Once bearing faults occur they will seri-ously affect the normal operation of equipment and theymay even cause accidents and economic losses ereforeit is necessary to diagnose and monitor bearing faultsbefore anything goes wrong [1 2] At present bearing faultdiagnosis is usually based on data-driven methods Bycollecting motor current signals or bearing vibrationsignals fault diagnosis methods are applied to completefault identification [3 4]

Data-driven fault diagnosis generally includes two stepsfault feature extraction and fault classification e commonmethods of feature extraction include Fast Fourier Trans-formation (FFT) [5] Wavelet Transform (WT) [6] Em-pirical Mode Decomposition (EMD) [7] Local MeanDecomposition (LMD) [8] and Variational Mode

Decomposition (VMD) [9] e common fault classificationalgorithms include support vector machine (SVM) [10] BPneural networks [11] Bayesian classifier [12] K-NearestNeighbor (KNN) [13] Random Forest (RF) [14] andClassification and Regression Tree (CART) [15] Seryasatet al [16] presented a diagnosis method based on wavelettransform and FFT to extract energy and root mean squareof different frequency bands which could accurately andeffectively identify bearing faults Yan and Jia [17] proposeda multidomain feature classification algorithm based onoptimized SVM which included three stages multidomainfeature extraction feature selection and fault recognitione algorithm has high diagnostic accuracy for rollingbearings under different working conditions Zhang et al[18] proposed a new method of rolling bearing fault diag-nosis based on Variational Mode Decomposition andcompared the performance of VMD and EMD in extractingbearing defect features from rolling bearing simulationsignals e VMD method can accurately extract the mainmode of bearing fault signal and is superior to EMD inbearing defect feature extraction Liu et al [19] presented afault diagnosis method for wind turbine bearings based on

HindawiShock and VibrationVolume 2020 Article ID 8846822 14 pageshttpsdoiorg10115520208846822

integral extension local mean decomposition (IELMD)which could effectively process nonstationary signalsKankar et al [20] extracted the statistical characteristics ofwavelet coefficients and completed the classification ofbearing faults combined with an artificial neural networkJiang et al [21] proposed a fault diagnosis method for rollingbearings based on high-order cumulant and BP neuralnetwork in view of the fact that the vibration signals ofrolling bearings were susceptible to the influence of Gaussiannoise

e basic steps of these traditional fault diagnosismethods can be summarized as follows acquiring faultsignals analyzing the characteristics of fault signalsextracting appropriate features and selecting appropriateclassifiers according to the specific diagnosis problems isprocess requires high professional knowledge and experi-ence of signal processing for fault diagnosis personnel Withthe development of modern industry fault monitoringequipment obtains a large amount of data and the data typesare diverse which brings great challenges to traditional faultdiagnosis methods

Deep learning has been widely used in recent years echaracteristic of the deep learning method is that it canautomatically complete the task of feature extraction andclassification [22] Deep learning has also been introducedinto the field of mechanical fault diagnosis to overcome theshortcomings of traditional methods recently Zhang et al[23ndash25] proposed a fault diagnosis method for rollingbearings based on deep convolution neural networks(CNN) which avoided manual feature extraction and re-alized automatic feature learning Shao et al [26] proposedan enhanced depth feature fusion method for fault diagnosisof rotating machinery A new depth autoencoder methodwas constructed by combining Denoising Autoencoder(DAE) with Contractive Autoencoder (CAE) to improve thelearning ability of features Jia et al [27] proposed a deepnormalized convolution neural networks (DNCNN) whichcould effectively deal with unbalanced classification prob-lems Liu et al [28] proposed an unsupervised fault diagnosismethod for rolling bearings based on the generativeadversarial networks is method has higher generalizationaccuracy under noisy and varied workload situations esedeep learning methods have been successfully applied tobearing fault diagnosis from different perspectives and ap-plication scenarios Compared with traditional methodsthey have higher diagnostic accuracy However the problemof low generalization ability of deep neural network modelremains unsolved

e fault diagnosis of bearing includes fault locationfault type and fault degree In the existing fault diagnosismethods all kinds of samples are generally used as trainingsamples of the training model to achieve fault diagnosis andthe relationship between them and the impact on the finalfault diagnosis results are less considered For the hierar-chical classification of deep learning Yan et al [29] firstproposed the hierarchical deep convolution neural networkmodel to classify images It first classifies the easily separatedclasses roughly and then classifies them at a fine level [28]Based on this idea Guo et al [30] andQu et al [31] proposed

a hierarchical intelligent fault diagnosis algorithm based onan adaptive deep convolution neural network model(ADCNN) which classified bearing fault location first andthen classified fault severity e design of this hierarchicalclassification model requires training multiple CNN rec-ognition models taking pretraining and fine-tuning It canthus lead to a cumbersome training process more trainingsamples interlayer error propagation and difficulty inmodel level expansion

erefore a hierarchical multitask bearing fault diag-nosis method based on the deep convolution neural net-works is proposed in this paper By adding multilearningtasks to the convolution neural network the multitaskslearning of bearing fault diagnosis is realized and thegeneralization performance of the proposed model is im-proved e main contributions of this paper are as follows

(1) Based on the CNN fault classification model theHMCNN model is formed by adding several relatedclassification tasks representing different dimensioninformation for parallel auxiliary diagnosis In theproposed model final classification results are ob-tained by fusing the classification results of the maintask and subtasks of different dimensions accordingto the weight obtained by training which can reducethe interlayer error propagation of tasks

(2) e proposed model can extract more valuablefeatures from fewer training samples for fault clas-sification and improve the classification accuracy ofthe model In the proposed model multiple tasks canshare network parameters and information and onlyone network structure needs to be trained that re-duced computational consumption and trainingcomplexity e parallel structure of multiple tasksalso has good scalability

e remainder of the paper is structured as follows estructure of the hierarchical multitask convolutional neuralnetwork (HMCNN) and some main techniques used inHMCNN is introduced in Section 2 In Section 3 experi-ments are carried out to prove that HMCNN has betterperformance than traditional intelligent methods and sometypical deep learning models After that the structure ofHMCNN model is extended to demonstrate its ability toextend Lastly the diagnostic results of HMCNN model arecompared with CNNmodel and analyzed visually to exploreits mechanism e conclusion of this paper is presented inSection 4

2 Proposed Method

In this paper a novel method called hierarchical multitaskconvolutional neural network (HMCNN) is proposed for theintelligent fault diagnosis of bearings e proposed modelincludes four parts CNN model hierarchical classifiersmultitask learning and hierarchical multitask convolutionalneural network e HMCNN model only needs to train anetwork model to realize multitask classification in whichthe sharing layer can reduce the number of network pa-rameters thereby reducing the computational load e

2 Shock and Vibration

multitask learning hierarchical classification and jointclassification layer design in the HMCNN model can im-prove network generalization ability More details are de-scribed in the following sections

21 Introduction to CNN Model Convolutional neuralnetwork (CNN) is a kind of feed-forward multistage neuralnetwork It mainly contains three kinds of layers con-volutional layer pooling layer and fully connected layereconvolution layer is designed to extract different features ofinput data e pooling layer following the convolutionallayer is to reduce the parameters of the network throughextracting the local mean or maximum value of input data Afully connected layer is usually built in the last part of thehidden layer of the convolutional neural network Its mainfunction is to connect all features and send the output valueto the classifier Convolutional neural network (CNN) is oneof the common deep learning models It is used to extractfeatures and classify vibration signals in bearing faultdiagnosis

