a multimodel decision fusion method based on dcnn-idst for … · 2020. 8. 27. · idst diagnosis...

Research ArticleAMultimodel Decision Fusion Method Based on DCNN-IDST forFault Diagnosis of Rolling Bearing

Weixiao Xu Luyang Jing Jiwen Tan and Lianchen Dou

College of Mechanical Engineering Qingdao University of Technology Qingdao 266520 China

Correspondence should be addressed to Luyang Jing jingluyangquteducn

Received 27 August 2020 Accepted 27 November 2020 Published 15 December 2020

Academic Editor Zhixiong Li

Copyright copy 2020 Weixiao Xu 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

Each pattern recognitionmethod has its advantages and disadvantages to diagnose the state of rotatingmachinery)ere aremanyfault types of rolling bearings with apparent uncertainty)e optimal fusion level is usually challenging to be selected for a specificfault diagnosis task and extensive human labour and prior knowledge are also highly required during these selections To solve theabove problems a multimodel decision fusion method based on Deep Convolutional Neural Network and Improved Dempster-Shafer Evidence )eory (DCNN-IDST) is proposed for the inspection of rolling bearing To solve the defect of the originalevidence theory method in the fusion of high-conflict evidence the fuzzy consistency matrix is introduced By calculating thefactor weight the reliability and rationality of D-S evidence theory are improved )e DCNN model can learn features from theoriginal data and carry out adaptive feature extraction for multiple sensor information )e features extracted by DCNNadaptively are input into multiple network models for decision fusion )e new method of DCNN-IDST multimodel decisionfusion is applied to detect the damage of rolling bearings To evaluate the effectiveness of the proposedmethod both the BP neuralnetwork and RBF neural network are used to set up a multigroup comparison test )e result demonstrates that the proposedmethod can detect the fault of the rolling bearing effectively and achieve the highest diagnosis accuracy among all the testedmethods in the experiment

1 Introduction

Mechanical fault diagnosis technology is a newly developingsubject to monitor diagnose and predict the condition andthe malfunction of continuously operating mechanicalequipment to guarantee its safe operation It can effectivelyimprove the safety and the stability of rotating machineryequipment [1] )e rolling bearing plays an essential role inthe running process of mechanical equipment where itsstatus will directly affect the running efficiency and life of themechanical system According to statistics CNC machiningby rolling bearings caused by mechanical failure accountedfor about 30 of the total fault It can be seen that timelydiagnosis of the status information and fault diagnosis ofrolling bearing is vital which can reduce maintenance costsand ensure the regular operation of equipment

)ere are many fault types of rolling bearing with ap-parent uncertainty It is impossible to predict and diagnose

the bearing state comprehensively by collecting a singlesensor data )erefore data from different sources arecombined to achieve the purpose of effective diagnosis ofcomplex systems [2 3] DempsterndashShafer evidence theory(DST) has the advantage of expressing ldquouncertainrdquo andldquounknownrdquo without knowing prior probability which hasbeen widely used in information fusion technology [4 5]Niu et al [6] collected the current signal and the vibrationsignal of electrical machinery integrating voting decisionswith Bayesrsquo detective method raising the multiagent deci-sion-making layer blending approach to incorporate theinformation from the results of multisensor signalsrsquo mal-function diagnosis Li et al using D-S evidence theory toprocess decision-making layerrsquos information integrate thusto diagnose the malfunction of the diesel engine [7] Zhanget al adopt the SVDD approach to improve D-S evidencetheory setting up a two-stage fusion model to process ex-perimental verification in the malfunction diagnosis for

HindawiShock and VibrationVolume 2020 Article ID 8856818 12 pageshttpsdoiorg10115520208856818

chisel engine and finally achieve hierarchical and multilevelmalfunction diagnosis [8] Cao et al improved D-S evidencetheory set up the integrating relations between each evi-dence and increased the recognition rate of malfunctiondiagnosis according to the problem of highly conflict evi-dence which appeared in malfunction diagnosis for large-scale equipment [9] Liu et al adopted the method ofcombining quantum medical neural network with D-S ev-idence theory to achieve the high precision diagnosis formechanical characteristics of circuit breakers [10] Jiang andLin et al attained the goal of improving D-S evidence theoryby changing the combination rules in the evidence theorywhich also had specific application effects [11 12]

In the last few years deep learning has played an es-sential role in the field of artificial intelligence Deep con-volutional neural network (DCNN) has strong ability of datamining and information integration [13ndash19] It has beenwidely applied to the state monitoring and diagnosis re-search of rotating machinery Ga et al classified the faults ofrolling bearings by analyzing vibration signals with wavelettransform and extracting features and feeding them into thedeep learning model [17] Jing et al used the deep convo-lution model to adaptively extract the original fault signalcharacteristics and identified the fault of the motor [19]Zhao et al combined the depth convolution model with theLSTM model to monitor and estimate tool wear andachieved good fault diagnosis results [20]

As an emerging machine learning method deep learninghas strong capabilities of feature extraction and functionmapping Deep learning method can meet the analysis re-quirements of diverse nonlinear and high-dimensionalhealth monitoring data which can be applied in the lifeprediction of rotating machinery equipment Babu GS et al[21] first used the Convolution Neural Network (CNN) topredict the residual life of bearings and verified the effec-tiveness of the method Li [22] combined the convolutionalneural network with the short-time memory neural networkand used CNNrsquos features of convolution and weight sharingto extract deep features and input them into the LSTMnetwork effectively realizing the prediction of the remainingservice life of the rolling bearing Zhao et al [20] combinedthe depth convolution model with the LSTM model tomonitor and estimate tool wear which achieved good faultdiagnosis results Shi et al [23] based on complementing theadvantages of CNN and LSTM proposed the space-timeseries prediction method based on ConvLSTM Luo et al[24] proposed a ConvLSTM-AE framework which betterencodes the change of appearance and motion for regularevents Qiao et al used the TD-ConvlSTM time series modelto analyze the space-time characteristics of multisensor dataon different time scales [25]

