fault diagnosis method research of mechanical equipment...

Research ArticleFault Diagnosis Method Research of Mechanical EquipmentBased on Sensor Correlation Analysis and Deep Learning

Tangbo Bai12 Jianwei Yang 12 Lixiang Duan3 and Yanxue Wang12

1School of Mechanical-Electronic and Vehicle Engineering Beijing University of Civil Engineering and ArchitectureBeijing 100044 China2Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit VehiclesBeijing University of Civil Engineering and Architecture Beijing 100044 China3College of Safety and Ocean Engineering China University of Petroleum Beijing 102249 China

Correspondence should be addressed to Jianwei Yang yangjianweibuceaeducn

Received 20 June 2020 Revised 8 July 2020 Accepted 22 August 2020 Published 4 September 2020

Academic Editor Anil Kumar

Copyright copy 2020 Tangbo Bai 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

Large-scale mechanical equipment monitoring involves various kinds and quantities of information and the present research onmultisensor information fusion may face problems of information conflicts and modeling complexity is paper proposes ananalysis method combining correlation analysis and deep learning According to the characteristics of monitoring data threetypes of correlation coefficients between sensors in different states are obtained and a new composite correlation analytical matrixis established to fuse the multisource heterogeneous data e matrix represents fault feature information of different equipmentstates and helps further image generation Meanwhile a convolutional neural network-based deep learning method is developedto process the matrix and to discover the relationship between results and equipment states for fault diagnosis To verify themethod of this paper experimental and field case studies are performede results show that it can accurately identify fault statesand has higher diagnostic efficiency and accuracy than traditional methods

1 Introduction

With the development of technology mechanical equipmentpresents the characteristics of complexity automation andhigh speed which greatly increases the difficulty of equip-ment condition monitoring and fault diagnosis Multiplesensors can receive more fault information and improve theaccuracy of fault diagnosis [1 2] and thus a large number ofdifferent types of them are applied for data collection in themonitoring of the large-scale mechanical equipment [3ndash5]which has produced various kinds and quantities of mon-itoring data How to make effective use of these multisensordata to improve the accuracy of the equipment fault diag-nosis has become a hot issue

Due to many data sources and different types datafusion is needed in order to perform the fault diagnosisGenerally there are two kinds of fault diagnosis based onmultiple sensors the decision-level fusion diagnosis and the

feature-level fusion diagnosis respectively For the decision-level fusion diagnosis methods like DS evidence theory[6ndash9] and fuzzy decision theory [10 11] are mostly usedese kinds of methods firstly use a single sensor to identifythe information of the equipment state generate the evi-dence and then make the final decision with certain rulesHowever due to the nonlinear and nonstationary equip-ment states there are often evidence conflicts problems ofinformation from different sensors erefore the methodsof information entropy [6 8] weighted combination [7 9]and fuzzy reasoning [10] are needed to solve these problemswhich lack universality e feature-level fusion is to extractthe features of a single sensor signal by using the time-frequency domain analysis method of fast Fourier transform[2] and wavelet transform [3] then combine the features ofall sensors into a new feature vector according to certainmethods and then use the machine learning methods suchas support vector machine (SVM) [12] artificial neural

HindawiShock and VibrationVolume 2020 Article ID 8898944 11 pageshttpsdoiorg10115520208898944

networks (ANNs) [13] and K-nearest neighbor (KNN) [14]to diagnose the fault Nevertheless with the increase of thesensors the dimension of the feature vector becomes toohigh to cope with this some scholars have adopted thestatistical analysis [13] the principal component analysis(PCA) [15] the relevance vector machine (RVM) [16] andother methods for data dimensionality reduction Also deeplearning approaches such as convolutional neural network(CNN) [17 18] and long short-term memory (LSTM) [1920] are applied for information fusion and fault diagnosisRelative to the diagnosis method based on the decision-levelfusion feature-level fusion diagnosis methods have betteradaptability and diagnostic accuracy However this kind ofmethod is mainly adaptable for the same type of sensorswhen sensors of different kinds are analyzed effective in-formation is often lost due to differences in the character-istics and distribution of data

Most previous studies treated the information of mul-tiple sensors as a single signal and ignored the couplingrelationship between signals resulting in the loss of effectiveinformation [14] However for certain mechanical equip-ment the interaction and mutual influence occurs betweensubsystems and there must be some relationship between thedifferent sources of monitoring data When the equipmentstate changes the corresponding relations will also change[21] Correlation analysis as one kind of mathematicalmethod to analyze the changes of the correlation betweendifferent variables can describe the overall change rules ofequipment states and thus it could applied to the field offault signal analysis [22ndash25] and the multisensor fault di-agnosis [26ndash29] Kang et al [21] correlated the differentbattery voltages with different sensors and used the recursivecorrelation coefficient to diagnose the fault signals andaccurately identified the locations and types of faults Xionget al [27] proposed a new fault diagnosis method for therotating machinery fusing the dimensionless indices and thePearson correlation coefficient ey then analyzed thevariation of the correlations among the multiple sensors bycalculating the correlation coefficients and derived thethreshold value for fault diagnosis Zhou et al [28] devel-oped a fast fault detection and location method based oncapacitive voltage similarity analysis in which the correla-tion coefficient was adopted to represent the fault state andthe threshold was used for fast fault detection and location(FDL) Zhao et al [29] established the feature matrix of theexpanded acoustic vibration signal by using the value ofPearson correlation coefficient as the matrix element andperformed fault diagnosis by using convolutional neuralnetwork and thus realized the effective utilization of soundand vibration signals e results of multisensor correlationanalysis are usually presented in the form of matrix but theconventional threshold processing methods only diagnoseby individual correlation coefficient losing the meaning ofcorrelation analysis When intelligent diagnosis methods areadopted conventional methods are difficult to directly dealwith the matrix and one-dimensional processing will lead tothe problem of high dimension At the same time becausedifferent types of correlation analysis methods have differentrequirements on data distribution the distribution laws of

equipment monitor data of different types are quite dif-ferent so it is necessary to establish a new correlationanalysis method to adapt to different types of data