22 Hierarchical Classification e main idea of hierar-chical fault diagnosis based on convolutional neural networkis proposed in this paper as shown in Figure 1 e mainstructure of hierarchical classification includes the sharinglayer coarse classification layer fine classification layer andjoint classification layer in which the sharing layer canreduce the number of network parameters and thus reducethe computation e coarse classification layer is mainlyused for coarse classification of bearing fault location suchas bearing recognition as health inner ring fault and outerring fault e fine classification is achieved through the fineclassification layer e joint classification layer which re-ceives fine classification results as well as coarse classificationresults produces a weighted probability as the final classi-fication results it can be described as follows

p xj1113872 1113873 1113944N

j1

pc xj1113872 1113873

1113936Ni1 pc xi( 1113857

pF xj1113872 1113873 (1)

where pc(xj) is the probability of coarse classification madeby the coarse classification layer pF(xj) is the fine classifi-cation made by the fine classification layer N is the numberof hierarchical tasks

e coarse classification layer fine classification layerand joint classification layer are all based on softmax clas-sification function for the final classification tasks In thisway the output of the network is transformed into aprobability distribution the softmax function is described asfollows

pcF xj1113872 1113873 softmax xj1113872 1113873 e

xj

1113936nk1 e

xk (2)

where zj is the logits of the j th output n is the number ofcategories

23 Multitask Learning In this paper bearing fault diag-nosis has multiple learning tasks such as fault location faulttype and fault severity From the perspective of machinelearning multitask learning can be regarded as inductivetransfer learning which can improve the learning perfor-mance of the model by using multiple related tasks in-cluding improving generalization accuracy learning speedand comprehensibility of the learning model In this paperthe related learning tasks are fault or fault location whichhelps the final classification of severity tasks of fault cate-gories In the training process of the model the joint trainingmethod is adopted which combines the loss functions ofmultiple tasks and carries out the optimization trainingtogether e loss function is described as

loss 1113944N

i1kilossi

lossi minus1m

1113944

m

k11113944

j

pj

k log qj

k

(3)

where ki is the coefficient lossi is the loss function for eachtask N is the number of hierarchical tasks m is the size oftrainingminibatch pj

k is the true predicted output value andq

j

k is the one-hot type vector with target distribution

24 Hierarchical Multitask Convolutional Neural Network(HMCNN) Model e HMCNN model is shown in Fig-ure 1 which consists of the following four parts

e first part is the sharing layer which consists of twomodules e two modules are composed of 2 convolutionlayers and 1 pooling layer e 3times1 size convolution kernelwith stride of 2 is used in all convolutional layers Forpooling layers the 8times1 sized max-pooling with the stride of8 is done

e second part is the coarse classification layer which isconnected to the shared layer It consists of 2 full connectionlayers and 1 softmax layer which are used to complete theclassification of bearing fault location fault type and faultseverity

e third part is the fine classification layer which isconnected to the shared layer and consists of 3 convolutionlayers 1 pooling layer 2 full connection layers and 1softmax layer It is used to complete the fine classification ofbearing fault

e fourth part is the joint classification layer whichreceives fine classification results as well as coarse classifi-cation results and produces a weighted probability as thefinal classification results e HMCNN model trainingparameters are shown in Table 1

3 Experimental Verification

31 Data Description Experimental data were collectedfrom the bearing test rig of Paderborn University in Ger-many [32] e experimental data were obtained by the testrig for condition monitoring of rolling bearings e test rigconsisted of several modules an electric motor (1) a torque-

Shock and Vibration 3

measurement shaft (2) a rolling bearing test module (3) aflywheel (4) and a load motor (5) as shown in Figure 2

e test bearing was ball bearings of type 6203 Bearingsare run at a rotational speed of 900 rpm with a load torque of07Nm and a radial force on the bearing of 1000N efrequency of the data acquisition system is 64 kHz ebearing temperature was kept roughly at 45ndash50degC reekinds of bearing states are used in this experiment inner ringdamage outer ring damage and healthy e detailed sit-uation of data is shown in Table 2 In Table 2 the bearingfault location damage method and fault severity are listedFor fault location H is the bearing with no fault IR is thebearing with an inner race fault and OR is the bearing withan outer race fault e damage methods of bearing areshown in Figure 3 e bearing damage used in this paperwas caused by three different methods electric discharge

machining (trench of 025mm length in rolling directionand depth of 1-2mm) drilling (diameter 09mm 2mmand 3mm) and manual electric engraving (damage lengthfrom 1 to 4mm)

As described in the document of the dataset eachbearing acquired 20 original vibration time-series signalseach of which recorded about 256000 data points In thisexperiment the 2048 data points were used to construct asample For each health condition of bearings 2000 sampleswere used in the training set and 500 samples were used inthe test set e vibration signals of each health state areshown in Figure 4 e experimental data are normalized bymaximum and minimum normalization and the normali-zation formula is as follows

xlowast

xi minus xmin

xmax minus xmin (4)

where xi is the value of the i-th point of sample data xmax isthe maximum value of sample data xmin is the minimumvalue of sample data

In this paper the proposed model is based on tensorflowdeep learning frameworke experiment was completed ona computer with CPU i7 8700 16GB memory and NVIDIAGTX 1070 GPU

32 Diagnosis Results of HMCNN e experiments are di-vided into three parts e first part is a comparison amongthe proposed model traditional method and intelligentalgorithm based on deep learning to demonstrate the su-periority of the proposed model in terms of generalizationperformance e second part is to extend and compare the

3

1

times32

Finalclassification

result

Filters Filters

Coarseprediction 3

3

1

times128

Coarseprediction 2

Sharedlayer

Fineclassification

layer

Fineprediction

Coarseclassification 3

Coarseclassification 2

Coarseclassification 1

Coarseprediction 1

Jointclassification

layer Input

Figure 1 Hierarchical multitasks convolutional neural network (HMCNN) model

Table 1 e HMCNN training parameters

Learning rate Training steps Batch size Optimizer0001 20000 256 Adam

(1) (2) (3) (4) (5)

Figure 2 Test rig for condition monitoring of rolling bearings

4 Shock and Vibration

network structure of the proposed model to verify the ef-fectiveness of multitask learning e third part is a com-parison between the proposed model (HMCNN) andADCNN model studies the propagation of errors betweenmodel levels and analyzes the reasons for the high recog-nition accuracy of the proposed model

321 5e Comparative Analysis of HMCNN Model withOther Models In the first part the proposed model(HMCNN) is compared with the commonly used fault di-agnosis models such as support vector machine (SVM)backpropagation neural networks (BPNN) convolutionalneural networks (CNN) and long short-term memory(LSTM) e inputs of SVM and BPNN are multidimen-sional features extracted after ensemble empirical modedecomposition e inputs of CNN LSTM and HMCNNmethods are normalized original signals Experimentalcomparison results are shown in Figure 4 From Figure 5 itcan be seen that the classification accuracy of traditionalmodels such as SVM and DNN is less than 80 while theclassification accuracy of deep learning model such as CNNand LSTM is about 90 e bearing fault diagnosis ac-curacy of HMCNN model reaches 997 Compared withtraditional bearing fault diagnosis models it does not needto extract features has higher diagnosis accuracy and hasbetter generalization ability than the current deep learningmodels

e HMCNN model and CNN model are also comparedand analyzed e CNN and HMCNN models use the sameoptimizationmethod and training parameters in this papereaccuracy of per 50 steps in HMCNN and CNNmodel is shownin Figure 6 Figure 6 shows that the bearing fault diagnosisaccuracy of HMCNNmodel is 997 and that of CNNmodel is921 Compared with CNN model HMCNN not only hashigher bearing fault diagnosis accuracy but also has fewertraining steps to achieve the highest diagnosis accuracy econfusion matrix of experimental results is compared as shownin Figure 7 From Figure 7 compared with CNN modelHMCNN model mainly reduces the confusion degree betweenouter ring bearing faults so as to improve the diagnosis ac-curacy of bearing faults

In the training processes the learning speed of HMCNNmodel and CNN model is compared as shown in Figure 8e convergence rate (learning speed) of HMCNN model isabout twice that of CNN model

In order to further verify the generalization performance ofHMCNNmodel the diagnosis accuracy of HMCNNwith othermodels under different training sets is also compared here ecomparison results are shown in Table 3 and Figure 9 As thenumber of training samples decreases the recognition accuracyof all methods decreases to varying degrees From Table 4 it canbe seen that theHMCNNmodel has better recognition accuracyin fewer training sets and the recognition accuracy can reach967 in the case of only 500 training samples