)ere are many fault types of rolling bearings withapparent uncertainty It is often challenging to select theoptimal feature or fusion level in state monitoring )ere-fore combining the advantages of multiple intelligentidentification methods this paper proposes a multimodeldecision fusion method based on DCNN-IDST for faultdiagnosis of rolling bearing By this method the fault

information of rotating machinery can be diagnosedcomprehensively

2 Theoretical Background

21 DempsterndashShafer Evidence eory DempsterndashShafertheory has the advantage of dealing with uncertainty and itsbasic formula is shown as follows

(1) Suppose there are proposition A and U as theframework 2U⟶ [0 1])ere is a function m that satisfies the followingconditions

U x1 x2 x3 middot middot middot (1)

m(ϕ) 0 (2)

where m (A) is the Basic Probability Assignment whichrepresents the exact trust function for A)e belief function can be defined as follows

Bel(A) 1113944BsubeA

m(B) (3)

)e plausibility functions are set to

Pls(A) 1 minus Bel(A) (4)

where Pls(A) and Bel(A) are the upper and lowerlimit function of A)e relationship between them isshown as follows Pls(A)geBel(A) AsubeΩ

(2) )e combination rule of DempsterndashShafer evidencetheory [26ndash29]Suppose that the basic probability assignment offrame U is m1 and m2 if A isin U and m(A)gt 0 thefocal target elements areA1 A2 An B1 B2 Bn)e combination rule of DempsterndashShafer evidencetheory is defined as follows

m(A)

1113936AicapBjA

m1(Ai)m2(Bj)

1 minus 1113936AicapBjϕ

m1(Ai)m2(Bj)(5)

(3) )e new improved method of DempsterndashShaferevidence theory (IDST)In this paper the improved DSTmethod proposed inthe literature [30] is adopted to diagnose the state ofrotating machinery )e specific steps are as follows

2 Shock and Vibration

Assuming m1 m2 middot middot middot mn as the Basic ProbabilityAssignment as the framework of U the framework isΘ A B C middot middot middot

)e IDST method is defined as follows

(1) )e original basic probability assignment is redis-tributed and a new fuzzy consistent matrix isestablishedAdd the fuzzy matrix in rows

R rij1113872 1113873M times N (6)

ri 1113944n

k1rik (i 1 2 middot middot middot n) (7)

On this basis the consistent fuzzy matrix is obtained bytransformation according to the following formula

rij rik minus rjk1113872 1113873

2n + 05 (8)

(2) Figure out the factor weight coefficientSuppose there is factor Ai and target of Ok and theweight sk

i is as follows

ski

1n

minus12α

+1113936

nj1 rij

nα i 1 2 middot middot middot n (9)

where αge (n minus 1)2 to improve the resolution of thesorting result and the values are α (n minus 1)2

(3) Recalculate the basic probability allocation)e adjusted value of basic probability distribution isdefined as follows

mi AK( 1113857rsquo ski mi AK( 1113857 (10)

where k 1 2 3 Since the sum of the changed basic probability dis-tribution values is not 1 the supplementary definitionis as follows to constitute the basic probability dis-tribution function

mi(Θ)rsquo 1 minus 1113944

di

k1mi AK( 1113857prime (11)

(4) Get the average evidence

m(A) 1n

1113944

n

i1mi(A) forallAsubeΘ (12)

(5) )e improved evidence theory formula as shownbelow

mlowast (A) 1113944

AicapBjA

m1 Ai( 1113857lowastm2 Bj1113872 1113873 + m(A)(13)

m(θ) 1 minus 1113944 m(A) (14)

where m(A) is the moderate support degree afterweighted the evidence

22 Basic eory of Multiple Network Models Deep con-volutional neural network (DCNN) was initially proposedby Hubel and Wiesel [31] based on the structural design ofthe visual nervous system It has a strong ability of datamining and information fusion and can effectively realize thelocal connection weight sharing space pooling and otherfunctions [16 18 32ndash37] It contains many convolutionallayers pooling layers and fully connected layers with vitaldata mining and information integration capabilities It caneffectively realize the local connection weight sharing spacepooling and other functions )e classical network ofconvolutional neural networks (CNN) is shown in Figure 1)e convolutional layer is the core component of deepconvolutional network which is composed of multiple setsof two-dimensional filters When the data enters the con-volutional layer it will conduct convolution operation withthe weight of the two-dimensional filter )e result afterprocedure is the output of the convolutional layer )e inputdata is processed by the down-sampling algorithm )ecommonly used down-sampling algorithms include maxi-mum pooling average pooling and nonuniform poolingamong which the maximum pooling method is the mostwidely used )e full connection layer is the last layer wherethe data has been processed by the previous convolutionlayer and the pooling layer which has been extracted andconverted into high-level information features )e fullconnection layer classifies the high-level information fea-tures to obtain the final recognition results Soft-max is thegeneralization of the logistic classifier which mainly solvesthe problem of multiclassification