In view of this this paper proposes a new analysismethod combining composite correlation analysis anddeep learning theory According to the characteristics ofthe traditional correlation analysis a kind of compositecorrelation coefficient is designed and calculated betweensensors of different states e correlation coefficientmatrix is treated as representation of fault feature in-formation of different equipment states and is trans-formed into images Deep mining of the correlationcoefficient is performed by the deep learning method withmultilayer network and thus the relationship between thecorrelation coefficient and equipment state is obtained forfault diagnosis CNN is selected for fault identification inthis paper because it has been successfully applied in thefield of mechanical equipment fault diagnosis and hasshown good performance [30 31] e specific proceduresare as follows firstly according to the data characteristicsof different signal types data preprocessing is carried outto obtain all kinds of eigenvalues and eigenvalue matricesunder different working states are constructed then thecomposite correlation coefficient is calculated on the ei-genvalue matrix to obtain the correlation coefficientmatrix representing the relationship among the sensorsand to realize the image generation of sensor data finallythe deep convolutional neural network algorithm is usedto directly identify the correlation coefficient matriximages so as to avoid the influence of artificially selectingfeatures and improve the accuracy and efficiency of di-agnosis Analysis of rotor faults experiments verifies theefficiency of the proposed method in complex fault di-agnosis by multisource sensor fusion e results showthat the proposed method can accurately identify faultstates and has higher accuracy than the traditionalmethod

rough the above analysis the main contributions inthis paper involve the following (1) A fault informationfusion method is proposed for multisource heteroge-neous data and a new correlation analysis matrix isestablished with the comprehensive advantages of severalrelated analysis methods By analyzing the correlation ofmultisource sensors the changes of equipment states arerepresented and the image generation of monitoringdata is realized It can reduce the data dimension im-prove the computational efficiency and prevent the faultinformation loss caused by the direct comparison ornormalization between data of different types and dif-ferent orders of magnitude (2) Considering the char-acteristic of high dimension and large amount of themonitoring data a fault diagnosis model based on cor-relation analysis and deep learning is built which directlytrains and recognizes the correlation matrix image of alarge number of monitoring data e method avoids theissues of low efficiency and dimensionality curse by theconventional pattern recognition method for large andhigh-dimensional data and the fault diagnosis accuracyis improved

2 Shock and Vibration

2 Theoretical Background

21 Correlation Analysis Correlation analysis generallyrefers to the analysis method to study the relationship be-tween variables that is to study the change relationship ofanother variable when one changes e value describingthis relationship is called correlation coefficient Data ofsensors in mechanical equipment monitoring are continu-ous variables For continuous variables correlation analysiscorrelation coefficients include Pearson and Spearmancorrelation coefficients and multiple correlation analysis iscommonly used Meanwhile since this paper focuses on therelationship between different sensors it needs the corre-lation analysis of signal from one-to-one and one-to-manysensors so the above three correlation analysis methods arediscussed in the paper

211 Pearson Correlation Analysis Pearson correlationcoefficient is a statistical index describing the degree ofcorrelation between variables and the value varies betweenminus1 and 1 When the changes between two variables areconsistent the value is greater than 0 and especially it iscalled complete correlation when the value is 1 On thecontrary when the changes between two variables are op-posite which is called negative correlation the value is lessthan 0 When there is no correlation between the changes oftwo variables the value is 0 which is called uncorrelated Let(xiyi) (i 1 2 n) be the sample from the continuousmonitoring variable (xi yi) then the Pearson correlationcoefficient is

rp 1113944

n

i1 xi minus x( 1113857 yi minus y( 1113857

1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 yi minus y( 11138572

1113969 (1)

where rp is Pearson correlation coefficient x and y are themean values of x and y samples respectively and n is thelength of the variable Pearson correlation coefficient re-quires the variable to conform to the normal distributionand if not the calculated results will be greatly deviated

212 Spearman Correlation Analysis Spearman rank cor-relation is a method to study the correlation between twovariables based on rank data e data requirements ofSpearman rank correlation are less strict than Pearsonrsquoscorrelation As long as the observed values of two variablesare rank data in pairs or the ones transformed by continuousvariable observation data Spearman rank correlation can beused regardless of the overall distribution of the two var-iables and the size of samples Spearman correlation coef-ficient rs is calculated as follows

rs 1 minus61113944

n

i1 R xi( 1113857 minus R yi( 1113857( 11138572

1113872 1113873

n n2

minus 11113872 11138731113872 1113873 (2)

where R(xi) and R(yi) are the rank of the two variables xi andyi in their respective column vectors and n is the length of thevariable Spearman correlation coefficient is improved from

Pearson correlation coefficient and has the effect of elimi-nating its error which is suitable for the case when thenormal distribution is not satisfied However due to theneed of data ranking during the calculation the effect isworse than Pearson correlation coefficient when normaldistribution is satisfied

213 Complex Correlation Analysis In practical analysis avariable is often subject to the comprehensive influence of avariety of variables e so-called complex correlation means tostudy the correlation between multiple variables with one at thesame time e index to measure the degree of complex cor-relation is the complex correlation coefficient e correlationbetween multiple variables with one at the same time cannot bedirectly measured and only indirect calculation can be donee complex correlation coefficient rc between a variable y andmultiple variables xi (i 1 2 n) is calculated as follows

rc corrx y x1 xn( 1113857

1113944n

i1 1113954yi minus y( 11138572

1113944n

i1 yi minus y( 11138572

11139741113972

(3)

where 1113954y is linear regression of y to xi and y is the mean valueof y Complex correlation coefficient is often used in mul-tiple linear regression analysis e correlation degree be-tween the dependent variable and a group of independentvariables is expected which is called complex correlationand the coefficient reflects the ldquocloserdquo degree between oneand a group of variables

22 Convolutional Neural Network 2eory Convolutionalneural network is a kind of bionics algorithm imitating bio-logical neural network Being a representative algorithm in deeplearning theory the difference with the traditional neuralnetwork is that it has a deeper network structure in order tosimulate biological neural networks more accurately e tra-ditional neural network has problems in establishing themultilayer structure such as the complex network too manynodes and parameters slow convergence and computationaldifficulty Convolutional neural network avoids these problemsby the approach of local connections and weight sharing [32]

Local connection is different from the full connection inthe traditional neural network It means that the neuronnodes in a certain layer of the neural network are notconnected to all the neurons in the upper and lower adjacentlayers but only connected to part of adjacent neuronsaccording to certain rules In this way the number ofneurons is greatly reduced and the size of the neural net-work is decreased Especially when dealing with high-di-mensional data due to the complexity of network structureand exponentially increasing neuron data it is difficult toapply the full connection method However through localconnection the neural network structure is simplified withless parameter and the network availability is improved

