Multiple Feature Vectors Based Fault Classification for WSN Integrated Bearing … · 2019. 7. 30. · F :SignalcollectedfromWSNof(a)normalstatus,(b)rollingbearingfault,(c)innerringfault,and(d)outerringfault

Research ArticleMultiple Feature Vectors Based Fault Classification forWSN Integrated Bearing of Rolling Mill

Bo Qin 1 Luyang Zhang 1 Heng Yin 1 and Yan Qin 2

1School of Mechanical Engineering Inner Mongolia University of Science and Technology Baotou 014010 China2College of Control Science and Engineering Zhejiang University Hangzhou 310027 China

Correspondence should be addressed to Yan Qin neuqinyan163com

Received 21 September 2017 Accepted 1 February 2018 Published 1 April 2018

Academic Editor Yongji Wang

Copyright copy 2018 Bo Qin et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

For rolling mill machines the operation status of bearing has a close relationship with process safety and production effectivenessTherefore reliable fault diagnosis and classification are indispensable Traditional methods always characterize fault feature usinga single fault vector which may fail to reveal whole fault influences caused by complex process disturbances Besides it may alsolead to poor fault classification accuracy To solve the above-mentioned problems a fault extraction method is put forward toextract multiple feature vectors and then a classification model is developed First to collect sufficient data a data acquisitionsystem based on wireless sensor network is constructed to replace the traditional wired system which may bring dangers duringproduction Second the measured signal is filtered by a morphological average filtering algorithm to remove process noise andthen the empirical mode decomposition method is applied to extract the intrinsic mode function (IMF) which contains the faultinformation On the basis of the IMFs a time domain index (energy) and a frequency index (singular values) are proposed throughHilbert envelope analysis From the above analysis the energy index and the singular value matrix are used for fault classificationmodeling based on the enhanced extreme learning machine (ELM) which is optimized by the bat algorithm to adjust the inputweights and threshold of hidden layer node In comparison with the fault classification methods based on SVM and ELM theexperimental results show that the proposed method has higher classification accuracy and better generalization ability

1 Introduction

As a key part of rolling mill bearing operates in theenvironment of high temperature high humidity and heavydust Besides bearing bears the largest impact force andload during production and it easily goes wrong under thiscircumstance Thus monitoring of bearing and timely classi-fying the faults into correct types are of great significance

Recently data-driven fault monitoring and classificationmethods have attracted more and more attention [1] Infact the diversity and quality of modeling data influence theeffectiveness of the fault classification Now operating dataof rolling mill are collected through wired communicationwhich needs high cost and are hard to be constructedHowever with the development of wireless communica-tion technology wireless sensor network (WSN) has beenwidely applied in industrial processes because it has theadvantages of low power consumption low cost wireless

communication and so forth [2] To the best of the authorsrsquoknowledge the studies on fault classification of bearing basedon WSN technology are rarely reported Using the well-developed networking technologies data transmissions andinformation exchanges within and between systems becomemore efficient fast and reliable [3 4]

After collection of data for fault classification of bearingseveral crucial points should be discussed (1) how to extractthe fault features from the collected signal (2) how to improvethe classification accuracy of the fault identification modelLiu andPan [5] extracted bearing fault feature in time domainbased on the analysis of data characteristic Similarly ShuangandMeng [6] analyzed the vibration signal of rolling bearingby using principal component analysis (PCA) and extracteddata element as the reflection of the main characteristics offault case However the vibration signals usually contain alarge number of nonlinear components while PCA is notcapable of copping with the nonlinear characteristics The

HindawiJournal of Control Science and EngineeringVolume 2018 Article ID 3041591 11 pageshttpsdoiorg10115520183041591

2 Journal of Control Science and Engineering

above-mentioned methods judge the status of the rollingbearings only from a view of single fault feature whichcould not give a comprehensive presentation of fault caseFor the multi-fault-features extraction Malhi and Gao [7]proposed a method to construct a mixed domain feature setbased on wavelet decomposition However the time seriesis only extracted by wavelet decomposition in the frequencydomain and time domain features are not considered Onthe contrary Lei et al [8] extracted features from frequencyinstead of time domain from six aspects which includeoriginal vibration signal and its spectrum and the filteredand demodulated signal by wavelet packet Qin et al [9]developed a fault classification model based on an improvedextreme learningmachine (ELM)methodHowever to betterdescribe fault more fault features are needed to measurethe fault influences That is multiple fault features should bedecomposed rather than one single fault vector

As for the fault classification intelligent algorithms havebeen gradually applied to bearing such as artificial neuralnetwork [10] and least squares support vector machines [11]The traditional back propagation neural network (BPNN)faces the problem of slow convergence rate difficulty ofconfiguring tunable parameters and easily falling into thelocal optimum In comparisonwithBPNN the generalizationperformance of support vector machine (SVM) is improvedHowever kernel function and its parameters are usually givenaccording to human experiences ELM [12] is a newly devel-oped single hidden layer feed-forward neural network whichdoes not require continuously to adjust parameters of hiddenlayer In ELM iterative parameter optimization process oftraditional neural network is replaced with solving linearequation groups and the outputs of the minimum norm leastsquares solution are employed as the weights of the networkTherefore the network is trained one time without iterationsCompared with BPNN and SVM ELM greatly improves thetraining speed and generalization ability which has beensuccessfully applied in the areas such as pattern recognition[13ndash18] The idea of introducing ELM into fault classificationfor bearing is given in this paper In fact the adjustment ofthe weights of the input and hidden layer adopts randomselection method which cannot guarantee the validity of theweight Because the structure parameters of fault identifica-tion model determine the classification ability how to obtainthe optimal structure parameters is the key to improve theclassification accuracy of fault identification model