Backpropagation neural network (BPNN) can realize thenonlinear mapping between input and output with oneinput layer one output layer and multiple hidden layerseach layer having various neurons )e output layer transferfunction uses the linear function With the minimum meansquare error as the training objective the BP algorithm isused as the learning algorithm of the network BP neuralnetwork can learn the network through the gradient descentmethod and adjust the weight of the system through thebackpropagation error )rough the above practices theoverall error of the network can be minimized

)e structure of Radial Basis Function neural network(RBFNN) is simple with self-learning adaptive ability fastconvergence speed function approximation ability and

Shock and Vibration 3

superior advantages thus having pervasive applications[38ndash40] Its network structure is mainly composed of theinput layer hidden layer (using radial basis function asactivation function) and output layer

23 A Multimodel Decision Fusion Method Based on DCNN-IDST

231 e Proposed Method In this paper the fault infor-mation of rolling bearings is collected by multiple sensorsand the extracted characteristic values are input into variousnetwork models (BPNN RBFNN and DCNN) by using theadaptive feature extraction feature of deep convolutionalneural network )e output results are normalized as thebasic probability distribution of evidence theory )eoriginal D-S synthesis formula is improved by consistentfuzzy matrix and the final fusion result is obtained bydecision level fusion

)e flowchart based on the DCNN-IDST method isshown in Figure 2 (1) Vibration signals of rolling bearings atthree different speeds are collected by two vibration sensors(2) Data preprocessing (3) )e vibration signals of threerates of the rolling bearing collected are fused at the datalevel and then input into the DCNN model (4) )e ei-genvalues of DCNN adaptive output were input into threenetwork models respectively for training (5) )e outputresults of the three network models are normalized and theninput into IDST for decision fusion

232 Set Up Comparative Test Methods )e flowcharts ofcomparative test methods are shown in Figure 3

)is research method verifies the feasibility of DCNN-IDST-based multimodel decision fusion method in rotatingmachinery equipment state monitoring by setting up mul-tiple groups of comparative tests)e PCAmethod is used tocompare the classification effect of artificial selection featureand DCNN adaptive feature extraction )e feature quantityextracted by artificial feature and the feature quantity re-moved by DCNN adaptively were input into BPNN andRBFNN respectively to verify the recognition effect of themodel )e diagnosis effect of the new method based onIDST and D-S synthesis formula is proved

3 Experiment and Discussion

31 Experimental Setup Four states of rolling bearing(normal inner ring fault outer ring fault and rolling bodyfault) are selected for test verification )e rolling bearing

fault diagnosis test is shown in Figure 4 Figure 5 shows thetypes of bearing fault)e sampling frequency is 20 kHz)emotor speed is set as 600 rpm 900 rpm and 1200 rpm Each2048 data point is used as a set of fault data samples )ereare 300 samples for each health condition under eachidentical operating speed )e data of rolling bearings usedin the test are shown in Table 1

32 Data Processing )e original vibration signal of therolling bearing at three rotational speeds (600 rpm 900 rpmand 1200 rpm) is preprocessed to improve the signalmonitoring ratio)e preprocessed data are fused at the datalevel Fifteen time-domain characteristics of vibration sig-nals at three speeds of the rolling bearing are extractedmanually )ere are ten dimensionless time-domain indexesincluding mean value root mean square value root am-plitude value absolute mean value variance maximumvalue and minimum value )ere are five dimensionlesstime-domain indexes including waveform index peakvalue pulse index margin index and kurtosis index )ereare three frequency-domain eigenvalues including meansquare frequency barycenter frequency and frequencyvariance )ese features will be input to BPNN and RBFNNfor pattern recognition Due to the limitation of space onlysome time-domain indexes are listed in Table 2

At the same time the time-domain signal of the originalrolling bearing is directly input into the DCNN modelTwenty feature values are adaptively extracted and input intoBPNN and RBFNN for pattern recognition

33 Model Design

331 Backpropagation Neural Network )e number ofnodes in the input layer of Backpropagation Neural Network(BPNN) is set as fifteen (fifteen characteristic quantities))e number of nodes in the output layer is set as four (fourfault types) )e number of nodes in the hidden layer can bedetermined as fifteen after several tests )e learning rate isset at 005 and the expected error is 0002 )e desiredoutput can be set as follows normal [1000] inner ringpitting [0100] outer ring pitting [0010] and rolling el-ement pitting [0001] )e output of the BP network isnormalized and directly used as the basic probability dis-tribution function of DST Figure 6 shows the output of BP-adaptive network model

332 Radial Basis Function Neural Network For the RBFnetwork model structure the same training set and test set as

Input Convolution Convolution

SubsamplingSubsampling

Featuremaps

Featuremaps

C1 S2 C3 S4 C5

Output

Fullyconnection

Figure 1 )e classical network of convolutional neural networks (CNN)


Bearingfailure

teststand

Featurelearning

BPNN

DCNN

Decisionfusion IDST Diagnosis

resultMultiplesensor

Dataprocessing RBFNNData-level

fusion

Figure 2 )e flowchart based on the DCNN-IDST method

BPNN

DCNN

RBFNN

BPNN

DCNN

RBFNN

Dataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Featurelearning

orfeature

extration

Rawdata

Handcraftfeatures

Diagnosisresult 1

Diagnosisresult 2

(a)

BPNN

DCNN

RBFNNDataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Decisionfusion

IDST

Classical D-Scombination

rule

Featurelearning

Diagnosisresult

Diagnosisresult

(b)

Figure 3 Flowcharts of comparative methods (a) Advantages of artificial feature extraction and DCNN adaptive feature extraction (b))ediagnosis effect of the new approach based on IDSET and D-S synthesis formula is verified