Weight sharing is another characteristic of convolutionalneural networks e concept refers to the fact that in alocally connected network the parameters are same whendifferent upper and lower neurons are connected On the

Shock and Vibration 3

basis of local connection this method greatly reduces thenumber of parameters and improves the generalizationability of the network

In addition to the above two characteristics the networkstructure of convolutional neural network is different fromtraditional one which has more complex structure andmorelayers It usually consists of input layer multiple convolutionlayers pooling layers fully connected layer and outputlayer and the convolution and pooling layers are unique toCNN as shown in Figure 1

When training by the convolutional neural network ifthe training data are too less or the data image is too largeoverfitting phenomenon may occur Although bettertraining accuracy can be obtained the recognition rate islower when the trained model is applied toother data

In order to solve this problem Alex [33] proposed thedropout technology in this method some neurons stopworking when training which allows a neuron to not en-tirely depend on others us the neural network isdecomposed into multiple subnetworks with weight sharingand the same number of layers and finally the results of eachsubnetwork are averaged rough this method one canimprove the network generalization ability and stability andreduce overfitting of the network [34]

Figure 2 shows the difference between a fully connectedneural network and the one based on dropout techniquee calculation of neural network with full connection isperformed as follows

z(l+1)i w

(l+1)i y

l+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(4)

By using dropout the calculation equation is [35]

r(l+1)i sim Bernoulli(p)

yprime(l)

r(l) lowasty

(l)

z(l+1)i w

(l+1)i yprime

(l)+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(5)

In equation (5) the role of Bernoulli function is to maker

(l+1)i to be the value 1 or 0 with probability p so as to realizethe shielding of neurons assigned as 0

3 Proposed Method

In fault diagnosis of mechanical equipment based on multi-sensor information the key problem lies in how to makecomprehensive use of all monitoring information In order tofind an effective way to realize the diagnosis by multisourceheterogeneous multisensor information fusion a methodbased on composite correlation analysis and deep learning isproposed in the paper and a new correlationmatrix is set up torepresent the correlation changing relationship between dif-ferent sensors and the 1-dimensional data are transformedinto 2-dimensional images en combining the deep con-volutional neural network the fault diagnosis model is built todirectly analyze the image to realize the fault diagnosis and to

improve fault recognition accuracy e framework of themethod is shown in Figure 3 It is composed of several modulesincluding data acquisition feature extraction correlationanalysis based on feature fusion and fault classification

Different kinds of sensors are used to collect the mon-itoring data of mechanical equipment and feature extractionis performed on the data according to the characteristics ofdifferent sensors en the characteristic values are used toanalyze the correlation between different sensors and thenew composite correlation matrix is calculated and visual-ized by image generation en a fault diagnosis modelbased on deep convolutional neural network is established toclassify the fault and to identify the fault pattern

31 Composite Correlation Analysis Matrix e multisourcesensor information fusion method studied in this papermakes use of the interrelationship between different sensorswhich requires correlation analysis of multidimensional ei-genvalues of signals collected by different sensors Accordingto Section 2 the commonly used Pearson correlation analysisrequires the to-be-analyzed data satisfying normal distribu-tion however in mechanical fault diagnosis due to thenonstationarity and noise influence of data part of the datasatisfies normal distribution while the other part does not Atthe same time when the fault occurs it may cause correlationchanges between two sensors or a sensor with other multipleones In this situation the traditional correlation analysismethod is unable to deal with the problem simultaneouslyerefore based on the characteristics of Pearson Spearmanand complex correlation coefficient a comprehensive cor-relation analysis coefficient rn is established in this paper Forn sensors each characteristic vector is calculated respectivelyto form an eigenvalue matrix with n columns As to thecharacteristic vector xi xj (i= 1 2 n) of arbitrary twosensors the composite correlation coefficient calculationequation is as follows

rn

1113944n

i1 xi minus x( 1113857 xj minus x1113872 1113873

1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 xj minus x1113872 11138732

1113969 igt j

corrx xix1 ximinus1 xi+1xn( 1113857 i j

1 minus61113944

n

i1 R xi( 1113857 minus R xj1113872 11138731113872 11138732i

1113874 1113875

n n2

minus 11113872 11138731113872 1113873 ilt j

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)

where each item is the same as in equations (1)ndash(3)According to equation (6) the element rn(xi xj) in the

composite correlation matrix is calculated differentlyaccording to different indices when the index i is greaterthan j Pearson correlation coefficient equation is used whenthe index i is equal to j the complex correlation coefficientequation is used and when the index i is less than j theSpearman correlation coefficient equation is usedroughthe correlation coefficient matrix calculation by this methodthe three methods of correlation coefficient are combined toform the composite correlation analysis matrix which


Inputlayer

Convolutionallayer

Poolinglayer

Fully connectedlayer

Outputlayer

Figure 1 Structure of convolutional neural network

(a)

Dropoutlayer

(b)

Figure 2 Comparison of neural network (a) and (b) neural network with dropout layer

NS IB MA RI BSL CFRM CFBM

NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4

V1XV1YV2XV2YV3XV3YV4XV4Y

F1F2F3F4

Image generationEstablishment ofdiagnosis modelFault classification

Data acquisition Feature extraction

Sensor 1

Sensor 2

Sensor N

F1

F2

Fn

Correlation analysis

Figure 3 Framework of the proposed method


realizes the comprehensive consideration of the changesbetween sensors under different states and avoids the loss ofinformation

32 Establishment of Fault Diagnosis Model Based on Con-volutional Neural Network How to use the compositecorrelation coefficient matrix of multisource sensors to buildthe fault diagnosis model has great influence on diagnosisaccuracy e traditional methods need to transform thematrix into a one-dimensional vector and then methodssuch as neural network SVM and cluster analysis are usedfor diagnosis According to the characteristics of compositecorrelation coefficient matrix the diagnosis model based onconvolutional neural network is established and thenprocessing is performed in the form of a two-dimensionalmatrix in order to improve the calculation efficiency andaccuracy