To solve the above-mentioned problems a comprehen-sive and effective fault feature extraction and classificationalgorithm is proposed in this paper First a WSN is con-structed in gearbox to collect the vibration signal Secondto overcome the influence of disturbances morphologicalaverage filtering algorithm is given to filter the collectedsignals and then the intrinsic mode function (IMF) isobtained through empirical mode decomposition (EMD)[19] after denoising IMF presents fault features and IMFcomponents that have large correlation coefficients and areused to calculate energy index in time domain Besideson the other hand envelope spectrums of these IMFs areobtained byHilbert envelope spectrumanalysis which can beused to obtain the singular values by singular decomposition

on envelope spectrum matrix The singular matrix and theenergy index reconstructed multiple feature vectors used forclassificationThird bat algorithm [20] is utilized to optimizethe weights of input and hidden layers of ELM which usedynamic control of global and local search to avoid the resultsfalling into the local optimum At last the fault classificationmodel is developed by these feature vectors and the optimizedELM algorithm The major contribution of this article issummarized as follows

(1) A data acquisition system based on wireless sensornetwork is constructed to replace the traditionalwired system

(2) A multiple fault features decomposition method isproposed to explain the fault influences using twoindices with physical significance

(3) A bat algorithm optimized ELM algorithm is pro-posed to determine the parameters to achieve betterclassification accuracy

The remainder of this article is organized as followsIn Section 2 a simple description of rolling bearing andthe developed WSN is briefly given Next the extractionof multiple feature vectors is proposed in Section 3 InSection 4 fault classification method is formulated basedon the enhanced ELM algorithm Experiment results clearlydemonstrate the efficacy and feasibility of the proposedmethod in the last section

2 Description of Rolling Bearing and theDeveloped Wireless Sensor Network

Rolling bearing has been widely used in industry which ismainly composed of four parts inner ring outer ring rollingbody and the holder Figure 1 shows the physical structureof rolling bearing Its main function is transforming slidingfriction between the shaft and seat into rolling friction Thebearing studied in this paper is from Baotou Iron and SteelGroup of which the type is S-21062-C produced by the SORCompany US

To collect data from rolling bearing wireless sensornetwork (WSN) is constructed WSN usually consists of anumber of sensor nodes cluster head nodes and sink nodesBesides it forms a multihop ad hoc network system throughthe wireless communication which can be used to receivesend and process the information of monitoring objectswithin the covered area [17] Considering that the object isa low speed and heavy load mill we design a WSN that isbattery-powered and of low power consumption low costand rapid deployment tomonitor the vibration of rollingmill

Figure 2 shows the developed network topology ofCSP-F1rolling mill gearbox which consists of sensor nodes clusterhead and sink nodesThe sensor node collects and then sendsvibration signals to cluster head node according to the givensampling interval meanwhile it also receives commandsfrom the cluster head nodes Cluster head node collectsmeasured vibration data from sensor nodes and transmits thedata to sink node Besides cluster head node has three roleswhich are sending command to cluster measured vibration

Journal of Control Science and Engineering 3

Outer ring

Rolling elements

Inner ring

Retainer

I axis

II axis

Figure 1 Physical structure of rolling bearing

InternetSensor field

Sensor nodesCluster head nodes

Cluster headSink nodes

Figure 2 Network topology of wireless sensor network

node receiving the convergence order and maintenancetime synchronization The main functions of sink node arecollecting data from cluster head node and transmitting thedata to monitoring system

3 The Extraction of Multiple Feature Vectors

In order to effectively extract plenty of information underdifferent status of rolling bearing the signals collected byWSN are denoised by morphological averaged filter Afterdenosing Figure 3 shows the proposed procedure of featureextraction Specifically it includes three parts (1) employingthe EMD method to get intrinsic mode components (IMFs)that have large correlation coefficients (2) calculating energyindex based on the obtained IMFs (3) performing Hilbertenvelope analysis to IMFs to obtain the envelope spectrumand get their singular values Through the above steps thecalculated energy index and singular values are employed asmultiple feature vectors for bearing fault classification

31 Denoising of Original Signals To remove the noise con-tained in the data collected fromWSN system mathematical

morphology (MM) and average filtering algorithm [18] areused for filtering The idea of MM is to use some structuralelements that have certain shapes to measure and extractimages corresponding to the shape and achieve the purpose ofimage analysis Based on the geometric characteristics of thesignal MM based average filter can cope with the nonlinearsignal noise by morphological operations between structuralelements and the original signal The proposed filter inheritsthe advantages of MM including simple operation andanalysis in time domain Therefore it is advantageous for theprocessing of mechanical fault signals

Opening operator ∘ and closing operator ∙ are two basicoperations of MM which are shown as follows respectively

(119891 ∘ 119892) (119899) = (119891Θ119892 oplus 119892) (119899) (1)

(119891 ∙ 119892) (119899) = (119891 oplus 119892Θ119892) (119899) (2)

where Θ is erosion operation presenting the relationship in(3) oplus is dilation operation having the relationship in (4)

(119891Θ119892) (119899) = min [119891 (119899 + 119898) minus 119892 (119898)] (3)

(119891 oplus 119892) (119899) = max [119891 (119899 minus 119898) + 119892 (119898)] (4)

where symbols 119899 and 119898 indicate sampling time satisfying 119899larger than119898

The linear combination of (1) and (2) can be used toconstruct the average filter (AVG)

AVG (119891) = (119891 ∙ 119892 + 119891 ∘ 119892)2 (5)

In this way positive and negative impulses of the signalare eliminated Besides it can smooth the signal and reducethe signal noise

32 Extraction of Multiple Feature Vectors

321 Calculation of IMF Components Due to harsh opera-tion conditions of rolling bearing its vibration signal alwayscontains process disturbances including the resonance andexternal noise Therefore after denoising using (5) the EMD