In addition the performance differences betweenHMCNNmodel and SVM BPNN CNN and LSTM model under noiseare compared Comparison results are shown in Table 3 andFigure 10 It can be seen that the diagnosis accuracy ofHMCNN is 991 in noise environment (SNR 10dB) whilethe diagnosis accuracy of other models is not more than 90At the same time the diagnosis accuracy of HMCNNmodel innoise environment (SNR minus2dB) is more than 90 SoHMCNN has good antinoise performance

322 5e Comparative Analysis of HMCNN with DifferentTasks Numbers In the second part we study and analyze therelationship between the hierarchical tasksrsquo number ofHMCNNmodel and its diagnosis accuracy According to thedataset the HMCNN model is used to learn one two andthree classification tasks (bearing fault location fault typeand fault severity) which are named HMCNN1 HMCNN2and HMCNN3 respectively e comparison results areshown in Figures 11 and 12 e results show that bothHMCNN3 and HMCNN2 model can achieve a high diag-nosis accuracy e accuracy of HMCNN2 model is 08higher than that of HMCNN1 model Compared with CNNHMCNN contributes more to the accuracy improvement byadding the task of bearing fault location In HMCNN3model the diagnosis accuracy of fault type reaches 997which shows that the task of bearing fault position faulttype and fault severity diagnosis is effective and feasible andthe final diagnosis accuracy is improved to a certain extent

Table 2 Situation of damaged bearings

Bearing code K001 KA03 KA07 KA08 KI01 KI03 KI07Fault location H OR OR OR IR IR IRDamage method No fault Electric engrave Drilling Drilling EDM Electric engraver Electric engraverFault severity 0 2 1 2 1 1 2

(a) (b) (c)

Figure 3 e methods of bearing damage (a) EDM (b) drilling and (c) electric engraver

Shock and Vibration 5

e comparison between HMCNN1 HMCNN2 andHMCNN3 models proves that the proposed model can beextended to diagnosis multiple tasks In practical applica-tion the location type and severity of bearing fault can beoutput in HMCNN model which provides more detailedguidance for fault maintenance

323 5e Comparative Analysis of HMCNN Model withADCNN Model In the third part the ADCNN model pro-posed by Guo et al [30] is compared with HMCNNmodeleidea of ADCNNmodel for bearing fault diagnosis is to identify

the location of bearing fault first and then identify the faultseverity of each location of bearing on this basis Accuracyresults of ADCNN and HMCNNmodels for diagnosis bearingfault locations and final fault severity are shown in Tables 5 and6 respectively We can see that the ADCNN modelrsquos hierar-chical diagnosis of the bearing will make the error of bearingfault location diagnosis spread to the result of bearing faultseverity diagnosis and the more the number of tasks the moreserious the error propagationeHMCNNmodel has a sharedlayer and a weighted joint classification layer which can solvethe problem of error propagation and make the model morescalable

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(a)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(b)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(c)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(d)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(e)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(f )1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(g)

Figure 4 Vibration signals for each health condition of bearings (a) K001 (b) KA03 (c) KA07 (d) KA08 (e) KI01 (f ) KI03 and (g) KI07

6 Shock and Vibration

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

multitask learning hierarchical classification and jointclassification layer design in the HMCNN model can im-prove network generalization ability More details are de-scribed in the following sections

21 Introduction to CNN Model Convolutional neuralnetwork (CNN) is a kind of feed-forward multistage neuralnetwork It mainly contains three kinds of layers con-volutional layer pooling layer and fully connected layereconvolution layer is designed to extract different features ofinput data e pooling layer following the convolutionallayer is to reduce the parameters of the network throughextracting the local mean or maximum value of input data Afully connected layer is usually built in the last part of thehidden layer of the convolutional neural network Its mainfunction is to connect all features and send the output valueto the classifier Convolutional neural network (CNN) is oneof the common deep learning models It is used to extractfeatures and classify vibration signals in bearing faultdiagnosis

22 Hierarchical Classification e main idea of hierar-chical fault diagnosis based on convolutional neural networkis proposed in this paper as shown in Figure 1 e mainstructure of hierarchical classification includes the sharinglayer coarse classification layer fine classification layer andjoint classification layer in which the sharing layer canreduce the number of network parameters and thus reducethe computation e coarse classification layer is mainlyused for coarse classification of bearing fault location suchas bearing recognition as health inner ring fault and outerring fault e fine classification is achieved through the fineclassification layer e joint classification layer which re-ceives fine classification results as well as coarse classificationresults produces a weighted probability as the final classi-fication results it can be described as follows

p xj1113872 1113873 1113944N

j1

pc xj1113872 1113873

1113936Ni1 pc xi( 1113857

pF xj1113872 1113873 (1)

where pc(xj) is the probability of coarse classification madeby the coarse classification layer pF(xj) is the fine classifi-cation made by the fine classification layer N is the numberof hierarchical tasks

e coarse classification layer fine classification layerand joint classification layer are all based on softmax clas-sification function for the final classification tasks In thisway the output of the network is transformed into aprobability distribution the softmax function is described asfollows

pcF xj1113872 1113873 softmax xj1113872 1113873 e

xj

1113936nk1 e

xk (2)

where zj is the logits of the j th output n is the number ofcategories

23 Multitask Learning In this paper bearing fault diag-nosis has multiple learning tasks such as fault location faulttype and fault severity From the perspective of machinelearning multitask learning can be regarded as inductivetransfer learning which can improve the learning perfor-mance of the model by using multiple related tasks in-cluding improving generalization accuracy learning speedand comprehensibility of the learning model In this paperthe related learning tasks are fault or fault location whichhelps the final classification of severity tasks of fault cate-gories In the training process of the model the joint trainingmethod is adopted which combines the loss functions ofmultiple tasks and carries out the optimization trainingtogether e loss function is described as

loss 1113944N

i1kilossi

lossi minus1m

1113944

m

k11113944

j

pj

k log qj

k

(3)

where ki is the coefficient lossi is the loss function for eachtask N is the number of hierarchical tasks m is the size oftrainingminibatch pj

k is the true predicted output value andq

j

k is the one-hot type vector with target distribution

24 Hierarchical Multitask Convolutional Neural Network(HMCNN) Model e HMCNN model is shown in Fig-ure 1 which consists of the following four parts

e first part is the sharing layer which consists of twomodules e two modules are composed of 2 convolutionlayers and 1 pooling layer e 3times1 size convolution kernelwith stride of 2 is used in all convolutional layers Forpooling layers the 8times1 sized max-pooling with the stride of8 is done

e second part is the coarse classification layer which isconnected to the shared layer It consists of 2 full connectionlayers and 1 softmax layer which are used to complete theclassification of bearing fault location fault type and faultseverity

e third part is the fine classification layer which isconnected to the shared layer and consists of 3 convolutionlayers 1 pooling layer 2 full connection layers and 1softmax layer It is used to complete the fine classification ofbearing fault

e fourth part is the joint classification layer whichreceives fine classification results as well as coarse classifi-cation results and produces a weighted probability as thefinal classification results e HMCNN model trainingparameters are shown in Table 1

3 Experimental Verification

31 Data Description Experimental data were collectedfrom the bearing test rig of Paderborn University in Ger-many [32] e experimental data were obtained by the testrig for condition monitoring of rolling bearings e test rigconsisted of several modules an electric motor (1) a torque-

Shock and Vibration 3

measurement shaft (2) a rolling bearing test module (3) aflywheel (4) and a load motor (5) as shown in Figure 2

e test bearing was ball bearings of type 6203 Bearingsare run at a rotational speed of 900 rpm with a load torque of07Nm and a radial force on the bearing of 1000N efrequency of the data acquisition system is 64 kHz ebearing temperature was kept roughly at 45ndash50degC reekinds of bearing states are used in this experiment inner ringdamage outer ring damage and healthy e detailed sit-uation of data is shown in Table 2 In Table 2 the bearingfault location damage method and fault severity are listedFor fault location H is the bearing with no fault IR is thebearing with an inner race fault and OR is the bearing withan outer race fault e damage methods of bearing areshown in Figure 3 e bearing damage used in this paperwas caused by three different methods electric discharge

machining (trench of 025mm length in rolling directionand depth of 1-2mm) drilling (diameter 09mm 2mmand 3mm) and manual electric engraving (damage lengthfrom 1 to 4mm)