When using the convolutional neural network forclassification the input of training and classification modelis required to be images erefore the composite corre-lation coefficient matrix is firstly visualized by image gen-eration Since the matrix is two-dimensional it istransformed into an 8 bit gray image in this paper as follows

g x minus xmin

xmax minus xmin1113892 1113893 times 255 (7)

where x represents the element in the composite corre-lation coefficient matrix xmax and xmin are the maximumand minimum values of the elements and g is thegray value of the corresponding image pixel aftertransformation

According to the requirements of mechanical equipmentmonitoring and the characteristics of correlation coefficientmatrix the CNN structure is designed for the gray image ofcomposite correlation coefficient matrix in this paper asillustrated in Figure 4 where the number of the convolutionlayers and the number of pooling layers are both two thenumber and size of convolution kernel of each layer aredetermined according to the actual situation and the acti-vation function of each layer is chosen as the ReLU functionIn order to avoid the overfitting phenomenon in the trainingof convolutional neural network the second pooling layer isfollowed by a single-layer perceptron and then connected toa dropout layer with the shielding probability of 04 Softmaxclassifier is adopted in the output layer and the final outputis the fault recognition result

At the same time because the speed of parameterupdation in the model is determined by the learning rate theadaptive learning rate is used in the experiment to speed upmodel optimization guaranteeing better performance thanexperience-based approaches e initial learning rate is setto 0001 During the training at the end of each epoch lossand precision of the current model are evaluated in thevalidation sete loss value changes are checked every otherepoch and when it is less than 00001 the learning rate lr isattenuated with the calculation of attenuated lrlowast as follows

lrlowast

lrlowast 01 (8)

4 Experimental Studies

A variety of different faults might occur in the runtime oflarge mechanical equipment sometimes even two or moreconcurrent or coupling faults occur at the same time Inorder to solve such problems the researchers introduceddifferent monitoring tools for example in rotor fault di-agnosis in addition to the traditional vibration monitoringthe temperature field monitoring by infrared image canbetter solve the concurrent or coupling faults [36 37] Giventhis background the rotor fault experiment is conducted inthe paper and the data of both vibration and infrared imageare collected for fault diagnosis States of normal and 6 faultsare simulated including coupling faults difficult to solve bytraditional methods

41Experimental Setup e testbed is built in the laboratoryto simulate different working states of rotating machineryand to collect data e experimental hardware includes theZT-3 rotor test bed FLIR E50 infrared thermal camera andMDES fault diagnosis system Besides the computer andsignal cables are included Figure 4 illustrates the distri-bution of the system

e ZT-3 rotor testbed is composed of a governor basemotor coupling and dual-rotor system e rotor systemconsists of a rotating shaft rotor bearing coupling andbearing bracket In the experiment the motor speed is6000 rpm

e vibration signal is collected by the MDES fault di-agnosis system which includes a computer accelerationsensor and multichannel vibration signal acquisition in-strument As shown in Figure 5 the measurement points arechosen at four bearing supports which are denoted as V1V2 V3 and V4 from the motor end respectively At eachmeasurement point signals are collected in both vertical andhorizontal directions e sampling frequency of each vi-bration signal is 20 kHz and the sampling length is 20000points

1 3

2 4

Figure 4 Experimental setup 1 variable speed controller 2thermal camera 3 rotor test stand 4 GUI in computer


Infrared images are collected by the FLIR E50 infraredthermal imager During the experiment the infrared thermalimager is fixed on a tripod to ensure that all infrared imagesare collected under the same condition

7 states are simulated in the experiment includingnormal state (NS) imbalance (IB) misalignment (MA) rubimpact (RI) bearing set loose (BSL) coupling faults of rubimpact and misalignment (CFRM) and coupling faults ofbearing set loose and misalignment (CFBM) 40 images and40 sets of vibration data in each channel are collected at eachstate of which 20 datasets are used for training and theremaining data are used for testing e experiment wasconducted under the Keras deep learning framework andhardware with an I9-9700 CPU and a RTX2080ti GPU

42 Data Processing In the experiment firstly the vibrationand infrared data in rotating equipment monitoring arecollected en feature extraction is performed on the in-frared image and vibration signal respectively e correla-tion coefficients of each infrared and vibration signal arecalculated and the composite correlation coefficient matrix isconstructed for information fusion and converted into grayimage Finally the deep learningmodel based on CNN is usedfor training and classification to realize fault diagnosis

e infrared images are processed in accordance with themethod in literature [37] In this method the infrared imagescaptured from the thermal camera are firstly segmented intorectangular regions of different divisions and regions whichare sensitive to faults are then picked out by dispersion degreecriterion one specific region corresponds to a relevant in-dependent fault After processing the infrared image by thismethod four regions of interest (ROIs) in the infrared imagesare selected as shown in Figure 6 ese four regions showgreater differences at different fault states so the backgroundinterference is eliminated and key fault information isretained by using ROI for fault diagnosis Since each ROIrepresents the temperature change at a certain range they canbe regarded as four independent data sources when these fourROIs are extracted from the imageerefore these four ROIsare taken as data collected by four sensors

Histogram features of each ROI are calculated as thecharacteristic values of four temperature sensors e cal-culation of gray histogram information refers to equation(9) and the equations for calculating histogram features areshown in Table 1

H(g) P(g)

T g 0 1 N (9)

where g represents the gray level P(g) represents thenumber of pixel points with a gray level of g in the image Trepresents the total number of pixels in the image and Nrepresents the maximum value of the gray level in the image

Similar to the infrared image feature extraction methodin order to simplify the analysis and avoid the differencesintroduced by the complex algorithm the vibration datafeature values obtained by the 8 vibration sensors are

calculated by the commonly used nondimensional indica-tors in the time domain as shown in Table 2

A 12times 6 eigenvalue matrix is constructed by the fourtemperature eigenvectors and eight vibration eigenvectorse matrix is calculated according to equation (6) and thecomposite correlation coefficient matrix is obtained Take aset of correlation coefficient matrix at normal state as anexample as shown in Table 3

It can be seen from Table 3 that the vibration signalsare highly correlated from the sensors in two directions atthe same measuring point and the signals from sensors inthe same direction at different measuring points are alsohighly correlated e correlation of infrared data fromeach ROI is relatively high and the correlation betweeninfrared and vibration signals is relatively low which is inaccordance with the situation in signal collection ecorrelation coefficient matrix obtained at six fault states isvisualized by image generation and illustrated as inFigure 7