Calculate IMFs that have largecorrelation coefficients

Obtain energy index

Singular value decomposition

Get the combined feature vectors

Hilbert envelope demodulation

Construct energy feature matrixObtain singular value matrix

Output to intelligent fault classification model

Collect signal x(k)

Perform EMD to x(k)

Figure 3 Flow chart of the extraction of fault feature vectors

algorithm is employed to extract the inherent characteristicsof signals The concrete calculation procedures are given asfollows

Note the denoised signal still as 119909(119896) for brevity anddecompose it according to EMD

119909 (119896) = 119898sum119894=1

119888119894 (119896) + 119903119898 (119896) (6)

where 119888119894(119896) 119894 isin [1119898] is IMF 119903119898(119896) is the residual of thesignal and 119896 is the index of sampling time

In fact different IMFs have different significances in com-parison with the original signal 119909(119896) And the significancecan be evaluated by a correlation coefficient Inspired bythe definition of cross-correlation function the correlationcoefficient 120588119909119888119894 between the original signal 119909(119896) and IMF 119888119894(119896)is defined as follows

120588119909119888119894 = sum119870119896=0 119909 (119896) 119888119894 (119896)radicsum119870119896=0 119909 (119896)2sum119870119896=0 119888119894 (119896)2

(7)

where 119909(119896) is the denoised signal 119888119894(119896) is the 119894th IMF and 119870is the number of sampling times

A large value of the coefficient means that the corre-sponding IMF is relevant to the original signal In this wayit eliminates the interference component and obtains theintrinsic componentmode component that contains themostinformation of the original signal

322 Energy Index The values of 120588119909119888119894 calculated from (7)are sorted in descending order Then 01 is defined as thethreshold of correlation coefficient and the first119898 IMFs larger

than the threshold are selected On the basis of this theenergy index can be calculated as follows

119864119894 =119870sum119896=1

119888119894 (119896) 119894 = 1 2 119898 (8)

After that an energy eigenvector T = [1198641 1198642 119864119898]is developed For easy comparison and processing T isnormalized as follows

T = [1198641119864 1198642119864 119864119898119864 ]119879 (9)

where 119864 = (sum119898119894=1 |119864119894|2)12323 IMF Based Hilbert Envelope Spectrum Analysis TheIMFs 1198881 1198882 119888119898 calculated from Section 322 are taken toperform Hilbert transform according to

119867[119888119894 (119896)] = 1120587119870sum119903=1

119888119894 (119903)119896 minus 119903 (10)

Combined with (10) the envelope spectrum of each IMFis calculated as follows

119861119894 (119896) = radic1198882119894 (119896) + 1198672 [119888119894 (119896)] (11)

Finally the envelope spectrum of each IMF constructs amatrix B By performing the singular value decompositiontheory [18] on B it obtains

B = USV119879 (12)


BA-ELM based fault classification model

Input

Output

Energy index and multiple feature vectors

Different fault classes

Figure 4 Flow chart of intelligent fault classification

where S = diag(1205901 1205902 120590119897) is the singular values of thematrix B U = [1199061 1199062 119906119898] and V = [V1 V2 V119899] areorthogonal matrixes

By processing each group of the signal under differentstatus according to the above steps we obtain the IMFHilbertenvelope spectrum singular value matrix and combine thesesingular value matrixes and energy features as multiple fea-ture vectors to classify fault of rolling bearing And multiplefeature vectors are employed to train classification model ofrolling bear based on bat algorithm (BA) optimized ELMwhich will be given in the following section

4 Enhanced ELM Algorithm forFault Classification

The accuracy of fault classification depends on the intelligentmodel used in the process of machine learning methodsIn comparison with the BP method and the SVM methodELM only needs to determine the number of nodes of hiddenlayer during the training of the network Besides it hasthe advantages of high efficiency fast learning speed andthe unique solution However two structure parameters ofELM that is input weights and hidden layer threshold arerandomly given which may result in poor accuracy Havingthe advantages of dynamic control of global and local searchconversion and avoiding falling into local optimum BA isemployed to optimize the two structure parameters of ELMThus BAoptimized ELM is proposed in the developed rollingbearing fault classification model to improve the precisionand generalization ability

41 The Establishment of Fault Classification Model In thispart the fault classification model is developed based onELM Figure 4 shows the proposed method Only determin-ing the number of neurons in hidden layer ELM randomlygenerates connection weights and threshold of hidden layerneurons between the input layer and hidden layer and it canobtain the unique optimal solution

Assuming that the number of samples is 119873 the numberof nodes of hidden layer is 119871 and the activation function is119892(119909) the mathematical model of ELM is defined as follows

119910119894 =119871sum119895=1

120573119895119892 (119908119895119909119894 + 119887119895) (13)

where119908119895 = [1198961198951 1198961198952 119896119895119899] is the connectionweights vectorbetween the input node and the 119895th node of hidden layer 119887119895is threshold of the 119895th node in hidden layer

In (13) a feed-forward neural network model of singlehidden layer is developed of which the output is close to zeroerror

119873sum119894=1

1003817100381710038171003817119910119894 minus 11990511989410038171003817100381710038172 = 0 (14)

Sequentially parameters 119908119895 119887119895 and 120573119895 satisfy the follow-ing relationship

119873sum119894=1

120573119895119892 (119908119895119909119894 + 119887119895) = 119905119894 119894 = 1 2 119873 (15)

And (14) can be further simplified asH120573 = T in which

H = [[[

119892 (1198961 1198871 1199091) 119892 (119896119871 119887119871 1199091)

119892 (1198961 1198871 119909119873) 119892 (119896119871 119887119871 119909119873)]]]119873times119871

120573 = [[[[[

1205731198791120573119879119871

]]]]]

T = [[[[

1198791198791 119879119879119873

]]]]119873times119898

(16)