As described in the document of the dataset eachbearing acquired 20 original vibration time-series signalseach of which recorded about 256000 data points In thisexperiment the 2048 data points were used to construct asample For each health condition of bearings 2000 sampleswere used in the training set and 500 samples were used inthe test set e vibration signals of each health state areshown in Figure 4 e experimental data are normalized bymaximum and minimum normalization and the normali-zation formula is as follows

xlowast

xi minus xmin

xmax minus xmin (4)

where xi is the value of the i-th point of sample data xmax isthe maximum value of sample data xmin is the minimumvalue of sample data

In this paper the proposed model is based on tensorflowdeep learning frameworke experiment was completed ona computer with CPU i7 8700 16GB memory and NVIDIAGTX 1070 GPU

32 Diagnosis Results of HMCNN e experiments are di-vided into three parts e first part is a comparison amongthe proposed model traditional method and intelligentalgorithm based on deep learning to demonstrate the su-periority of the proposed model in terms of generalizationperformance e second part is to extend and compare the

3

1

times32

Finalclassification

result

Filters Filters

Coarseprediction 3

3

1

times128

Coarseprediction 2

Sharedlayer

Fineclassification

layer

Fineprediction

Coarseclassification 3

Coarseclassification 2

Coarseclassification 1

Coarseprediction 1

Jointclassification

layer Input

Figure 1 Hierarchical multitasks convolutional neural network (HMCNN) model

Table 1 e HMCNN training parameters

Learning rate Training steps Batch size Optimizer0001 20000 256 Adam

(1) (2) (3) (4) (5)

Figure 2 Test rig for condition monitoring of rolling bearings

4 Shock and Vibration

network structure of the proposed model to verify the ef-fectiveness of multitask learning e third part is a com-parison between the proposed model (HMCNN) andADCNN model studies the propagation of errors betweenmodel levels and analyzes the reasons for the high recog-nition accuracy of the proposed model

321 5e Comparative Analysis of HMCNN Model withOther Models In the first part the proposed model(HMCNN) is compared with the commonly used fault di-agnosis models such as support vector machine (SVM)backpropagation neural networks (BPNN) convolutionalneural networks (CNN) and long short-term memory(LSTM) e inputs of SVM and BPNN are multidimen-sional features extracted after ensemble empirical modedecomposition e inputs of CNN LSTM and HMCNNmethods are normalized original signals Experimentalcomparison results are shown in Figure 4 From Figure 5 itcan be seen that the classification accuracy of traditionalmodels such as SVM and DNN is less than 80 while theclassification accuracy of deep learning model such as CNNand LSTM is about 90 e bearing fault diagnosis ac-curacy of HMCNN model reaches 997 Compared withtraditional bearing fault diagnosis models it does not needto extract features has higher diagnosis accuracy and hasbetter generalization ability than the current deep learningmodels

e HMCNN model and CNN model are also comparedand analyzed e CNN and HMCNN models use the sameoptimizationmethod and training parameters in this papereaccuracy of per 50 steps in HMCNN and CNNmodel is shownin Figure 6 Figure 6 shows that the bearing fault diagnosisaccuracy of HMCNNmodel is 997 and that of CNNmodel is921 Compared with CNN model HMCNN not only hashigher bearing fault diagnosis accuracy but also has fewertraining steps to achieve the highest diagnosis accuracy econfusion matrix of experimental results is compared as shownin Figure 7 From Figure 7 compared with CNN modelHMCNN model mainly reduces the confusion degree betweenouter ring bearing faults so as to improve the diagnosis ac-curacy of bearing faults

In the training processes the learning speed of HMCNNmodel and CNN model is compared as shown in Figure 8e convergence rate (learning speed) of HMCNN model isabout twice that of CNN model

In order to further verify the generalization performance ofHMCNNmodel the diagnosis accuracy of HMCNNwith othermodels under different training sets is also compared here ecomparison results are shown in Table 3 and Figure 9 As thenumber of training samples decreases the recognition accuracyof all methods decreases to varying degrees From Table 4 it canbe seen that theHMCNNmodel has better recognition accuracyin fewer training sets and the recognition accuracy can reach967 in the case of only 500 training samples

In addition the performance differences betweenHMCNNmodel and SVM BPNN CNN and LSTM model under noiseare compared Comparison results are shown in Table 3 andFigure 10 It can be seen that the diagnosis accuracy ofHMCNN is 991 in noise environment (SNR 10dB) whilethe diagnosis accuracy of other models is not more than 90At the same time the diagnosis accuracy of HMCNNmodel innoise environment (SNR minus2dB) is more than 90 SoHMCNN has good antinoise performance

322 5e Comparative Analysis of HMCNN with DifferentTasks Numbers In the second part we study and analyze therelationship between the hierarchical tasksrsquo number ofHMCNNmodel and its diagnosis accuracy According to thedataset the HMCNN model is used to learn one two andthree classification tasks (bearing fault location fault typeand fault severity) which are named HMCNN1 HMCNN2and HMCNN3 respectively e comparison results areshown in Figures 11 and 12 e results show that bothHMCNN3 and HMCNN2 model can achieve a high diag-nosis accuracy e accuracy of HMCNN2 model is 08higher than that of HMCNN1 model Compared with CNNHMCNN contributes more to the accuracy improvement byadding the task of bearing fault location In HMCNN3model the diagnosis accuracy of fault type reaches 997which shows that the task of bearing fault position faulttype and fault severity diagnosis is effective and feasible andthe final diagnosis accuracy is improved to a certain extent

Table 2 Situation of damaged bearings

Bearing code K001 KA03 KA07 KA08 KI01 KI03 KI07Fault location H OR OR OR IR IR IRDamage method No fault Electric engrave Drilling Drilling EDM Electric engraver Electric engraverFault severity 0 2 1 2 1 1 2

(a) (b) (c)

Figure 3 e methods of bearing damage (a) EDM (b) drilling and (c) electric engraver

Shock and Vibration 5

e comparison between HMCNN1 HMCNN2 andHMCNN3 models proves that the proposed model can beextended to diagnosis multiple tasks In practical applica-tion the location type and severity of bearing fault can beoutput in HMCNN model which provides more detailedguidance for fault maintenance

323 5e Comparative Analysis of HMCNN Model withADCNN Model In the third part the ADCNN model pro-posed by Guo et al [30] is compared with HMCNNmodeleidea of ADCNNmodel for bearing fault diagnosis is to identify

the location of bearing fault first and then identify the faultseverity of each location of bearing on this basis Accuracyresults of ADCNN and HMCNNmodels for diagnosis bearingfault locations and final fault severity are shown in Tables 5 and6 respectively We can see that the ADCNN modelrsquos hierar-chical diagnosis of the bearing will make the error of bearingfault location diagnosis spread to the result of bearing faultseverity diagnosis and the more the number of tasks the moreserious the error propagationeHMCNNmodel has a sharedlayer and a weighted joint classification layer which can solvethe problem of error propagation and make the model morescalable

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(a)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(b)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(c)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(d)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(e)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(f )1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(g)

Figure 4 Vibration signals for each health condition of bearings (a) K001 (b) KA03 (c) KA07 (d) KA08 (e) KI01 (f ) KI03 and (g) KI07