Motor Torque sensor Vibration sensor

Figure 4 Rolling bearing fault diagnosis test


BP neural network are used to train and test the system )eoutput result is normalized as the basic probability as-signment function of evidence theory

333 Deep Convolutional Neural Network In this paper theparameters of the selectedmodel of DCNN are chosen by themethod of ergodic reference It is necessary to adjust thelength of input data the number of convolution kernel sizeof convolution kernel etc Parameters of the selected modelof DCNN are shown in Table 3 )e main structure ofDCNN is shown in Table 4

4 Experimental Results

41 Principal Component Analysis (PCA) To verify theadaptive feature extraction capability of DCNN principalcomponent analysis (PCA) was used to analyze the manuallyselected features and the adaptive feature extraction capa-bility of DCNN )e output graph of principal componentanalysis (PCA) method is shown in Figure 7

As can be seen from Figure 7 the classification effect offeatures extracted by DCNN is better than the result ofmanual selection It can be seen that DCNN has the ad-vantage of adaptive feature extraction which can lay afoundation for subsequent equipment fault diagnosis


421 e Comparison Test Results of Several NetworkModels )e fifteen time-domain frequency-domain andtwenty DCNN adaptive features extracted manually wereinput into BPNN RBFNN and DCNN respectively forpattern recognition 80 of these data are selected fortraining and 20 for testing )e comparison test results ofseveral network models are shown in Table 5 Figure 8 showsthe testing accuracy of several network models

As can be seen from Table 5 and Figure 8 DCNNadaptive feature extraction was used to input the extractedfeature into each network model and the recognition ac-curacy was higher than that of the manually removed part Itcan effectively improve the diagnostic accuracy of the modelwhich provides a new diagnostic idea for the state

monitoring of rotating machinery and the decision fusion ofmultiple models

422 Decision Fusion Results In this paper the general-ization ability of the network model is used to construct theBPA of D-S evidence theory )e output results of BPNNRBFNN and DCNN are normalized and used as the BPA ofD-S evidence theory )e output results of the three net-works are shown in Tables 6ndash8 wherem(A) m(B) m(C) andm(D) represented the BPA ofnormal inner ring fault outer ring fault and rolling bodyfault m(θ) is the uncertainty and ε is the reliability(FL feature learning)

As shown in Table 6 the output of each network isuncertain After the fusion of the three network models theoutput results of the network are all inner ring faults Withthe addition of credible evidence to the fusion process theBPA of B is continuously increasing Based on the proposedmethod in this paper the final diagnosis accuracy ratereaches 9482 which is higher than that of any singlenetwork model

To further compare the advantages of DCNN-IDSTmultimodel decision fusion method two groups of com-parative experiments were set up (1) )ree network modelswere fused under D-S synthesis formula (2) )ree networkmodels were fused under the IDSETmethod )e ε betweenthe two fusion rules is shown in Table 9 Figure 9 offers thefusing by D-S synthesis formula and Figure 10 shows thefusing by the IDSET method

By comparing Tables 7ndash9 it can be seen that the outputresults of the three networks were normalized and then fusedagain which significantly improved the recognition accu-racy With the increasing of supporting evidence the reli-ability of the IDSTmethod for decision fusion has a steadyrise and the pattern recognition rate is also greatly improved

(a) (b) (c)

Figure 5 )e types of bearing fault (a) outer ring fault (b) inner ring fault and (c) rolling body fault

Table 1 )e data of rolling bearings used in the test

Pattern label Bearing state Input speed (rpm) Load1 Normal 600 900 1200 02 Inner ring fault 600 900 1200 03 Outer ring fault 600 900 1200 04 Rolling body fault 600 900 1200 0


0 200 400 600 800 1000 1200 1400 1600 1800 2000

Best training performance is 00028693 at epoch 2000

Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4

Figure 6 )e output of the BP-adaptive network model

Table 3 Parameters of the selected model of DCNN

Number Input data Number of the convolution kernels Size of the convolution kernel Accuracy ()1 2048 16 10 15 7752 2048 32 10 15 73333 2048 64 10 15 80334 2048 128 10 15 84835 2048 256 10 15 7666

Table 2 Some of the dimension time-domain features

Number Meanvalue

Root mean squarevalue

Root amplitudevalue

Crookeddegree

Peakvalue Variance Maximum

valueFeng-Feng

value1 0008435 0219334 0136023 0017431 0017919 0048107 1440957 18727662 minus000601 0198404 0129573 0009372 0007169 0039364 0912906 12815963 0029603 0245241 01616 0018736 0016446 0060143 117327 15948324 0040591 025593 0167282 0021668 0025214 00655 1600798 20930335 minus00324 0192693 0126626 000949 0007472 0037131 0977287 13701146 minus003391 0167655 011473 0004182 0003009 0028108 0685338 1048837 minus000774 019325 0126156 0008213 0006361 0037346 0827895 12028468 minus000372 0219194 0136029 0020222 0020906 0048046 1332877 1701796


Table 4 Main structure of DCNN

Layer Type Parameters1 Convolution layer Size 128 number102 Pooling layer S 23 Convolution layer Size 128 number154 Pooling layer S 25 )e connection layer ReLU Nodes106 Soft-max 4 outputs

6

4

2

0

ndash2

Seco

nd co

mpo

nent

s

ndash2 0 2 4 6ndash4First components

Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts

ndash2 0 2 4ndash4First components

Class 1Class 2

Class 3Class 4

(b)

1 20 3 4ndash1First components

05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)

1 20 3First components

Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)