In Figure 7 the brightness of the gray-scale imagerepresents the correlation degree Higher brightness refers tohigher correlation degree and lower brightness representslower correlation degree It can be seen from Figure 7 thatcolors change differently with different faults ereforethrough correlation analysis it can be seen that the corre-lation between relevant monitoring parameters changes atdifferent states of the equipment and the fault can be di-agnosed according to the changes

43 Result Analysis In this classification experiment 20 setsof composite correlation coefficient matrix images arerandomly selected as the training data at each state of rotorsystem and the remaining 20 sets of images are taken as testdata which means that 140 sets of images form the trainingset and the remaining 140 sets form the test set According tothe image resolution the structure of CNN network isshown in Figure 8 the number of convolution cores in thefirst and second convolutional layers is 16 and 32 with thesize of 3fe and 2times 2 respectively e size of the poolinglayer is 2times 2

e classification result after 300 times of training isshown in Figure 9 and the accuracy in the test is 9929

In this case based on the diagnosis model in this paperPearson Spearman and complex correlation coefficientmatrices are applied for fault diagnosis simultaneously

Figure 5e arrangement of measuring points of vibration signal


replacing the proposed composite feature coefficient matrixMoreover in order to compare with the traditional methodsafter feature extraction 4 temperature feature vectors and 8vibration feature vectors are directly combined and the

traditional BP SVM and KNN are used for fault diagnosise results are shown in Table 4

It can be seen from Table 4 that in the case of mul-tisensor data acquisition due to the high eigenvector

(a) (b) (c)

Figure 6 Acquisition of sensitive areas of infrared images (a) Original image (b) Image segmentation (c) Extraction of sensitive areas

Table 1 Expression of histogram features of the infrared image

e index name Expression

Mean hMV 1113936Nminus1g0 gH(g)

Standard deviation hS D 1113936

Nminus1g0 (g minus hMV)2H(g)

1113969

Skewness hS 1h3S D1113936


Kurtosis hK 1113936Nminus1g0 (g minus hMV)4h4

SD

Energy hEG 1113936Nminus1g0 [H(g)]2

Entropy hEP minus1113936Nminus1g0 H(g)log2[H(g)]

Table 2 List of time domain features


Mean xMV 1n 1113936ni1 xi

Standard deviation xSD

1113936ni1 (xi minus xMV)2n minus 1

1113969

Root mean square xRMS 1113936

ni1 x2

i n1113969

Peak xCF max1leilenxi

Skewness xS 1113936ni1 x3

i nKurtosis xK 1113936

ni1 x4

i nx i (i 1 2 n) is the amplitude of the vibration signal of the time domain sequence

Table 3 Correlation coefficient matrix at normal state

Sensor V1X V1Y V2X V2y V3x V3y V4x V4y F1 F2 F3 F4V1x 049 097 095 047 097 043 096 040 037 045 035 031V1y 039 038 065 089 061 096 058 098 061 064 059 050V2x 074 022 064 027 095 022 089 019 072 065 055 065V2y 053 063 015 031 049 100 061 100 028 010 007 032V3x 084 036 069 054 042 046 097 042 072 052 047 065V3y 068 053 044 081 071 049 057 100 014 035 026 008V4x 071 006 071 022 076 018 046 055 081 056 051 083V4y 034 051 044 066 035 083 025 026 010 030 019 006F1 012 005 027 007 003 015 025 010 043 088 078 097F2 020 002 047 004 009 013 051 030 088 055 095 079F3 029 003 057 000 022 022 063 019 078 095 063 064F4 037 016 058 011 042 035 061 006 097 079 064 057


V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4

V1XV1YV2XV2YV3XV3YV4XV4YF1F2F3F4

(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )

Figure 7 Correlation coefficient matrices under different fault conditions (a) IB (b) MA (c) BSL (d) RI (e) CFRM (f) CFBM

1 times 7

Convolutional

1 times 12 times 12

16 times 10 times 10

16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128

ConvolutionalPooling Pooling Fully connected Output

Figure 8 Structure of convolutional neural network in this study


NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

Figure 9 Classification result by the method in this paper


dimension the diagnosis result is not ideal by using thetraditional feature-level fusion and classification modelwhen there are many fault types especially when complexfaults exist Besides the proposed method avoids theshortcoming of single correlation analysis makes com-prehensive use of all effective information and gets thesatisfied diagnosis results by combining the advantages ofthe deep learning method

5 Conclusions

In this paper a new fault diagnosis method based on cor-relation analysis and deep learning is proposed A newcomposite correlation analysis method is established toperform feature-level fusion of sensor data from differentsources and then the correlation coefficient matrix image isprocessed directly by CNN algorithm to complete faultdiagnosis rough case study the following conclusions aredrawn

(1) e changes of equipment state can be representedthrough the correlation analysis of multiple sensorsand multisource information fusion is carried out Itcan reduce the data dimension improve the com-puting efficiency and avoid the loss of fault infor-mation caused by direct comparison ornormalization between data of different data typesand different orders of magnitude

(2) e new correlation analysis method is built whichintegrates the advantages of several correlationanalysis methods is suitable for heterogeneoussensor data with different distributions and in-fluences relationships so as to obtain better resultsin fault diagnosis

(3) By constructing the fault diagnosis method com-bining the correlation analysis and deep learningmodel the images are trained and identified directlywhich are transformed from the correlation matrix ofthe monitoring data Compared with the traditionalmethod the model is simplified and the fault diag-nosis accuracy is higher

Data Availability

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

Conflicts of Interest

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

Acknowledgments

e authors acknowledge the financial support provided bythe National Natural Science Foundation of China(51975038 and 51605023) Beijing Municipal Natural Sci-ence Foundation China (19L00001) General Project ofScientific Research Program of Beijing Education Com-mission (KM202010016003 and SQKM201810016015)Postdoctoral Science Foundation of Beijing China (ZZ2019-98) Support Plan for the Construction of High-LevelTeachers in Beijing Municipal Universities(CITampTCD201904062 and CITampTCD201704052) ScientificResearch Fund of Beijing University of Civil EngineeringArchitecture (00331615015) BUCEA Post Graduate Inno-vation Project (PG2019092) and Fundamental ResearchFunds for Beijing University of Civil Engineering and Ar-chitecture (X18133)