6 Shock and Vibration

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

measurement shaft (2) a rolling bearing test module (3) aflywheel (4) and a load motor (5) as shown in Figure 2

e test bearing was ball bearings of type 6203 Bearingsare run at a rotational speed of 900 rpm with a load torque of07Nm and a radial force on the bearing of 1000N efrequency of the data acquisition system is 64 kHz ebearing temperature was kept roughly at 45ndash50degC reekinds of bearing states are used in this experiment inner ringdamage outer ring damage and healthy e detailed sit-uation of data is shown in Table 2 In Table 2 the bearingfault location damage method and fault severity are listedFor fault location H is the bearing with no fault IR is thebearing with an inner race fault and OR is the bearing withan outer race fault e damage methods of bearing areshown in Figure 3 e bearing damage used in this paperwas caused by three different methods electric discharge

machining (trench of 025mm length in rolling directionand depth of 1-2mm) drilling (diameter 09mm 2mmand 3mm) and manual electric engraving (damage lengthfrom 1 to 4mm)

As described in the document of the dataset eachbearing acquired 20 original vibration time-series signalseach of which recorded about 256000 data points In thisexperiment the 2048 data points were used to construct asample For each health condition of bearings 2000 sampleswere used in the training set and 500 samples were used inthe test set e vibration signals of each health state areshown in Figure 4 e experimental data are normalized bymaximum and minimum normalization and the normali-zation formula is as follows

xlowast

xi minus xmin

xmax minus xmin (4)

where xi is the value of the i-th point of sample data xmax isthe maximum value of sample data xmin is the minimumvalue of sample data

In this paper the proposed model is based on tensorflowdeep learning frameworke experiment was completed ona computer with CPU i7 8700 16GB memory and NVIDIAGTX 1070 GPU

32 Diagnosis Results of HMCNN e experiments are di-vided into three parts e first part is a comparison amongthe proposed model traditional method and intelligentalgorithm based on deep learning to demonstrate the su-periority of the proposed model in terms of generalizationperformance e second part is to extend and compare the

3

1

times32

Finalclassification

result

Filters Filters

Coarseprediction 3

3

1

times128

Coarseprediction 2

Sharedlayer

Fineclassification

layer

Fineprediction

Coarseclassification 3

Coarseclassification 2

Coarseclassification 1

Coarseprediction 1

Jointclassification

layer Input

Figure 1 Hierarchical multitasks convolutional neural network (HMCNN) model

Table 1 e HMCNN training parameters

Learning rate Training steps Batch size Optimizer0001 20000 256 Adam

(1) (2) (3) (4) (5)

Figure 2 Test rig for condition monitoring of rolling bearings

4 Shock and Vibration

network structure of the proposed model to verify the ef-fectiveness of multitask learning e third part is a com-parison between the proposed model (HMCNN) andADCNN model studies the propagation of errors betweenmodel levels and analyzes the reasons for the high recog-nition accuracy of the proposed model

321 5e Comparative Analysis of HMCNN Model withOther Models In the first part the proposed model(HMCNN) is compared with the commonly used fault di-agnosis models such as support vector machine (SVM)backpropagation neural networks (BPNN) convolutionalneural networks (CNN) and long short-term memory(LSTM) e inputs of SVM and BPNN are multidimen-sional features extracted after ensemble empirical modedecomposition e inputs of CNN LSTM and HMCNNmethods are normalized original signals Experimentalcomparison results are shown in Figure 4 From Figure 5 itcan be seen that the classification accuracy of traditionalmodels such as SVM and DNN is less than 80 while theclassification accuracy of deep learning model such as CNNand LSTM is about 90 e bearing fault diagnosis ac-curacy of HMCNN model reaches 997 Compared withtraditional bearing fault diagnosis models it does not needto extract features has higher diagnosis accuracy and hasbetter generalization ability than the current deep learningmodels

e HMCNN model and CNN model are also comparedand analyzed e CNN and HMCNN models use the sameoptimizationmethod and training parameters in this papereaccuracy of per 50 steps in HMCNN and CNNmodel is shownin Figure 6 Figure 6 shows that the bearing fault diagnosisaccuracy of HMCNNmodel is 997 and that of CNNmodel is921 Compared with CNN model HMCNN not only hashigher bearing fault diagnosis accuracy but also has fewertraining steps to achieve the highest diagnosis accuracy econfusion matrix of experimental results is compared as shownin Figure 7 From Figure 7 compared with CNN modelHMCNN model mainly reduces the confusion degree betweenouter ring bearing faults so as to improve the diagnosis ac-curacy of bearing faults

In the training processes the learning speed of HMCNNmodel and CNN model is compared as shown in Figure 8e convergence rate (learning speed) of HMCNN model isabout twice that of CNN model

In order to further verify the generalization performance ofHMCNNmodel the diagnosis accuracy of HMCNNwith othermodels under different training sets is also compared here ecomparison results are shown in Table 3 and Figure 9 As thenumber of training samples decreases the recognition accuracyof all methods decreases to varying degrees From Table 4 it canbe seen that theHMCNNmodel has better recognition accuracyin fewer training sets and the recognition accuracy can reach967 in the case of only 500 training samples

In addition the performance differences betweenHMCNNmodel and SVM BPNN CNN and LSTM model under noiseare compared Comparison results are shown in Table 3 andFigure 10 It can be seen that the diagnosis accuracy ofHMCNN is 991 in noise environment (SNR 10dB) whilethe diagnosis accuracy of other models is not more than 90At the same time the diagnosis accuracy of HMCNNmodel innoise environment (SNR minus2dB) is more than 90 SoHMCNN has good antinoise performance

322 5e Comparative Analysis of HMCNN with DifferentTasks Numbers In the second part we study and analyze therelationship between the hierarchical tasksrsquo number ofHMCNNmodel and its diagnosis accuracy According to thedataset the HMCNN model is used to learn one two andthree classification tasks (bearing fault location fault typeand fault severity) which are named HMCNN1 HMCNN2and HMCNN3 respectively e comparison results areshown in Figures 11 and 12 e results show that bothHMCNN3 and HMCNN2 model can achieve a high diag-nosis accuracy e accuracy of HMCNN2 model is 08higher than that of HMCNN1 model Compared with CNNHMCNN contributes more to the accuracy improvement byadding the task of bearing fault location In HMCNN3model the diagnosis accuracy of fault type reaches 997which shows that the task of bearing fault position faulttype and fault severity diagnosis is effective and feasible andthe final diagnosis accuracy is improved to a certain extent

Table 2 Situation of damaged bearings

Bearing code K001 KA03 KA07 KA08 KI01 KI03 KI07Fault location H OR OR OR IR IR IRDamage method No fault Electric engrave Drilling Drilling EDM Electric engraver Electric engraverFault severity 0 2 1 2 1 1 2

(a) (b) (c)

Figure 3 e methods of bearing damage (a) EDM (b) drilling and (c) electric engraver

Shock and Vibration 5

e comparison between HMCNN1 HMCNN2 andHMCNN3 models proves that the proposed model can beextended to diagnosis multiple tasks In practical applica-tion the location type and severity of bearing fault can beoutput in HMCNN model which provides more detailedguidance for fault maintenance

323 5e Comparative Analysis of HMCNN Model withADCNN Model In the third part the ADCNN model pro-posed by Guo et al [30] is compared with HMCNNmodeleidea of ADCNNmodel for bearing fault diagnosis is to identify

the location of bearing fault first and then identify the faultseverity of each location of bearing on this basis Accuracyresults of ADCNN and HMCNNmodels for diagnosis bearingfault locations and final fault severity are shown in Tables 5 and6 respectively We can see that the ADCNN modelrsquos hierar-chical diagnosis of the bearing will make the error of bearingfault location diagnosis spread to the result of bearing faultseverity diagnosis and the more the number of tasks the moreserious the error propagationeHMCNNmodel has a sharedlayer and a weighted joint classification layer which can solvethe problem of error propagation and make the model morescalable

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(a)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(b)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(c)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(d)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(e)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(f )1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(g)

Figure 4 Vibration signals for each health condition of bearings (a) K001 (b) KA03 (c) KA07 (d) KA08 (e) KI01 (f ) KI03 and (g) KI07