Figure 7)e output graph of principal component analysis (PCA)method (a) Input data at a single rotation speed (b) input data after datalevel fusion (c) input data extracted by manual features (d) adaptive feature learned through DCNN

Table 5 )e comparison test results of several network models

Number Model Feature learning fromraw data ()

Time-domainfeatures ()

Manual feature extraction frequency-domain features ()

Time-frequency-domainfeatures ()

Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500

BPNN RBFNN DCNN BPNN RBFNN DCNNSensor 1 Sensor 2

Feature learningHandcraft features-time domain

Handcraft features- frequency domainHandcraft features-time-frequency domain

Figure 8 Testing the accuracy of several network models

Table 6 )e actual outputs of the three network models are compared with the expected results

Models Actual outputs Expect results Diagnosis results

BPNN-FL1

0000000 0960499 0000000 0000045 0100 Inner ring fault0000000 0986047 0000002 0000483 0100 Inner ring fault0000026 0414734 0408441 0068637 0100 Uncertainty0000000 0982463 0004014 0030370 0100 Inner ring fault0000000 0925475 0000000 0000172 0100 Inner ring fault0000000 0725717 0000043 0003560 0100 Inner ring fault

RBFNN-FL1

minus0349173 0283555 0650220 0415404 0100 Uncertaintyminus0048801 1123021 0128835 minus0203042 0100 Inner ring fault0221095 0833929 0189633 minus0244645 0100 Inner ring fault

minus0441047 0937030 0526606 minus0022593 0100 Inner ring faultminus0041985 1174574 minus0290296 0157707 0100 Inner ring fault0312547 1065893 minus0560675 0182236 0100 Inner ring fault

DCNN-FL1

0000067 0552400 0446572 0000961 0100 Uncertainty0000000 0989853 0000146 0000001 0100 Inner ring fault0000000 0940449 0059551 0000000 0100 Inner ring fault0000000 0981931 0018045 0000025 0100 Inner ring fault0000000 0976631 0000069 0000000 0100 Inner ring fault0000000 0973404 0026596 0000001 0100 Inner ring fault


025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3

Figure 9 Fusing by D-S synthesis formula

067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3

Figure 10 Fusing by the IDSET method

Table 7 )e result of the convergence of BPNN and RBGNN

Number ε m(A) m(B) m(C) m(D) m(θ) Results1 0675797 0000000 0819113 0132410 0101339 0127043 Inner ring fault2 0986144 0000800 0999710 0001722 0000003 0000193 Inner ring fault3 0656522 0059662 0610154 0276491 0009481 0144536 Inner ring fault4 0994518 0000000 0987882 0004749 0010135 0000030 Inner ring fault5 0928233 0005859 0992027 0000000 0010629 0005345 Inner ring fault6 0761354 0055722 0904836 0000004 0049402 0065069 Inner ring fault

Table 8 )e result of the convergence of three networks



)e test results show that the DCNN-IDST multimodeldecision fusion can achieve better diagnosis results andperfect diagnosis system

5 Conclusions

)is paper gives a multimodel decision fusion method basedon DCNN-IDSTfor the damage detection of rolling bearingCombining the advantages of DCNN and D-S evidencetheory the DCNN model presents a convincing adaptivefeature extraction ability with a better effect than the manualfeature extraction )e D-S evidence theory method isimproved by fuzzy consistency matrix and multimodelintegration decision-making system of rotating mechanicalmalfunction diagnosis is established based on experimentalresearch )e basic probability assignment after decisionfusion is generally higher than the initial recognition resultof a single network model With the increase of supportingevidence the BPA and reliability after fusion recognitionincrease further )e work demonstrates that the proposedmethod combines the advantages of every single networkand overcomes the defects of a single network with un-certainty effectively with the best recognition accuracyamong all the tested methods

Data Availability

)e basic data for the study were obtained from thelaboratory

Conflicts of Interest

)e authors declare that they have no conflicts of interest

Acknowledgments

)e research was supported by the National Key Researchand Development Program of China (Grant no2018YFB1701302) Key Research and Development Programof Shandong Province (Grant no 2018GGX103016) andShandong university science and technology plan project(Grant no J15LB10)

References

[1] G Wang Z J He X F Chen and Y N Lai ldquoBasic researchon machinery fault diagnosis-what is the prescriptionrdquoJournal of Mechanical Engineering vol 49 no 01 pp 63ndash722013

[2] F Alam R Mehmood I Katib N N Albogami andA Albeshri ldquoData fusion and IoT for smart ubiquitous en-vironments a surveyrdquo Institute of Electrical and ElectronicsEngineers Access vol 5 pp 9533ndash9554 2017

[3] B Khaleghi A Khamis F O Karray and S N RazavildquoMultisensor data fusion a review of the state-of-the-artrdquoInformation Fusion vol 14 no 1 pp 28ndash44 2013

[4] A P Dempster ldquoUpper and lower probabilities induced by amultivalued mappingrdquo in Classic Works of the DempsterndashShafer eory of Belief Functions pp 57ndash72 Springer BerlinHeidelberg Germany 2008

[5] G Shafer A Mathematical )eory of Evidence vol 42Princeton Univ Press Princeton NJ USA 1976

[6] G Niu T Han B-S Yang and A C C Tan ldquoMulti-agentdecision fusion for motor fault diagnosisrdquo Mechanical Sys-tems and Signal Processing vol 21 no 3 pp 1285ndash1299 2007

[7] H K Li X J Ma and Z Wang ldquoDiesel engine fault diagnosisbased on multi-symptom information fusionrdquo Transactions ofthe Chinese Society for Agricultural Machinery vol 35 no 1pp 121ndash124 2004