References

[1] M K Liu M Q Tran and P Y Weng ldquoFusion of vibrationand current signatures for the fault diagnosis of inductionmachinesrdquo Shock and Vibration vol 2019 Article ID7176482 17 pages 2019

[2] Z H Duan T H Wu S W Guo T Shao M Reza andZ X Li ldquoDevelopment and trend of condition monitoringand fault diagnosis of multi-sensors information fusion forrolling bearings a reviewrdquo International Journal of AdvancedManufacturing Technology vol 96 no 1-4 pp 803ndash819 2018

[3] B Sergio M Mario A Alberto C Pablo L Alberto andM Raquel ldquoDissolved gas analysis equipment for onlinemonitoring of transformer oil a reviewrdquo Sensors vol 19pp 1ndash21 2019

[4] G Qian S Lu D Pan H Tang Y Liu and Q Wang ldquoEdgeComputing a promising framework for real-time fault di-agnosis and dynamic control of rotating machines usingmulti-sensor datardquo IEEE Sensors Journal vol 19 no 11pp 4211ndash4220 2019

[5] T Praveenkumar M Saimurugan R B H Hari S Siddharthand K I Ramachandran ldquoA multi-sensor information fusionfor fault diagnosis of a gearbox utilizing discrete waveletfeatures Praveenrdquo Measurement Science and Technologyvol 30 no 8 Article ID e085101 2019

[6] F Xiao ldquoMulti-sensor data fusion based on the belief di-vergence measure of evidences and the belief entropyrdquo In-formation Fusion vol 46 pp 23ndash32 2019

[7] F Y Xiao and B W Qin ldquoA weighted combination methodfor conflicting evidence in multi-sensor data fusionrdquo Sensorsvol 18 no 5 pp 1ndash20 2018

[8] Y C Tang D Y Zhou S Xu and Z C He ldquoA weighted beliefentropy-based uncertainty measure for multi-sensor datafusionrdquo Sensors vol 17 no 4 pp 1ndash15 2017

[9] W Jiang W W Hu and C H Xie ldquoA new engine faultdiagnosis method based on multi-sensor data fusionrdquo AppliedSciences-Basel vol 7 no 3 pp 1ndash18 2017

Table 4 Comparison of test accuracy from different diagnosticmodels

Methods Accuracy ()BP 8714SVM 8857KNN 9357Pearson +CNN 9643Spearman+CNN 9500Complex correlation coefficient +CNN 8285e proposed method 9929


[10] J An M Hu L Fu and J Zhan ldquoA novel fuzzy approach forcombining uncertain conflict evidences in the Dempster-Shafer theoryrdquo IEEE Access vol 7 pp 7481ndash7501 2019

[11] H Hao M Wang Y Tang and Q Li ldquoResearch on datafusion of multi-sensors based on fuzzy preference relationsrdquoNeural Computing and Applications vol 31 no S1pp 337ndash346 2019

[12] L L Jiang H K Yin X J Li and S W Tang ldquofault diagnosisof rotating machinery based on multisensor informationfusion using SVM and time-domain featuresrdquo Shock andVibration vol 2014 Article ID 418178 8 pages 2014

[13] J Kamal M Mohammadsadegh J M Ruholla and R ElahehldquoMisfire and valve clearance faults detection in the com-bustion engines based on a multi-sensor vibration signalmonitoringrdquo Measurement vol 128 pp 527ndash536 2018

[14] X Yan Z Sun J Zhao Z Shi and C-a Zhang ldquoFault di-agnosis of rotating machinery equipped with multiple sensorsusing space-time fragmentsrdquo Journal of Sound and Vibrationvol 456 no 15 pp 49ndash64 2019

[15] V Yolanda P Francesc and T Christian ldquoWind turbinemulti-fault detection and classification based on SCADAdatardquo Energies vol 11 no 11 pp 1ndash18 2018

[16] A Dameshghi and M H Refan ldquoWind turbine gearboxcondition monitoring and fault diagnosis based on multi-sensor information fusion of SCADA and DSER-PSO-WRVM methodrdquo International Journal of Modelling andSimulation vol 39 no 1 pp 48ndash72 2019

[17] Y Liu X S Yan C A Zhang and W Liu ldquoAn ensembleconvolutional neural networks for bearing fault diagnosisusing multi-sensor datardquo Sensors vol 19 no 23 pp 1ndash202019

[18] L Y Jing T Y Wang M Zhao and P Wang ldquoAn adaptivemulti-sensor data fusion method based on deep convolutionalneural networks for fault diagnosis of planetary gearboxrdquoSensors vol 17 no 2 pp 1ndash15 2017

[19] L Gao D H Li D Li L L Yao L M Liang and Y N GaoldquoA novel chiller sensors fault diagnosis method based onvirtual sensorsrdquo Sensors vol 19 no 13 pp 1ndash15 2019

[20] J Wang P Fu L Zhang R X Gao and R Zhao ldquoMultilevelinformation fusion for induction motor fault diagnosisrdquoIEEEASME Transactions on Mechatronics vol 24 no 5pp 2139ndash2150 2019

[21] Y Kang B Duan Z Zhou Y Shang and C Zhang ldquoA multi-fault diagnostic method based on an interleaved voltagemeasurement topology for series connected battery packsrdquoJournal of Power Sources vol 417 pp 132ndash144 2019

[22] S Mohanty K K Gupta and K S Raju ldquoHurst based vibro-acoustic feature extraction of bearing using EMD and VMDrdquoMeasurement vol 117 pp 200ndash220 2018

[23] J Chen D Zhou C Lyu and C Lu ldquoAn integrated methodbased on CEEMD-SampEn and the correlation analysis al-gorithm for the fault diagnosis of a gearbox under differentworking conditionsrdquo Mechanical Systems and Signal Pro-cessing vol 113 pp 102ndash111 2018

[24] X Zhang Q Miao H Zhang and L Wang ldquoA parameter-adaptive VMD method based on grasshopper optimizationalgorithm to analyze vibration signals from rotating ma-chineryrdquo Mechanical Systems and Signal Processing vol 108pp 58ndash72 2018