6 Shock and Vibration

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

network structure of the proposed model to verify the ef-fectiveness of multitask learning e third part is a com-parison between the proposed model (HMCNN) andADCNN model studies the propagation of errors betweenmodel levels and analyzes the reasons for the high recog-nition accuracy of the proposed model

321 5e Comparative Analysis of HMCNN Model withOther Models In the first part the proposed model(HMCNN) is compared with the commonly used fault di-agnosis models such as support vector machine (SVM)backpropagation neural networks (BPNN) convolutionalneural networks (CNN) and long short-term memory(LSTM) e inputs of SVM and BPNN are multidimen-sional features extracted after ensemble empirical modedecomposition e inputs of CNN LSTM and HMCNNmethods are normalized original signals Experimentalcomparison results are shown in Figure 4 From Figure 5 itcan be seen that the classification accuracy of traditionalmodels such as SVM and DNN is less than 80 while theclassification accuracy of deep learning model such as CNNand LSTM is about 90 e bearing fault diagnosis ac-curacy of HMCNN model reaches 997 Compared withtraditional bearing fault diagnosis models it does not needto extract features has higher diagnosis accuracy and hasbetter generalization ability than the current deep learningmodels

e HMCNN model and CNN model are also comparedand analyzed e CNN and HMCNN models use the sameoptimizationmethod and training parameters in this papereaccuracy of per 50 steps in HMCNN and CNNmodel is shownin Figure 6 Figure 6 shows that the bearing fault diagnosisaccuracy of HMCNNmodel is 997 and that of CNNmodel is921 Compared with CNN model HMCNN not only hashigher bearing fault diagnosis accuracy but also has fewertraining steps to achieve the highest diagnosis accuracy econfusion matrix of experimental results is compared as shownin Figure 7 From Figure 7 compared with CNN modelHMCNN model mainly reduces the confusion degree betweenouter ring bearing faults so as to improve the diagnosis ac-curacy of bearing faults

In the training processes the learning speed of HMCNNmodel and CNN model is compared as shown in Figure 8e convergence rate (learning speed) of HMCNN model isabout twice that of CNN model

In order to further verify the generalization performance ofHMCNNmodel the diagnosis accuracy of HMCNNwith othermodels under different training sets is also compared here ecomparison results are shown in Table 3 and Figure 9 As thenumber of training samples decreases the recognition accuracyof all methods decreases to varying degrees From Table 4 it canbe seen that theHMCNNmodel has better recognition accuracyin fewer training sets and the recognition accuracy can reach967 in the case of only 500 training samples

In addition the performance differences betweenHMCNNmodel and SVM BPNN CNN and LSTM model under noiseare compared Comparison results are shown in Table 3 andFigure 10 It can be seen that the diagnosis accuracy ofHMCNN is 991 in noise environment (SNR 10dB) whilethe diagnosis accuracy of other models is not more than 90At the same time the diagnosis accuracy of HMCNNmodel innoise environment (SNR minus2dB) is more than 90 SoHMCNN has good antinoise performance

322 5e Comparative Analysis of HMCNN with DifferentTasks Numbers In the second part we study and analyze therelationship between the hierarchical tasksrsquo number ofHMCNNmodel and its diagnosis accuracy According to thedataset the HMCNN model is used to learn one two andthree classification tasks (bearing fault location fault typeand fault severity) which are named HMCNN1 HMCNN2and HMCNN3 respectively e comparison results areshown in Figures 11 and 12 e results show that bothHMCNN3 and HMCNN2 model can achieve a high diag-nosis accuracy e accuracy of HMCNN2 model is 08higher than that of HMCNN1 model Compared with CNNHMCNN contributes more to the accuracy improvement byadding the task of bearing fault location In HMCNN3model the diagnosis accuracy of fault type reaches 997which shows that the task of bearing fault position faulttype and fault severity diagnosis is effective and feasible andthe final diagnosis accuracy is improved to a certain extent

Table 2 Situation of damaged bearings

Bearing code K001 KA03 KA07 KA08 KI01 KI03 KI07Fault location H OR OR OR IR IR IRDamage method No fault Electric engrave Drilling Drilling EDM Electric engraver Electric engraverFault severity 0 2 1 2 1 1 2

(a) (b) (c)

Figure 3 e methods of bearing damage (a) EDM (b) drilling and (c) electric engraver

Shock and Vibration 5

e comparison between HMCNN1 HMCNN2 andHMCNN3 models proves that the proposed model can beextended to diagnosis multiple tasks In practical applica-tion the location type and severity of bearing fault can beoutput in HMCNN model which provides more detailedguidance for fault maintenance

323 5e Comparative Analysis of HMCNN Model withADCNN Model In the third part the ADCNN model pro-posed by Guo et al [30] is compared with HMCNNmodeleidea of ADCNNmodel for bearing fault diagnosis is to identify

the location of bearing fault first and then identify the faultseverity of each location of bearing on this basis Accuracyresults of ADCNN and HMCNNmodels for diagnosis bearingfault locations and final fault severity are shown in Tables 5 and6 respectively We can see that the ADCNN modelrsquos hierar-chical diagnosis of the bearing will make the error of bearingfault location diagnosis spread to the result of bearing faultseverity diagnosis and the more the number of tasks the moreserious the error propagationeHMCNNmodel has a sharedlayer and a weighted joint classification layer which can solvethe problem of error propagation and make the model morescalable

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(a)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(b)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(c)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(d)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(e)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(f )1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(g)

Figure 4 Vibration signals for each health condition of bearings (a) K001 (b) KA03 (c) KA07 (d) KA08 (e) KI01 (f ) KI03 and (g) KI07

6 Shock and Vibration

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

e comparison between HMCNN1 HMCNN2 andHMCNN3 models proves that the proposed model can beextended to diagnosis multiple tasks In practical applica-tion the location type and severity of bearing fault can beoutput in HMCNN model which provides more detailedguidance for fault maintenance

323 5e Comparative Analysis of HMCNN Model withADCNN Model In the third part the ADCNN model pro-posed by Guo et al [30] is compared with HMCNNmodeleidea of ADCNNmodel for bearing fault diagnosis is to identify

the location of bearing fault first and then identify the faultseverity of each location of bearing on this basis Accuracyresults of ADCNN and HMCNNmodels for diagnosis bearingfault locations and final fault severity are shown in Tables 5 and6 respectively We can see that the ADCNN modelrsquos hierar-chical diagnosis of the bearing will make the error of bearingfault location diagnosis spread to the result of bearing faultseverity diagnosis and the more the number of tasks the moreserious the error propagationeHMCNNmodel has a sharedlayer and a weighted joint classification layer which can solvethe problem of error propagation and make the model morescalable

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(a)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(b)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(c)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(d)1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(e)

1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(f )1

08

06

04

02

00 200 400 600 800 12001000 1400 1600 1800 2000

(g)

Figure 4 Vibration signals for each health condition of bearings (a) K001 (b) KA03 (c) KA07 (d) KA08 (e) KI01 (f ) KI03 and (g) KI07

6 Shock and Vibration

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

762

0

766

921

906

997

Accuracy1000

900

800

700

600

500

400

300

200

100

00

SVMBPNNCNN

LSTMHMCNN

Figure 5 Accuracy of SVM BPNN CNN LSTM and HMCNN

1

08

06

04

02

00 50 100 150 200 250 300 350 400

HMCNNCNN

Figure 6 Accuracy per 50 steps in HMCNN and CNN model

095 0

0

0 0 08 02

1

0 0 0052 0 0

0 0 0

0 0

0

0

0 0 0

0000

0 00

0 0 00

0

0

0

0004

0 0

013 085 0026

011

1

1

089

0002 0

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(a)

1

1

1

1

1

1

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0 0

0

0

0 0 0

0 0

0

0

0

0 0

0 0 0

0 0 0

0 0

0

0

0022

0002

0002

0004

098

Confusion matrix

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

(b)