[8] Y Zhang and J Cui ldquoCrankshaft bearing fault diagnosis basedon SVDD and D-S theoryrdquo Journal of Chongqing University ofTechnology (Natural Science) vol 11 13 pages 2019

[9] J F Cao and W Cao ldquoFault diagnosis of large manufacturingequipment based on improved evidence fusion theoryrdquoJournal of Vibration Measurement amp Diagnosis vol 32 no 4pp 532ndash538 2012

[10] J H Liu M P Zhou and C C Hou ldquoMechanical charac-teristics fault diagnosis of circuit breaker based on quantumgenetic neural network and D-S evidence theoryrdquo HighVoltage Apparatus vol 54 no 1 pp 230ndash235 2018

[11] W Jiang B Wei C Xie and D Zhou ldquoAn evidential sensorfusion method in fault diagnosisrdquo Advances in MechanicalEngineering vol 8 2016

[12] L Yun Y Li X Yin and D Zheng ldquoMultisensor fault di-agnosis modeling based on the evidence theoryrdquo Institute ofElectrical and Electronics Engineers Transactions on Reliabilityvol 67 pp 513ndash521 2018

[13] Y Bengio A Courville and P Vincent ldquoRepresentationlearning a review and new perspectivesrdquo Institute of Electricaland Electronics Engineers Transactions on Pattern Analysisand Machine Intelligence vol 35 no 8 pp 1798ndash1828 2013

[14] Y Lecun Y Bengio and G Hinton ldquoDeep learningrdquo Naturevol 521 no 7553 pp 436ndash444 2015

[15] L Jing M Zhao P Li and X Xu ldquoA convolutional neuralnetwork based feature learning and fault diagnosis method forthe condition monitoring of gearboxrdquoMeasurement vol 111pp 1ndash10 2017

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

[17] P Tamilselvan Y Wang and P Wang ldquoDeep belief networkbased state classification for structural health diagnosisrdquo inProceedings of the Institute of Electrical and Electronics En-gineers Aerospace Conference pp 1ndash11 Big Sky USA March2012

[18] T Ince S Kiranyaz L Eren M Askar and M GabboujldquoReal-time motor fault detection by 1-D convolutional neuralnetworksrdquo Institute of Electrical and Electronics Engineers

Table 9 )e ε between the two fusion rules

k Or ε 1 2 3 4 5 6

Comparison test 1 m1 m2 02541 07821 06359 07002 07587 06123m1 m2 m3 06544 08512 05534 08401 07105 07111



Transactions on Industrial Electronics vol 63 no 11pp 7067ndash7075 2016

[19] L Jing T Wang M Zhao and P Wang ldquoAn adaptive multi-sensor data fusion method based on deep convolutionalneural networks for fault diagnosis of planetary gearboxrdquoSensors vol 17 no 2 pp 414ndash429 2017

[20] R Zhao R Yan J Wang and K Mao ldquoLearning to monitormachine health with convolutional bi-directional LSTMnetworksrdquo Sensors vol 17 no 2 pp 273ndash296 2017

[21] G S Babu P Zhao and X L Li ldquoDeep Convolutional NeuralNetwork Based Regression Approach for Estimation ofRemaining Useful Liferdquo in Proceedings of the InternationalConference on Database Systems for Advanced Applicationspp 214ndash228 Dallas TX USA April 2016

[22] S P Li Research on Remaining Useful Life Prediction Methodof a Rolling Bearing Combining CNN and LSTM HarbinUniversity of Science and Technology Harbin HeilongjiangChina 2019

[23] X Shi Z Chen and H Wang ldquoConvolutional LSTM net-work a machine learning approach for precipitation now-castingrdquo in Proceedings of the 29th Annual Conference onNeural Information Processing Systems vol 24 Montreal QCCanada December 2015

[24] W Luo W Liu and S Gao ldquoRemembering history withconvolutional LSTM for anomaly detectionrdquo in Proceedings ofthe Institute of Electrical and Electronics Engineers Interna-tional Conference on Multimedia and Expo vol 25 HongKong China July 2017

[25] H Qiao T Wang P Wang S Qiao and L Zhang ldquoA time-distributed spatiotemporal feature learning method for ma-chine health monitoring with multi-sensor time seriesrdquoSensors vol 18 no 9 p 2932 2018

[26] X Deng and W Jiang ldquoDependence assessment in humanreliability analysis using an evidential network approachextended by belief rules and uncertainty measuresrdquo Annals ofNuclear Energy vol 117 pp 183ndash193 2018

[27] L Yin X Deng and Y Deng ldquo)e negation of a basicprobability assignmentrdquo Institute of Electrical and ElectronicsEngineers Transactions on Fuzzy Systems vol 27 no 1pp 135ndash143 2019

[28] F T Wang X J Ma and H Zhu ldquoResearch on Fault Di-agnosis method based on Dempster-Shafer evidential theoryrdquoJournal of Dalian University of Technology vol 4 pp 470ndash4742003

[29] Q Sun X Q Ye and W K Gu ldquoA new combination rules ofevidence theoryrdquo Journal of Electronic vol 8 no 8pp 117ndash119 2000

[30] W X Xu J W Tan and H Zhan ldquoResearch and applicationof the improved DST new method based on fuzzy consistentmatrix and the weighted averagerdquo Advanced Materials Re-search vol 8 2014

[31] D H Hubel and T N Wiesel ldquoReceptive fields binocularinteraction and functional architecture in the catrsquos visualcortexrdquo Journal of Physiology vol 160 no 1 1962