[25] Y Song S Zeng J Ma and J Guo ldquoA fault diagnosis methodfor roller bearing based on empirical wavelet transform de-composition with adaptive empirical mode segmentationrdquoMeasurement vol 117 pp 266ndash276 2018

[26] F Ye Z S Zhang Z J Xia Y F Zhou and H ZhangldquoMonitoring and diagnosis of multi-channel profile databased on uncorrelated multilinear discriminant analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 103 no 9-12 pp 4659ndash4669 2019

[27] J Xiong Q Liang J Wan Q Zhang X Chen and R Maldquoe order statistics correlation coefficient and PPMCC fusenon-dimension in fault diagnosis of rotating petrochemicalunitrdquo IEEE Sensors Journal vol 18 no 11 pp 4704ndash47142018

[28] D Zhou H Qiu S Yang and Y Tang ldquoSubmodule voltagesimilarity-based open-circuit fault diagnosis for modularmultilevel convertersrdquo IEEE Transactions on Power Elec-tronics vol 34 no 8 pp 8008ndash8016 2019

[29] S Zhao E Wang and J Hao ldquoFault diagnosis method forenergy storage mechanism of high voltage circuit breakerbased on CNN characteristic matrix constructed by sound-vibration signalrdquo Journal of Vibroengineering vol 21 no 6pp 1665ndash1678 2019

[30] S Wang J Xiang Y Zhong and Y Zhou ldquoConvolutionalneural network-based hidden Markov models for rolling el-ement bearing fault identificationrdquo Knowledge-Based Systemsvol 144 pp 65ndash76 2018

[31] S Wang and J Xiang ldquoA minimum entropy deconvolution-enhanced convolutional neural networks for fault diagnosis ofaxial piston pumpsrdquo Soft Computing vol 24 no 4pp 2983ndash2997 2020

[32] N Strom ldquoSparse connection and pruning in large dynamicartificial neural networksrdquo European Conference on SpeechCommunication and Technology vol 5 pp 2807ndash2810 1997

[33] A Krizhevsky I Sutskever and G E Hinton ldquoImageNetclassification with deep convolutional neural networksrdquoConference on Neural Information Processing Systems vol 1pp 1ndash9 2012

[34] H Wu and X Gu ldquoTowards dropout training for convolu-tional neural networksrdquo Neural Networks vol 71 pp 1ndash102015

[35] L Cao X Zhang W Ren and K Huang ldquoLarge scale crowdanalysis based on convolutional neural networkrdquo PatternRecognition vol 48 no 10 pp 3016ndash3024 2015

[36] T Bai L Zhang L Duan and J Wang ldquoNSCT-based infraredimage enhancement method for rotating machinery faultdiagnosisrdquo IEEE Transactions on Instrumentation and Mea-surement vol 65 no 10 pp 2293ndash2301 2016

[37] L Duan M Yao J Wang T Bai and L Zhang ldquoSegmentedinfrared image analysis for rotating machinery fault diag-nosisrdquo Infrared Physics amp Technology vol 77 pp 267ndash2762016


networks (ANNs) [13] and K-nearest neighbor (KNN) [14]to diagnose the fault Nevertheless with the increase of thesensors the dimension of the feature vector becomes toohigh to cope with this some scholars have adopted thestatistical analysis [13] the principal component analysis(PCA) [15] the relevance vector machine (RVM) [16] andother methods for data dimensionality reduction Also deeplearning approaches such as convolutional neural network(CNN) [17 18] and long short-term memory (LSTM) [1920] are applied for information fusion and fault diagnosisRelative to the diagnosis method based on the decision-levelfusion feature-level fusion diagnosis methods have betteradaptability and diagnostic accuracy However this kind ofmethod is mainly adaptable for the same type of sensorswhen sensors of different kinds are analyzed effective in-formation is often lost due to differences in the character-istics and distribution of data

Most previous studies treated the information of mul-tiple sensors as a single signal and ignored the couplingrelationship between signals resulting in the loss of effectiveinformation [14] However for certain mechanical equip-ment the interaction and mutual influence occurs betweensubsystems and there must be some relationship between thedifferent sources of monitoring data When the equipmentstate changes the corresponding relations will also change[21] Correlation analysis as one kind of mathematicalmethod to analyze the changes of the correlation betweendifferent variables can describe the overall change rules ofequipment states and thus it could applied to the field offault signal analysis [22ndash25] and the multisensor fault di-agnosis [26ndash29] Kang et al [21] correlated the differentbattery voltages with different sensors and used the recursivecorrelation coefficient to diagnose the fault signals andaccurately identified the locations and types of faults Xionget al [27] proposed a new fault diagnosis method for therotating machinery fusing the dimensionless indices and thePearson correlation coefficient ey then analyzed thevariation of the correlations among the multiple sensors bycalculating the correlation coefficients and derived thethreshold value for fault diagnosis Zhou et al [28] devel-oped a fast fault detection and location method based oncapacitive voltage similarity analysis in which the correla-tion coefficient was adopted to represent the fault state andthe threshold was used for fast fault detection and location(FDL) Zhao et al [29] established the feature matrix of theexpanded acoustic vibration signal by using the value ofPearson correlation coefficient as the matrix element andperformed fault diagnosis by using convolutional neuralnetwork and thus realized the effective utilization of soundand vibration signals e results of multisensor correlationanalysis are usually presented in the form of matrix but theconventional threshold processing methods only diagnoseby individual correlation coefficient losing the meaning ofcorrelation analysis When intelligent diagnosis methods areadopted conventional methods are difficult to directly dealwith the matrix and one-dimensional processing will lead tothe problem of high dimension At the same time becausedifferent types of correlation analysis methods have differentrequirements on data distribution the distribution laws of

equipment monitor data of different types are quite dif-ferent so it is necessary to establish a new correlationanalysis method to adapt to different types of data