Figure 7 Confusion matrix of (a) CNN and (b) HMCNN

Shock and Vibration 7

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

33VisualizationAnalysis e principle of HMCNNmodelis further analyzed by t-SNE visualization technology In thispaper the test set data are used as input and the output dataof the pooling layer in the HMCNN model are extracted asoutput ese output data are reduced to two-dimensionalfeature vectors by t-SNE and then these outputs are plottedas scatter plots representing their classes with differentcolors as shown in Figure 13 e visualization results show

that with the increase of network layers of HMCNN modelthe separation degree of features extracted from originalsignals becomes more and more obvious At last the outputfeatures of softmax classifier have seven distinct distribu-tions (the final classification of bearing faults)

By comparing the output of two identical pooling layers ofHMCNN and CNN models as shown in Figure 14 it can beseen that HMCNN has a better classification effect than CNN

7

65

6

55

5

45

4

350 50 100 150 200 250 300 350 400

Train loss-HMCNN

(a)

2

19

18

17

16

15

14

13

12

110 50 100 150 200 250 300 350 400

Train loss-CNN

(b)

Figure 8 Train loss of (a) HMCNN and (b) CNN

Table 3 Comparison of diagnosis accuracy with other models in different noise environments

MethodsSNR

minus4 minus2 0 2 4 6 8 10SVM 0663 0724 0735 0761 0812 0822 0823 0826BPNN 0601 0623 0656 0683 0702 0832 0845 0854CNN 0651 0687 0787 0811 0832 0856 0864 0886LSTM 0652 0663 0752 0787 0822 0834 0850 0852HMCNN 0845 0916 0932 0950 0972 0983 0985 0991

60006500700075008000850090009500

10000

Accu

racy

()

500500 1000500 1500500 2000500Trainingtesting samples

SVMBPNNCNN

LSTMHMCNN

Figure 9 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

8 Shock and Vibration

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

Table 4 Performance comparison of accuracy metric between other models and the proposed HMCNN model on bearing fault dataset

Case Number training samples Number testing samplesAccuracy

SVM BPNN CNN LSTM HMCNN1 500 500 0716 0682 0856 0846 09672 1000 500 0753 0712 0897 0886 09783 1500 500 0761 0842 0912 0893 09914 2000 500 0762 0856 0921 0906 0997

60006500700075008000850090009500

10000

Accu

racy

()

ndash2 0 2 4 6 8 10ndash4SNR (dB)

SVMBPNNCNN

LSTMHMCNN

Figure 10 Comparison of diagnosis accuracy with other models in different noise environments

921

0

989

0

996

0

997

0

CNN HMCNN1 HMCNN2 HMCNN3

1000090008000700060005000()4000300020001000

000

Figure 11 Accuracy of CNN HMCNN1 HMCNN2 and HMCNN3

096 0 0 0 004 0 0

0 1 0 0 0 0 0

0 0 076 024 0 0 0

0 0 013 086 0 0 0012

012 0 0 0 088 0 0

0 0 0 0 0 1 0

0 0 0 0016 0 1 098KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

Confusion matrix

(a)

095 0 0 0 0054 0 0

0 1 0 0 0 0 0

0 0 099 0012 0 0 0

0 0 0008 099 0 0 0004

003 0 0 0002 097

0 0 0 0 0 01

0 0 0 002 0 0980

0 0

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(b)

Figure 12 Continued

Shock and Vibration 9

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

099 0 0 0 0008 0 0

0 1 0 0 0 0 0

0 0 1 0004 0 0 0

0 0 001 099 0 0 0

002 0 0 0 098 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001Tr

ue la

bel

Confusion matrix

(c)

099 0 0 0 0006 0 0

0 1 0 0 0 0 0

0 0 1 0002 0 0 0

0 0 0 1 0 0 0

0012 0 0 0 099 0 0

0 0 0 0 0 1 0

0 0 0 0 0 0 1

KA01 KA07 KA08 KI01 KI03 KI07K001Predicted label

KI07

KI03

KI01

KA08

KA07

KA01

K001

True

labe

l

Confusion matrix

(d)

Figure 12 Confusion matrix of (a) CNN (b) HMCNN1 (c) HMCNN2 and (d) HMCNN3

Table 5 e accuracy of fault location for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Inner race fault 81 98Outer race fault 92 100Health 86 100Overall accuracy 863 994

Table 6 e accuracy of fault severity for ADCNN and HMCNN model

Case ADCNN () HMCNN ()Fault severity accuracy 817 997

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

Figure 13 Continued

10 Shock and Vibration

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

model Compared with the second pool layer of HMCNN andCNN model the classification of KI07 (Inner Race Fault 2)bearings KA07 (Outer Race Fault 1) bearings andKA08 (OuterRace Fault 2) bearings by CNN model is not obvious butHMCNN model has been able to separate KI07 bearings ob-viously is shows that in the second pooling layer ofHMCNN model the fault location of bearing is well classifiede visual output of HMCNN and CNN third pool layer showsthat CNNmodel has no obvious effect on the diagnosis of KA07andKA08 bearings whileHMCNNmodel has an obvious effecton the diagnosis of KA07 and KA08 bearings is proves thatin the third pooling layer of HMCNN model the bearing faultseverity is clearly classified From the network of HMCNN thesecond pooling layer is essentially the last layer of shared layer

In the shared layer the proposed model learns the features ofbearing fault location fault type and fault severity

HMCNN model can share more fault information thanCNN model through multitasks learning In particular thetask of fault location focuses the network attention on thepossible neglected fault location information which en-hances the classification ability of bearing fault location ofHMCNN model and the KI07 bearing can be separatedobviously by HMCNNmodel in the second pool layer Aftershared layer the HMCNN model only needs to recognizeKA07 and KA08 bearings but CNN model also needs torecognize KI07 KA07 and KA08 bearings which may leadto the final recognition accuracy of the CNNmodel which islower than that of the HMCNN model

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(e)

Figure 13 e visualization of learned features for HMCNN (a) the input layer (b) the first pooling layer (c) the second pooling layer (d)the third pooling layer and (e) the softmax layer

Shock and Vibration 11

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

From the analysis of the learning process of HMCNNmodel multitask learning in HMCNN model may improvethe generalization accuracy of the model by using the in-formation hidden in training signals of multiple tasks as aninductive bias Multitask learning plays the same role asregularization and reduces the risk of model overfitting Atthe same time it reduces the ability to fit random noise andmakes the model have better generalization performance

4 Conclusions

e hierarchical multitask learning CNN model (HMCNN)is proposed which reflects hierarchical classification Onlyone model needs to be trained to achieve a multitaskclassification Compared with the experimental results ofother models the HMCNNmodel can improve the accuracy

of the final fault diagnosis and the diagnosis accuracyreaches 997 Compared with CNN model the HMCNNmodel has a faster learning speed We compare the diagnosisaccuracy of HMCNNwith other models in different trainingsamples and noise environments HMCNNmodel has betterdiagnosis accuracy than other models It is proposed that theHMCNNmodel can be extended to diagnosis multiple taskse fault location fault type and fault severity of bearingfault diagnosis are given which can provide more detailedguidance for fault maintenance Compared with theADCNN model the HMCNN model solves the problem oferror propagation and makes the model scalable

rough the visual analysis of the HMCNN and CNNmodel learning process the reason why HMCNN has highergeneralization accuracy is further explored HMCNNmodelshares more fault information than the CNN model In

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(a)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(b)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(c)

10

08

06

04

02

00

00 02 04 06 08 10

K001KA01KA07KA08

KI01KI03KI07

(d)

Figure 14e visualization of learned features for CNN and HMCNN (a) the second pooling layer of HMCNN (b) the third pooling layerof CNN (c) the second pooling layer of HMCNN and (d) the third pooling layer of CNN

12 Shock and Vibration

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

particular the task of fault location focuses the networkattention on the possible neglected fault position informa-tion which enhances the classification ability to bear faultlocation of the HMCNN model

Data Availability

e data that support the findings of this study areavailable at httpsmbuni-paderborndeenkatmain-researchdatacenterbearing-datacenterdata-sets-and-downloadtdsourcetags_pcqq_aiomsg At the sametime the data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was supported by National Key RampD Programof China (2017YFB1201201)