H is the output matrix of hidden layer and H(119894 119895) standsfor the output of the 119894th training data in the 119895th hidden node

The goal of adjustment is to find a set of optimalparameters 119908119895 119887119895 120573119895 that make the (H120573)119879 minus Tminimum

42 Enhanced ELM Based on BA The weights of input layerand thresholds of hidden layer might be zero which mayresult in the functionless of some hidden layers Thus thenumber of hidden layer nodes has to be increased to achievehigher classification accuracy However it may lead to pooradaptability and low generalization capacity for testing dataTo solve this problem BA is employed to optimize the inputweights and threshold of hidden layer of ELM In this waythe classification accuracy and generalization ability will beimproved Figure 5 shows the specific process

BA is a new heuristic algorithm proposed by Yang et al[21] and it has the advantages of fast convergence speed andhigh convergence precision It is used to find the optimalsolution of the problem by simulating the foraging behaviorsof bat The specifics are as follows

(1) Initialize the bat population location 119909119905119894 and speedV119905119894 (119894 = 1 2 119899) in which 119905 is the time index Definethe pulse frequency 119891119894 of the 119894ℎ119905 bats at position 119909119894Then initialize the pulse firing rate 119903119905119894 and loudness119860119905119894According to the fitness value determine the currentoptimal solution 119909lowast


Start

Initialization population number N the initial pulse frequency f the biggest voice loudness A loudness attenuation coefficient alpha pulse enhancement coefficient of beta the largest number of iterations D

Calculate the fitness value of each individual for a population (mean square error)

Is it the optimal solution conditions

To get optimal weights of input and hidden layer bias

EndAdjust the frequency to produce new and update

the velocity and position

Is the new solutionacceptable

Update the loudness and transmitting frequency

Yes

Yes

No

No

Figure 5 The flow chart of BA optimized ELM algorithm

(2) Update the bat pulse frequency speed and positionaccording to (17) through (19) respectively

119891119894 = 119891min + 120573 (119891max minus 119891min) (17)

V119905119894 = V119905minus1119894 + 119891119894 (119909119905119894 minus 119909lowast) (18)

119909119905119894 = 119909119905minus1119894 + V119905119894 (19)

where 120573 isin [0 1] is a random number uniformlydistributed V119905119894 V

119905minus1119894 are speed at time 119905 and 1199051 119909119905119894 119909119905minus1119894

represent the position of the bat at times 119905 and 1199051(3) Generate uniformly distributed random number 1205881

If 1205881 gt 119903119894 it means that a new solution is producedby random perturbations and then carry out cross-border for new solution

(4) Generate uniformly distributed random number 1205882If 1205882 gt 119860 119894 and 119891(119909119894) lt 119891(119909lowast) the solution of Step (3)is acceptable Then update 119903119894 and 119860 119894 according to

119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)

(5) Sort the fitness value of all bats and find out theoptimal solution

Figure 6 The gearbox of rolling mill

(6) Repeat Steps (1)ndash(5) until a solution that meets thetermination condition is found

5 Results and Discussions

51 Data Preparations Theapplication object of this article isamill located in Baotou Iron and Steel Group China Figure 6is the gearbox of the mill which is the source of power andits operation status greatly affects the whole production line


0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)

Figure 7 Signal collected fromWSN of (a) normal status (b) rolling bearing fault (c) inner ring fault and (d) outer ring fault

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)

Figure 8 Waveforms after filtering (a) normal status (b) rolling bearing fault (c) inner ring fault and (d) outer ring fault

A data collection system based on WSN is constructed andvibration signal can be collected online In common there arethree types of fault rolling bearing fault inner ring fault andouter ring fault Combined with the normal status Figure 7shows the four kinds of signal collected for analysis

Morphological average filter is used to denoise the abovesignals The linear structural element is selected and eachstructural element value is 0 namely 119892 = 0 0 0 Accordingto the determined structural elements four states signalsrsquonoise is filtered by morphological average filter as shown inFigure 8 In Figures 7(a) and 8(a) it can be observed thatthe noise of the normal signals is significantly reduced aftermorphological average filtering The similar phenomena canbe observed from other three fault cases

For each operation status experiment was performed 30times Each experiment contains 2048 data points ThenEMD is used to decompose the state sample under differentstatus According to the rule given in Section 321 four IMFswill be retained Figure 9 shows the decomposition of oneexperiment under normal status

52The Development of ClassificationModel The correlationcoefficient between the original signal and obtained IMF after

minus02

0

02

1C

EMD results rolling body fault condition

minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times

Figure 9 The results of EMD for normal condition

decomposition of each state is evaluated Table 1 summarizedthe results Taking Hilbert envelope for these four IMFs theresults are shown in Figure 10 It is observed that approximatefault frequencies of different conditions are greatly different


50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)

Figure 10 Hilbert envelope demodulation spectrum for (a) normal status (b) rolling bearing fault (c) inner ring fault and (d) outer ringfault

0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es

Normal stateInner ring fault

Outer ring faultRolling element failure

01

0

Figure 11 Time domain index (energy) for four cases

Two indices one from time domain and one fromfrequency domain are calculated using the first four IMFsthrough theHilbert envelope demodulation Figures 11 and 12

Table 1 Correlation coefficients between IMFs and the originalsignal in four cases

IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352

plot these two indices respectively The normal state has thehighest energy value followedwith inner ring fault and outerring fault and the last one is rolling fault However outerring fault presents the highest singular value of the Hilbertenvelope and then is followed by the inner ring fault rolling


0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es



Figure 12 Frequency domain index (Hilbert envelope singular value) under four cases

0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45

The sample of training set

Cate

gory

labe

l

NormalOuter ring fault

Inner ring faultRolling fault

100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal

Figure 13 Classification of testing data based on BA-ELM

bearing fault and normal status At the same time it can beseen that under different conditions the discrimination abilityof the two indices is very well and shows good performance