In view of this this paper proposes a new analysismethod combining composite correlation analysis anddeep learning theory According to the characteristics ofthe traditional correlation analysis a kind of compositecorrelation coefficient is designed and calculated betweensensors of different states e correlation coefficientmatrix is treated as representation of fault feature in-formation of different equipment states and is trans-formed into images Deep mining of the correlationcoefficient is performed by the deep learning method withmultilayer network and thus the relationship between thecorrelation coefficient and equipment state is obtained forfault diagnosis CNN is selected for fault identification inthis paper because it has been successfully applied in thefield of mechanical equipment fault diagnosis and hasshown good performance [30 31] e specific proceduresare as follows firstly according to the data characteristicsof different signal types data preprocessing is carried outto obtain all kinds of eigenvalues and eigenvalue matricesunder different working states are constructed then thecomposite correlation coefficient is calculated on the ei-genvalue matrix to obtain the correlation coefficientmatrix representing the relationship among the sensorsand to realize the image generation of sensor data finallythe deep convolutional neural network algorithm is usedto directly identify the correlation coefficient matriximages so as to avoid the influence of artificially selectingfeatures and improve the accuracy and efficiency of di-agnosis Analysis of rotor faults experiments verifies theefficiency of the proposed method in complex fault di-agnosis by multisource sensor fusion e results showthat the proposed method can accurately identify faultstates and has higher accuracy than the traditionalmethod

rough the above analysis the main contributions inthis paper involve the following (1) A fault informationfusion method is proposed for multisource heteroge-neous data and a new correlation analysis matrix isestablished with the comprehensive advantages of severalrelated analysis methods By analyzing the correlation ofmultisource sensors the changes of equipment states arerepresented and the image generation of monitoringdata is realized It can reduce the data dimension im-prove the computational efficiency and prevent the faultinformation loss caused by the direct comparison ornormalization between data of different types and dif-ferent orders of magnitude (2) Considering the char-acteristic of high dimension and large amount of themonitoring data a fault diagnosis model based on cor-relation analysis and deep learning is built which directlytrains and recognizes the correlation matrix image of alarge number of monitoring data e method avoids theissues of low efficiency and dimensionality curse by theconventional pattern recognition method for large andhigh-dimensional data and the fault diagnosis accuracyis improved





rp 1113944

n


1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 yi minus y( 11138572

1113969 (1)



rs 1 minus61113944

n

i1 R xi( 1113857 minus R yi( 1113857( 11138572

1113872 1113873

n n2

minus 11113872 11138731113872 1113873 (2)





1113944n

i1 1113954yi minus y( 11138572

1113944n

i1 yi minus y( 11138572

11139741113972

(3)











z(l+1)i w

(l+1)i y

l+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(4)



yprime(l)

r(l) lowasty

(l)

z(l+1)i w

(l+1)i yprime

(l)+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(5)



3 Proposed Method





rn

1113944n


1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 xj minus x1113872 11138732

1113969 igt j


1 minus61113944

n

i1 R xi( 1113857 minus R xj1113872 11138731113872 11138732i

1113874 1113875

n n2

minus 11113872 11138731113872 1113873 ilt j

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)




Inputlayer

Convolutionallayer

Poolinglayer


Outputlayer


(a)

Dropoutlayer

(b)



NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


F1F2F3F4



Sensor 1

Sensor 2

Sensor N

F1

F2

Fn







g x minus xmin





lrlowast

lrlowast 01 (8)






1 3

2 4








H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References













































rp 1113944

n


1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 yi minus y( 11138572

1113969 (1)



rs 1 minus61113944

n

i1 R xi( 1113857 minus R yi( 1113857( 11138572

1113872 1113873

n n2

minus 11113872 11138731113872 1113873 (2)





1113944n

i1 1113954yi minus y( 11138572

1113944n

i1 yi minus y( 11138572

11139741113972

(3)











z(l+1)i w

(l+1)i y

l+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(4)



yprime(l)

r(l) lowasty

(l)

z(l+1)i w

(l+1)i yprime

(l)+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(5)



3 Proposed Method





rn

1113944n


1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 xj minus x1113872 11138732

1113969 igt j


1 minus61113944

n

i1 R xi( 1113857 minus R xj1113872 11138731113872 11138732i

1113874 1113875

n n2

minus 11113872 11138731113872 1113873 ilt j

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)




Inputlayer

Convolutionallayer

Poolinglayer


Outputlayer


(a)

Dropoutlayer

(b)



NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


F1F2F3F4



Sensor 1

Sensor 2

Sensor N

F1

F2

Fn







g x minus xmin





lrlowast

lrlowast 01 (8)






1 3

2 4








H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References















































z(l+1)i w

(l+1)i y

l+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(4)



yprime(l)

r(l) lowasty

(l)

z(l+1)i w

(l+1)i yprime

(l)+ b

(l+1)i

y(l+1)i f z

(l+1)i1113872 1113873

(5)



3 Proposed Method





rn

1113944n


1113944n

i1 xi minus x( 11138572

1113969

1113944n

i1 xj minus x1113872 11138732

1113969 igt j


1 minus61113944

n

i1 R xi( 1113857 minus R xj1113872 11138731113872 11138732i

1113874 1113875

n n2

minus 11113872 11138731113872 1113873 ilt j

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(6)




Inputlayer

Convolutionallayer

Poolinglayer


Outputlayer


(a)

Dropoutlayer

(b)



NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


F1F2F3F4



Sensor 1

Sensor 2

Sensor N

F1

F2

Fn







g x minus xmin





lrlowast

lrlowast 01 (8)






1 3

2 4








H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References










































Inputlayer

Convolutionallayer

Poolinglayer


Outputlayer


(a)

Dropoutlayer

(b)



NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


F1F2F3F4



Sensor 1

Sensor 2

Sensor N

F1

F2

Fn







g x minus xmin





lrlowast

lrlowast 01 (8)






1 3

2 4








H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References













































g x minus xmin





lrlowast

lrlowast 01 (8)






1 3

2 4








H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References















































H(g) P(g)

T g 0 1 N (9)















(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References













































(a) (b) (c)







1113969




SD








1113969


ni1 x2

i n1113969




ni1 x4





V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References










































V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(a)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(b)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(c)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(d)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(e)

V1X

V1Y

V2X

V2Y

V3X

V3Y

V4X

V4Y F1 F2 F3 F4


(f )


1 times 7

Convolutional

1 times 12 times 12


16 times 5 times 5

32 times 4 times 4

32 times 2 times 2

1 times 128




NS

IB

MA

RI

BSL

CFRM

CFBM

20

20

20

20

20

19

20

1




5 Conclusions





Data Availability




Acknowledgments


References











































5 Conclusions





Data Availability




Acknowledgments


References










































fault diagnosis method research of mechanical equipment...

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