References

[1] M Cerrada R V Sanchez C Li et al ldquoA review on data-driven fault severity assessment in rolling bearingsrdquo Me-chanical Systems and Signal Processing vol 99 pp 169ndash1962018

[2] Y Lei J Lin Z He and M J Zuo ldquoA review on empiricalmode decomposition in fault diagnosis of rotating machin-eryrdquoMechanical Systems and Signal Processing vol 35 no 1-2 pp 108ndash126 2013

[3] B Muruganatham M A Sanjith S A V Satya Murty andS S Murty ldquoRoller element bearing fault diagnosis usingsingular spectrum analysisrdquo Mechanical Systems and SignalProcessing vol 35 no 1-2 pp 150ndash166 2013

[4] S S Refaat H Abu-Rub M S Saad E M Aboul-Zahab andA Iqbal ldquoANN-based for detection diagnosis the bearingfault for three phase induction motors using current signalrdquoin Proceedings of the 2013 IEEE International Conference onIndustrial Technology (ICIT) IEEE Cape Town South AfricaFebruary 2013

[5] V K Rai and A R Mohanty ldquoBearing fault diagnosis usingFFTof intrinsic mode functions in Hilbert-Huang transformrdquoMechanical Systems and Signal Processing vol 21 no 6pp 2607ndash2615 2007

[6] X Lou and K A Loparo ldquoBearing fault diagnosis based onwavelet transform and fuzzy Inferencerdquo Mechanical Systemsand Signal Processing vol 18 no 5 pp 1077ndash1095 2004

[7] Y Yang D J Yu and J S Cheng ldquoA roller bearing faultdiagnosis method based on EMD energy entropy and ANNrdquoJournal of Sound and Vibration vol 294 no 1-2 pp 269ndash2772006

[8] Y Li M Xu R Wang and W Huang ldquoA fault diagnosisscheme for rolling bearing based on local mean decompo-sition and improved multiscale fuzzy entropyrdquo Journal ofSound and Vibration vol 360 pp 277ndash299 2016

[9] C L Liu Y J Wu and C G Zhen ldquoRolling bearing faultdiagnosis based on variational mode decomposition and fuzzyC means clusteringrdquo Proceedings of the CSEE vol 35 no 13pp 3358ndash3365 2015

[10] Y Yang D J Yu and J S Cheng ldquoA fault diagnosis approachfor roller bearing based on IMF envelope spectrum and SVMrdquoMeasurement vol 40 no 9-10 pp 943ndash950 2007

[11] Z R Hou ldquoRolling bearing fault diagnosis based on waveletpacket and improved BP neural network for wind turbinesrdquoApplied Mechanics and Materials vol 347ndash350 pp 117ndash1202013

[12] V Muralidharan and V Sugumaran ldquoA comparative study ofNaıve Bayes classifier and Bayes net classifier for fault diag-nosis of monoblock centrifugal pump using wavelet analysisrdquoApplied Soft Computing vol 12 no 8 pp 2023ndash2029 2012

[13] F F Chen M Li B J Chen et al ldquoFault diagnosis of rollerbearing based on hybrid feature set and weighted KNNrdquoJournal of Mechanical Transmission vol 40 no 8 pp 138ndash143 2016

[14] Z Wang Q Zhang J Xiong M Xiao G Sun and J HeldquoFault diagnosis of a rolling bearing using wavelet packetdenoising and random forestsrdquo IEEE Sensors Journal vol 17no 17 pp 5581ndash5588 2017

[15] M Seera and C P Lim ldquoOnline motor fault detection anddiagnosis using a hybrid FMM-CART modelrdquo IEEE Trans-actions on Neural Networks and Learning Systems vol 25no 4 pp 806ndash812 2014

[16] O R Seryasat M A Shoorehdeli F Honarvar andA Rahmani ldquoMulti-fault diagnosis of ball bearing using FFTwavelet energy entropy mean and root mean square (RMS)rdquoin Proceedings of the IEEE International Conference on Sys-tems Man and Cybernetics pp 4295ndash4299 Istanbul TurkeyOctober 2010

[17] X Yan and M Jia ldquoA novel optimized SVM classificationalgorithm with multi-domain feature and its application tofault diagnosis of rolling bearingrdquo Neurocomputing vol 313pp 47ndash64 2018

[18] M Zhang Z Jiang and K Feng ldquoResearch on variationalmode decomposition in rolling bearings fault diagnosis of themultistage centrifugal pumprdquo Mechanical Systems and SignalProcessing vol 93 no 1 pp 460ndash493 2017

[19] W Y Liu Q W Gao G Ye R Ma X N Lu and J G HanldquoA novel wind turbine bearing fault diagnosis method basedon integral extension LMDrdquoMeasurement vol 74 pp 70ndash772015

[20] P K Kankar S C Sharma and S P Harsha ldquoRolling elementbearing fault diagnosis using wavelet transformrdquo Neuro-computing vol 74 no 10 pp 1638ndash1645 2011

[21] L Y Jiang Q Q Li J G Cui and J H Xi ldquoRolling bearingfault diagnosis based on higher-order cumulants and BPneural networkrdquo in Proceedings of the 27th Chinese Controland Decision Conference pp 2664ndash2667 Qingdao ChinaMay 2015

[22] H Zhao J Zheng W Deng and Y Song ldquoSemi-supervisedbroad learning system based on manifold regularization andbroad networkrdquo IEEE Transactions on Circuits and Systems IRegular Papers vol 67 no 3 pp 983ndash994 2020

[23] W Zhang G Peng C Li Y Chen and Z Zhang ldquoA new deeplearning model for fault diagnosis with good anti-noise anddomain adaptation ability on raw vibration signalsrdquo Sensorsvol 17 no 2 p 425 2017

[24] F Wang H Jiang H Shao et al ldquoAn adaptive deep con-volutional neural network for rolling bearing fault diagnosisrdquoMeasurement Science and Technology vol 28 no 9 Article ID095005 2017

[25] L Wen X Li and Li Gao Y Zhang ldquoA new convolutionalneural network-based data-driven fault diagnosis methodrdquo

Shock and Vibration 13

IEEE Transactions on Industrial Electronics vol 65 no 7pp 5990ndash5998 2018

[26] H Shao H Jiang F Wang and H Zhao ldquoAn enhancementdeep feature fusion method for rotating machinery fault di-agnosisrdquo Knowledge-Based Systems vol 119 pp 200ndash2202017

[27] F Jia Y Lei N Lu and S Xing ldquoDeep normalized con-volutional neural network for imbalanced fault classificationof machinery and its understanding via visualizationrdquo Me-chanical Systems and Signal Processing vol 110 pp 349ndash3672018

[28] H Liu J Zhou Y Xu Y Zheng X Peng and W JiangldquoUnsupervised fault diagnosis of rolling bearings using a deepneural network based on generative adversarial networksrdquoNeurocomputing vol 315 pp 412ndash424 2018

[29] Z Yan H Zhang R Piramuthu et al ldquoHD-CNN hierarchicaldeep convolutional neural networks for large scale visualrecognitionrdquo in Proceedings of the IEEE International Con-ference on Computer Vision pp 2740ndash2748 Santiago ChileDecember 2015

[30] X Guo L Chen and C Shen ldquoHierarchical adaptive deepconvolution neural network and its application to bearingfault diagnosisrdquo Measurement vol 93 pp 490ndash502 2016

[31] J L Qu L Yu T Yuan et al ldquoA novel hierarchical intelligentfault diagnosis algorithm based on convolutional neuralnetworkrdquo Control and Decision vol 12 pp 1ndash11 2018

[32] C Lessmeier J K Kimotho D Zimmer et al ldquoConditionmonitoring of bearing damage in electromechanical drivesystems by using motor current signals of electric motors abenchmark data set for data-driven classificationrdquo in Pro-ceedings of the European Conference of the Prognostics andHealth Management Society pp 1ndash17 Bilbao Spain July2016

14 Shock and Vibration