For the proposed fault classification model initial valuesof parameter of BA optimized ELM are as follows thepopulation number is 20 the range of pulse frequency isfrom [0 2] the initial pulse frequency is 00001 the biggestvoice loudness is 16 loudness attenuation coefficient is 09pulse enhancement coefficient is 099 and the largest numberof iterations is set to be 200 Totally experiment data arerepeated thirty times under each condition Twenty of themare used as training data and the remaining ten are used astesting data Using the energy index and Hilbert envelopespectrum singular value index as the input the fault classi-ficationmodel based on the BA-ELM algorithm is developedIn Figure 13 fault classification accuracy of BA-ELM modelfor testing samples is 975 which is a high accuracy Thevalue of 119910-axis stands for the different operation status Ifthe value is 1 it stands for normal condition Similarly innerring fault outer ring fault and rolling bearing fault are

Table 2 Comparisons of SVM ELM and BA-ELM

Algorithm Accuracy ()Normal Fault 1 Fault 2 Fault 3

SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95

identified when the value is 2 3 and 4 respectively To betterillustrate the performance of the proposedmethod SVM andthe traditional ELM method are employed for comparisonFigure 14 shows the results of SVM and Figure 15 showsthe results of ELM Besides these results are summarizedin Table 2 for clear comparison In summary the proposedmethod has higher classification accuracy

6 Conclusion

To solve the problems of data acquisition and fault classifica-tion for rolling bearing several crucial points are solved in


0 10 20 30 40 50 60 70 801

152

253

354

45

The sample of testing setC

ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault

Figure 14 Classification of testing data based on SVM

0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault

Figure 15 Classification of testing data based on ELM

this paper First a data acquisition system based on wirelesssensor network is constructed to replace the traditional wiredsystem to collect sufficient data Because rolling bearingworks under a complex environment the collected vibrationsignal is always polluted by noise To effectively remove noisea morphological average filtering algorithm is proposedThen the empirical mode decomposition method is per-formed on the filtered data to obtain multiple feature vectorsincluding a frequency domain index and a time domainindex Then these two indices are used as inputs for faultmodeling Finally the fault classification model is developedbased on enhanced extreme learning machine which isoptimized by bat algorithm to adjust the input weights andthreshold of hidden layer node In comparison with faultclassification methods based on support vector machineand traditional extreme learning machine the experimentalresults show that the proposed method has higher classifica-tion accuracy and better generalization ability

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research is supported by the National Natural ScienceFoundation of China (no 51565047) Natural Science Fund

of Inner Mongolia (no 2017MS0509) Innovation Fund ofInner Mongolia University of Science and Technology (no2015QDL12) and Innovation Fund of Inner Mongolia Post-graduate (no S20171012708)

References

[1] Y Qin C Zhao and F Gao ldquoAn iterative two-step sequentialphase partition (ITSPP) method for batch process modelingand online monitoringrdquoAIChE Journal vol 62 no 7 pp 2358ndash2373 2016

[2] Y Zhang S He and J Chen ldquoData gathering optimization bydynamic sensing and routing in rechargeable sensor networksrdquoIEEEACM Transactions on Networking vol 24 no 3 pp 1632ndash1646 2016

[3] YHu X Xue Z Jin andK Peng ldquoTime-varying fault diagnosisfor asynchronous multisensor systems based on augmentedIMM and strong tracking filteringrdquo Journal of Control Scienceand Engineering Art ID 5205698 8 pages 2018

[4] H Zhang P Cheng L Shi and J Chen ldquoOptimal denial-of-service attack scheduling with energy constraintrdquo Institute ofElectrical and Electronics Engineers Transactions on AutomaticControl vol 60 no 11 pp 3023ndash3028 2015

[5] R Liu and F Pan ldquoRoller Bearing Fault Diagnosis Basedon SVM and BP neural networkrdquo Mechanical Engineering ampAutomation vol 187 no 6 pp 32ndash134 2014

[6] L Shuang and L Meng ldquoBearing fault diagnosis based on PCAand SVMrdquo in Proceedings of the IEEE International Conference


on Mechatronics and Automation (ICMA rsquo07) pp 3503ndash3507Harbin China August 2007

[7] A Malhi and R X Gao ldquoPCA-based feature selection schemefor machine defect classificationrdquo IEEE Transactions on Instru-mentation and Measurement vol 53 no 6 pp 1517ndash1525 2004

[8] Y Lei Z He and Y Zi ldquoApplication of an intelligent classifica-tionmethod tomechanical fault diagnosisrdquo Expert Systems withApplications vol 36 no 6 pp 9941ndash9948 2009

[9] B Qin G D Sun L Y Zhang J G Wang and J Hu ldquoFaultFeatures Extraction and Identification based Rolling BearingFault Diagnosisrdquo Journal of Physics Conference Series vol 842no 1 Article ID 012055 2017

[10] N Zheng L Zhang W Wang B Zhang Y Liu and D ZhangldquoResearch on fault diagnosis method based on rule base neuralnetworkrdquo Journal of Control Science and Engineering Article ID8132528 7 pages 2017

[11] J Yang and J Ma ldquoA sparsity-based training algorithm for LeastSquares SVMrdquo in Proceedings of the 5th IEEE Symposium onComputational Intelligence and Data Mining CIDM 2014 pp345ndash350 USA December 2014

[12] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006

[13] A A Mohammed R Minhas Q M Jonathan Wu andM A Sid-Ahmed ldquoHuman face recognition based on mul-tidimensional PCA and extreme learning machinerdquo PatternRecognition vol 44 no 10-11 pp 2588ndash2597 2011