[33] J Schmidhuber ldquoDeep learning in neural networks anoverviewrdquo Neural Netw vol 61 pp 85ndash117 2014

[34] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural net-works a promising tool for fault characteristic mining andintelligent diagnosis of rotating machinery with massivedatardquo Mechanical Systems and Signal Processing vol 72-73pp 303ndash315 2016

[35] W Sun S Shao R Zhao R Yan X Zhang and X Chen ldquoAsparse auto-encoder-based deep neural network approach forinduction motor faults classificationrdquo Measurement vol 89pp 171ndash178 2016

[36] O Abdeljaber O Avci S Kiranyaz M Gabbouj andD J Inman ldquoReal-time vibration-based structural damagedetection using one-dimensional convolutional neural net-worksrdquo Journal of Sound and Vibration vol 388 pp 154ndash1702017

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

[38] W X Xu J W Tan and H Zhan ldquoImproved D-S evidencetheory in ball screw of CNC machine intelligent fault diag-nosis applicationsrdquo Manufacturing Technology and MachineTools no 9 pp 163ndash166 2019

[39] J Li L W Tian and Y Q Wang ldquoShort-term load predictionof power system based on GA-RBF neural networkrdquo Journalof Shanghai University of Electric Power vol 35 no 3pp 205ndash210 2019

[40] Y Liu and H X Chen ldquoFault diagnosis of gearbox based onRBF-PF and particle swarm optimization wavelet neuralnetworkrdquo Netural Computing and Applications vol 31pp 4463ndash4478 2019


chisel engine and finally achieve hierarchical and multilevelmalfunction diagnosis [8] Cao et al improved D-S evidencetheory set up the integrating relations between each evi-dence and increased the recognition rate of malfunctiondiagnosis according to the problem of highly conflict evi-dence which appeared in malfunction diagnosis for large-scale equipment [9] Liu et al adopted the method ofcombining quantum medical neural network with D-S ev-idence theory to achieve the high precision diagnosis formechanical characteristics of circuit breakers [10] Jiang andLin et al attained the goal of improving D-S evidence theoryby changing the combination rules in the evidence theorywhich also had specific application effects [11 12]

In the last few years deep learning has played an es-sential role in the field of artificial intelligence Deep con-volutional neural network (DCNN) has strong ability of datamining and information integration [13ndash19] It has beenwidely applied to the state monitoring and diagnosis re-search of rotating machinery Ga et al classified the faults ofrolling bearings by analyzing vibration signals with wavelettransform and extracting features and feeding them into thedeep learning model [17] Jing et al used the deep convo-lution model to adaptively extract the original fault signalcharacteristics and identified the fault of the motor [19]Zhao et al combined the depth convolution model with theLSTM model to monitor and estimate tool wear andachieved good fault diagnosis results [20]

As an emerging machine learning method deep learninghas strong capabilities of feature extraction and functionmapping Deep learning method can meet the analysis re-quirements of diverse nonlinear and high-dimensionalhealth monitoring data which can be applied in the lifeprediction of rotating machinery equipment Babu GS et al[21] first used the Convolution Neural Network (CNN) topredict the residual life of bearings and verified the effec-tiveness of the method Li [22] combined the convolutionalneural network with the short-time memory neural networkand used CNNrsquos features of convolution and weight sharingto extract deep features and input them into the LSTMnetwork effectively realizing the prediction of the remainingservice life of the rolling bearing Zhao et al [20] combinedthe depth convolution model with the LSTM model tomonitor and estimate tool wear which achieved good faultdiagnosis results Shi et al [23] based on complementing theadvantages of CNN and LSTM proposed the space-timeseries prediction method based on ConvLSTM Luo et al[24] proposed a ConvLSTM-AE framework which betterencodes the change of appearance and motion for regularevents Qiao et al used the TD-ConvlSTM time series modelto analyze the space-time characteristics of multisensor dataon different time scales [25]

)ere are many fault types of rolling bearings withapparent uncertainty It is often challenging to select theoptimal feature or fusion level in state monitoring )ere-fore combining the advantages of multiple intelligentidentification methods this paper proposes a multimodeldecision fusion method based on DCNN-IDST for faultdiagnosis of rolling bearing By this method the fault

information of rotating machinery can be diagnosedcomprehensively

2 Theoretical Background

21 DempsterndashShafer Evidence eory DempsterndashShafertheory has the advantage of dealing with uncertainty and itsbasic formula is shown as follows

(1) Suppose there are proposition A and U as theframework 2U⟶ [0 1])ere is a function m that satisfies the followingconditions

U x1 x2 x3 middot middot middot (1)

m(ϕ) 0 (2)

where m (A) is the Basic Probability Assignment whichrepresents the exact trust function for A)e belief function can be defined as follows

Bel(A) 1113944BsubeA

m(B) (3)

)e plausibility functions are set to

Pls(A) 1 minus Bel(A) (4)

where Pls(A) and Bel(A) are the upper and lowerlimit function of A)e relationship between them isshown as follows Pls(A)geBel(A) AsubeΩ

(2) )e combination rule of DempsterndashShafer evidencetheory [26ndash29]Suppose that the basic probability assignment offrame U is m1 and m2 if A isin U and m(A)gt 0 thefocal target elements areA1 A2 An B1 B2 Bn)e combination rule of DempsterndashShafer evidencetheory is defined as follows

m(A)

1113936AicapBjA

m1(Ai)m2(Bj)

1 minus 1113936AicapBjϕ

m1(Ai)m2(Bj)(5)