[14] M Van Heeswijk Y Miche T Lindh-Knuutila et al ldquoAdaptiveensemble models of extreme learning machines for time seriespredictionrdquo Lecture Notes in Computer Science (including sub-series Lecture Notes in Artificial Intelligence and Lecture Notes inBioinformatics) Preface vol 5769 no 2 pp 305ndash314 2009

[15] H-X Tian and Z-Z Mao ldquoAn ensemble ELM based on mod-ified AdaBoostRT algorithm for predicting the temperature ofmolten steel in ladle furnacerdquo IEEE Transactions on AutomationScience and Engineering vol 7 no 1 pp 73ndash80 2010

[16] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011

[17] Z Zhao Z Liu Y Sun and J Liu ldquoWOS-ELM-Based DoubleRedundancy Fault Diagnosis and Reconstruction for Aero-engine Sensorrdquo Journal of Control Science and Engineering vol2017 14 pages 2017

[18] J Wang G Xu Q Zhang and L Liang ldquoApplication ofimproved morphological filter to the extraction of impulsiveattenuation signalsrdquo Mechanical Systems and Signal Processingvol 23 no 1 pp 236ndash245 2009

[19] N E Huang ldquoReview of empirical mode decompositionrdquo inProceedings of the Wavelet Applications VIII pp 71ndash80 USAApril 2001

[20] C Rajeswari B Sathiyabhama S Devendiran and K Mani-vannan ldquoDiagnostics of gear faults using ensemble empiricalmode decomposition hybrid binary bat algorithm andmachinelearning algorithmsrdquo Journal of Vibroengineering vol 17 no 3pp 1169ndash1187 2015

[21] X-S Yang and A H Gandomi ldquoBat algorithm A novelapproach for global engineering optimizationrdquo EngineeringComputations vol 29 no 5 pp 464ndash483 2012

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above-mentioned methods judge the status of the rollingbearings only from a view of single fault feature whichcould not give a comprehensive presentation of fault caseFor the multi-fault-features extraction Malhi and Gao [7]proposed a method to construct a mixed domain feature setbased on wavelet decomposition However the time seriesis only extracted by wavelet decomposition in the frequencydomain and time domain features are not considered Onthe contrary Lei et al [8] extracted features from frequencyinstead of time domain from six aspects which includeoriginal vibration signal and its spectrum and the filteredand demodulated signal by wavelet packet Qin et al [9]developed a fault classification model based on an improvedextreme learningmachine (ELM)methodHowever to betterdescribe fault more fault features are needed to measurethe fault influences That is multiple fault features should bedecomposed rather than one single fault vector

As for the fault classification intelligent algorithms havebeen gradually applied to bearing such as artificial neuralnetwork [10] and least squares support vector machines [11]The traditional back propagation neural network (BPNN)faces the problem of slow convergence rate difficulty ofconfiguring tunable parameters and easily falling into thelocal optimum In comparisonwithBPNN the generalizationperformance of support vector machine (SVM) is improvedHowever kernel function and its parameters are usually givenaccording to human experiences ELM [12] is a newly devel-oped single hidden layer feed-forward neural network whichdoes not require continuously to adjust parameters of hiddenlayer In ELM iterative parameter optimization process oftraditional neural network is replaced with solving linearequation groups and the outputs of the minimum norm leastsquares solution are employed as the weights of the networkTherefore the network is trained one time without iterationsCompared with BPNN and SVM ELM greatly improves thetraining speed and generalization ability which has beensuccessfully applied in the areas such as pattern recognition[13ndash18] The idea of introducing ELM into fault classificationfor bearing is given in this paper In fact the adjustment ofthe weights of the input and hidden layer adopts randomselection method which cannot guarantee the validity of theweight Because the structure parameters of fault identifica-tion model determine the classification ability how to obtainthe optimal structure parameters is the key to improve theclassification accuracy of fault identification model

To solve the above-mentioned problems a comprehen-sive and effective fault feature extraction and classificationalgorithm is proposed in this paper First a WSN is con-structed in gearbox to collect the vibration signal Secondto overcome the influence of disturbances morphologicalaverage filtering algorithm is given to filter the collectedsignals and then the intrinsic mode function (IMF) isobtained through empirical mode decomposition (EMD)[19] after denoising IMF presents fault features and IMFcomponents that have large correlation coefficients and areused to calculate energy index in time domain Besideson the other hand envelope spectrums of these IMFs areobtained byHilbert envelope spectrumanalysis which can beused to obtain the singular values by singular decomposition

on envelope spectrum matrix The singular matrix and theenergy index reconstructed multiple feature vectors used forclassificationThird bat algorithm [20] is utilized to optimizethe weights of input and hidden layers of ELM which usedynamic control of global and local search to avoid the resultsfalling into the local optimum At last the fault classificationmodel is developed by these feature vectors and the optimizedELM algorithm The major contribution of this article issummarized as follows

(1) A data acquisition system based on wireless sensornetwork is constructed to replace the traditionalwired system

(2) A multiple fault features decomposition method isproposed to explain the fault influences using twoindices with physical significance

(3) A bat algorithm optimized ELM algorithm is pro-posed to determine the parameters to achieve betterclassification accuracy

The remainder of this article is organized as followsIn Section 2 a simple description of rolling bearing andthe developed WSN is briefly given Next the extractionof multiple feature vectors is proposed in Section 3 InSection 4 fault classification method is formulated basedon the enhanced ELM algorithm Experiment results clearlydemonstrate the efficacy and feasibility of the proposedmethod in the last section

2 Description of Rolling Bearing and theDeveloped Wireless Sensor Network

Rolling bearing has been widely used in industry which ismainly composed of four parts inner ring outer ring rollingbody and the holder Figure 1 shows the physical structureof rolling bearing Its main function is transforming slidingfriction between the shaft and seat into rolling friction Thebearing studied in this paper is from Baotou Iron and SteelGroup of which the type is S-21062-C produced by the SORCompany US

To collect data from rolling bearing wireless sensornetwork (WSN) is constructed WSN usually consists of anumber of sensor nodes cluster head nodes and sink nodesBesides it forms a multihop ad hoc network system throughthe wireless communication which can be used to receivesend and process the information of monitoring objectswithin the covered area [17] Considering that the object isa low speed and heavy load mill we design a WSN that isbattery-powered and of low power consumption low costand rapid deployment tomonitor the vibration of rollingmill

Figure 2 shows the developed network topology ofCSP-F1rolling mill gearbox which consists of sensor nodes clusterhead and sink nodesThe sensor node collects and then sendsvibration signals to cluster head node according to the givensampling interval meanwhile it also receives commandsfrom the cluster head nodes Cluster head node collectsmeasured vibration data from sensor nodes and transmits thedata to sink node Besides cluster head node has three roleswhich are sending command to cluster measured vibration


Outer ring

Rolling elements

Inner ring

Retainer

I axis

II axis












(119891 ∘ 119892) (119899) = (119891Θ119892 oplus 119892) (119899) (1)

(119891 ∙ 119892) (119899) = (119891 oplus 119892Θ119892) (119899) (2)


(119891Θ119892) (119899) = min [119891 (119899 + 119898) minus 119892 (119898)] (3)

(119891 oplus 119892) (119899) = max [119891 (119899 minus 119898) + 119892 (119898)] (4)



AVG (119891) = (119891 ∙ 119892 + 119891 ∘ 119892)2 (5)






Obtain energy index






Collect signal x(k)

Perform EMD to x(k)




119909 (119896) = 119898sum119894=1

119888119894 (119896) + 119903119898 (119896) (6)



120588119909119888119894 = sum119870119896=0 119909 (119896) 119888119894 (119896)radicsum119870119896=0 119909 (119896)2sum119870119896=0 119888119894 (119896)2

(7)





119864119894 =119870sum119896=1

119888119894 (119896) 119894 = 1 2 119898 (8)


T = [1198641119864 1198642119864 119864119898119864 ]119879 (9)


119867[119888119894 (119896)] = 1120587119870sum119903=1

119888119894 (119903)119896 minus 119903 (10)


119861119894 (119896) = radic1198882119894 (119896) + 1198672 [119888119894 (119896)] (11)


B = USV119879 (12)



Input

Output










119910119894 =119871sum119895=1

120573119895119892 (119908119895119909119894 + 119887119895) (13)



119873sum119894=1

1003817100381710038171003817119910119894 minus 11990511989410038171003817100381710038172 = 0 (14)


119873sum119894=1

120573119895119892 (119908119895119909119894 + 119887119895) = 119905119894 119894 = 1 2 119873 (15)


H = [[[

119892 (1198961 1198871 1199091) 119892 (119896119871 119887119871 1199091)

119892 (1198961 1198871 119909119873) 119892 (119896119871 119887119871 119909119873)]]]119873times119871

120573 = [[[[[

1205731198791120573119879119871

]]]]]

T = [[[[

1198791198791 119879119879119873

]]]]119873times119898

(16)







Start









Yes

Yes

No

No



119891119894 = 119891min + 120573 (119891max minus 119891min) (17)


119909119905119894 = 119909119905minus1119894 + V119905119894 (19)






119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)







0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Outer ring

Rolling elements

Inner ring

Retainer

I axis

II axis












(119891 ∘ 119892) (119899) = (119891Θ119892 oplus 119892) (119899) (1)

(119891 ∙ 119892) (119899) = (119891 oplus 119892Θ119892) (119899) (2)


(119891Θ119892) (119899) = min [119891 (119899 + 119898) minus 119892 (119898)] (3)

(119891 oplus 119892) (119899) = max [119891 (119899 minus 119898) + 119892 (119898)] (4)



AVG (119891) = (119891 ∙ 119892 + 119891 ∘ 119892)2 (5)






Obtain energy index






Collect signal x(k)

Perform EMD to x(k)




119909 (119896) = 119898sum119894=1

119888119894 (119896) + 119903119898 (119896) (6)



120588119909119888119894 = sum119870119896=0 119909 (119896) 119888119894 (119896)radicsum119870119896=0 119909 (119896)2sum119870119896=0 119888119894 (119896)2

(7)





119864119894 =119870sum119896=1

119888119894 (119896) 119894 = 1 2 119898 (8)


T = [1198641119864 1198642119864 119864119898119864 ]119879 (9)


119867[119888119894 (119896)] = 1120587119870sum119903=1

119888119894 (119903)119896 minus 119903 (10)


119861119894 (119896) = radic1198882119894 (119896) + 1198672 [119888119894 (119896)] (11)


B = USV119879 (12)



Input

Output










119910119894 =119871sum119895=1

120573119895119892 (119908119895119909119894 + 119887119895) (13)



119873sum119894=1

1003817100381710038171003817119910119894 minus 11990511989410038171003817100381710038172 = 0 (14)


119873sum119894=1

120573119895119892 (119908119895119909119894 + 119887119895) = 119905119894 119894 = 1 2 119873 (15)


H = [[[

119892 (1198961 1198871 1199091) 119892 (119896119871 119887119871 1199091)

119892 (1198961 1198871 119909119873) 119892 (119896119871 119887119871 119909119873)]]]119873times119871

120573 = [[[[[

1205731198791120573119879119871

]]]]]

T = [[[[

1198791198791 119879119879119873

]]]]119873times119898

(16)







Start









Yes

Yes

No

No



119891119894 = 119891min + 120573 (119891max minus 119891min) (17)


119909119905119894 = 119909119905minus1119894 + V119905119894 (19)






119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)







0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Obtain energy index






Collect signal x(k)