(3) )e new improved method of DempsterndashShaferevidence theory (IDST)In this paper the improved DSTmethod proposed inthe literature [30] is adopted to diagnose the state ofrotating machinery )e specific steps are as follows





R rij1113872 1113873M times N (6)

ri 1113944n




2n + 05 (8)


i is as follows

ski

1n

minus12α

+1113936

nj1 rij







di

k1mi AK( 1113857prime (11)


m(A) 1n

1113944

n



mlowast (A) 1113944

AicapBjA

m1 Ai( 1113857lowastm2 Bj1113872 1113873 + m(A)(13)

m(θ) 1 minus 1113944 m(A) (14)

















33 Model Design





Featuremaps

Featuremaps

C1 S2 C3 S4 C5

Output

Fullyconnection



Bearingfailure

teststand

Featurelearning

BPNN

DCNN




fusion


BPNN

DCNN

RBFNN

BPNN

DCNN

RBFNN

Dataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Featurelearning

orfeature

extration

Rawdata

Handcraftfeatures

Diagnosisresult 1

Diagnosisresult 2

(a)

BPNN

DCNN

RBFNNDataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Decisionfusion

IDST


rule

Featurelearning

Diagnosisresult

Diagnosisresult

(b)


















(a) (b) (c)





0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6































R rij1113872 1113873M times N (6)

ri 1113944n




2n + 05 (8)


i is as follows

ski

1n

minus12α

+1113936

nj1 rij







di

k1mi AK( 1113857prime (11)


m(A) 1n

1113944

n



mlowast (A) 1113944

AicapBjA

m1 Ai( 1113857lowastm2 Bj1113872 1113873 + m(A)(13)

m(θ) 1 minus 1113944 m(A) (14)

















33 Model Design





Featuremaps

Featuremaps

C1 S2 C3 S4 C5

Output

Fullyconnection



Bearingfailure

teststand

Featurelearning

BPNN

DCNN




fusion


BPNN

DCNN

RBFNN

BPNN

DCNN

RBFNN

Dataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Featurelearning

orfeature

extration

Rawdata

Handcraftfeatures

Diagnosisresult 1

Diagnosisresult 2

(a)

BPNN

DCNN

RBFNNDataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Decisionfusion

IDST


rule

Featurelearning

Diagnosisresult

Diagnosisresult

(b)


















(a) (b) (c)





0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6







































33 Model Design





Featuremaps

Featuremaps

C1 S2 C3 S4 C5

Output

Fullyconnection



Bearingfailure

teststand

Featurelearning

BPNN

DCNN




fusion


BPNN

DCNN

RBFNN

BPNN

DCNN

RBFNN

Dataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Featurelearning

orfeature

extration

Rawdata

Handcraftfeatures

Diagnosisresult 1

Diagnosisresult 2

(a)

BPNN

DCNN

RBFNNDataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Decisionfusion

IDST


rule

Featurelearning

Diagnosisresult

Diagnosisresult

(b)


















(a) (b) (c)





0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6




























Bearingfailure

teststand

Featurelearning

BPNN

DCNN




fusion


BPNN

DCNN

RBFNN

BPNN

DCNN

RBFNN

Dataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Featurelearning

orfeature

extration

Rawdata

Handcraftfeatures

Diagnosisresult 1

Diagnosisresult 2

(a)

BPNN

DCNN

RBFNNDataprocessing

Bearingfailure

teststand

Multiplesensor

Data-levelfusion

Decisionfusion

IDST


rule

Featurelearning

Diagnosisresult

Diagnosisresult

(b)


















(a) (b) (c)





0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6









































(a) (b) (c)





0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6




























0 200 400 600 800 1000 1200 1400 1600 1800 2000


Mea

n sq

uare

d er

ror (

mse

)

2000 epochs

TrainBestGoal

100

10ndash1

10ndash2

10ndash3

10ndash4





Number Meanvalue


Root amplitudevalue

Crookeddegree


valueFeng-Feng





6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6






























6

4

2

0

ndash2

Seco

nd co

mpo

nent

s


Class 1Class 2

Class 3Class 4

(a)

6

4

2

0

ndash2Se

cond

com

pone

nts


Class 1Class 2

Class 3Class 4

(b)


05

00

ndash05

ndash01

ndash15

ndash20

ndash25

ndash30

Seco

nd co

mpo

nent

s

Class 1Class 2

Class 3Class 4

(c)


Seco

nd co

mpo

nent

s

20

15

10

05

00

ndash05

ndash10

Class 1Class 2

Class 3Class 4

(d)







Vibratingsensor1

BPNN 8917 8625 8755 8878RBFNN 8708 6583 7035 7333DCNN 83 7250 7833 8062

Vibratingsensor2

BPNN 8958 8042 8125 8500RBFNN 9142 7792 8566 8866DCNN 9092 8051 8155 8333


5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6




























5000

5500

6000

6500

7000

7500

8000

8500

9000

9500







BPNN-FL1


RBFNN-FL1



DCNN-FL1



025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6




























025

41

078

21

063

59 070

02 075

87

061

23

065

44

085

12

055

34

084

01

071

05

071

11

1 2 3 4 5 6

BPA

m1 m2m1 m2 m3


067

57

098

61

065

65

099

45

092

82

076

14

061

36

098

96

066

38

097

06

096

93

088

761 2 3 4 5 6

BPA

m1 m2m1 m2 m3








5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6





























5 Conclusions


Data Availability




Acknowledgments


References




















k Or ε 1 2 3 4 5 6




























a multimodel decision fusion method based on dcnn-idst for … · 2020. 8. 27. · idst diagnosis...

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