Perform EMD to x(k)




119909 (119896) = 119898sum119894=1

119888119894 (119896) + 119903119898 (119896) (6)



120588119909119888119894 = sum119870119896=0 119909 (119896) 119888119894 (119896)radicsum119870119896=0 119909 (119896)2sum119870119896=0 119888119894 (119896)2

(7)





119864119894 =119870sum119896=1

119888119894 (119896) 119894 = 1 2 119898 (8)


T = [1198641119864 1198642119864 119864119898119864 ]119879 (9)


119867[119888119894 (119896)] = 1120587119870sum119903=1

119888119894 (119903)119896 minus 119903 (10)


119861119894 (119896) = radic1198882119894 (119896) + 1198672 [119888119894 (119896)] (11)


B = USV119879 (12)



Input

Output










119910119894 =119871sum119895=1

120573119895119892 (119908119895119909119894 + 119887119895) (13)



119873sum119894=1

1003817100381710038171003817119910119894 minus 11990511989410038171003817100381710038172 = 0 (14)


119873sum119894=1

120573119895119892 (119908119895119909119894 + 119887119895) = 119905119894 119894 = 1 2 119873 (15)


H = [[[

119892 (1198961 1198871 1199091) 119892 (119896119871 119887119871 1199091)

119892 (1198961 1198871 119909119873) 119892 (119896119871 119887119871 119909119873)]]]119873times119871

120573 = [[[[[

1205731198791120573119879119871

]]]]]

T = [[[[

1198791198791 119879119879119873

]]]]119873times119898

(16)







Start









Yes

Yes

No

No



119891119894 = 119891min + 120573 (119891max minus 119891min) (17)


119909119905119894 = 119909119905minus1119894 + V119905119894 (19)






119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)







0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Input

Output










119910119894 =119871sum119895=1

120573119895119892 (119908119895119909119894 + 119887119895) (13)



119873sum119894=1

1003817100381710038171003817119910119894 minus 11990511989410038171003817100381710038172 = 0 (14)


119873sum119894=1

120573119895119892 (119908119895119909119894 + 119887119895) = 119905119894 119894 = 1 2 119873 (15)


H = [[[

119892 (1198961 1198871 1199091) 119892 (119896119871 119887119871 1199091)

119892 (1198961 1198871 119909119873) 119892 (119896119871 119887119871 119909119873)]]]119873times119871

120573 = [[[[[

1205731198791120573119879119871

]]]]]

T = [[[[

1198791198791 119879119879119873

]]]]119873times119898

(16)







Start









Yes

Yes

No

No



119891119894 = 119891min + 120573 (119891max minus 119891min) (17)


119909119905119894 = 119909119905minus1119894 + V119905119894 (19)






119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)







0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Start









Yes

Yes

No

No



119891119894 = 119891min + 120573 (119891max minus 119891min) (17)


119909119905119894 = 119909119905minus1119894 + V119905119894 (19)






119860119905+1119894 = 120572119860119905119894119903119905+1119894 = 1198770 [1 minus exp (minus120574119905)] (20)







0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05Va

lues

minus05

Sampling points

(a)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

05

minus05

Sampling points

(b)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus1

0

1

Sampling points

(c)

Valu

es

0 200 400 600 800 1000 1200 1400 1600 1800 2000

minus2

0

2

Sampling points

(d)


0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(a)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(b)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus05

0

05

Sampling points

Valu

es

(c)

0 200 400 600 800 1000 1200 1400 1600 1800 2000minus1

0

1

Sampling points

Valu

es

(d)






minus02

0

02

1C


minus01

0

01

2C

minus01

0

01

3C

minus01

0

01

4C

Sampling times




50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

80

X 293Y 1064

(a)50 100 150 200 250 300 350 400 450 500

0

50

100

150

200

250

300

350

400

450

500

X 7471Y 1235X 293

Y 1033

(b)

100 200 300 400 500 600 700 8000

100

200

300

400

500

600

700

800

900

X 1553Y 7773

X 3091Y 2554

X 293Y 1627 X 4644

Y 1217

(c)100 200 300 400 500 600 700 800

0

200

400

600

800

1000

1200

1400

1600

1800

X 104Y 1628

X 2065Y 1143

X 3105Y 709

X 293Y 5169

(d)


0 5 10 15 20 25 30

02

03

04

05

06

07

08

09

1

Sampling times

Valu

es



01

0




IMF1 IMF2 IMF3 IMF4

Normal04452 05507 05020 0211700634 01692 03012 0050100419 01353 00801 00993

Fault 108769 04236 01818 0094001529 00680 00355 0002300311 00598 00047 00110

Fault 209929 00867 00115 0011400629 00045 00002 0004200446 00036 00015 00019

Fault 309529 01038 01520 0154601569 00253 01300 0073600410 00206 00751 00352



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

2000

Sampling times

Valu

es




0 10 20 30 40 50 60 70 801

15

2

25

3

35

4

45


Cate

gory

labe

l



100

100

95

95Inner ringfault

Outer ringfault

Rollingfault

Normal






SVM 90 100 100 45ELM 90 95 100 80BA-ELM 100 100 95 95


6 Conclusion



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 10 20 30 40 50 60 70 801

152

253

354

45


ateg

ory

labe

l



45

100

100

90Normal

Outer ringfault

Inner ringfault

Rollingfault


0 10 20 30 40 50 60 70 801

152

253

354

45

Cate

gory

labe

l




95

80

100

90

Inner ringfault

Outer ringfault

Normal

Rollingfault





Acknowledgments



References


























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Multiple Feature Vectors Based Fault Classification for WSN Integrated Bearing … · 2019. 7. 30. · F :SignalcollectedfromWSNof(a)normalstatus,(b)rollingbearingfault,(c)innerringfault,and(d)outerringfault