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Research ArticleA Framework for Final Drive Simultaneous FailureDiagnosis Based on Fuzzy Entropy and Sparse BayesianExtreme Learning Machine
Qing Ye1 Hao Pan1 and Changhua Liu2
1School of Computer Science and Technology Wuhan University of Technology Wuhan 430000 China2Yangtze University College of Technology and Engineering Jingzhou 430023 China
Correspondence should be addressed to Qing Ye yq0712163com
Received 6 October 2014 Revised 4 January 2015 Accepted 19 January 2015
Academic Editor J Alfredo Hernandez
Copyright copy 2015 Qing Ye 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
This research proposes a novel framework of final drive simultaneous failure diagnosis containing feature extraction training paireddiagnosticmodels generating decision threshold and recognizing simultaneous failuremodes In feature extractionmodule adoptwavelet package transform and fuzzy entropy to reduce noise interference and extract representative features of failure modeUse single failure sample to construct probability classifiers based on paired sparse Bayesian extreme learning machine whichis trained only by single failure modes and have high generalization and sparsity of sparse Bayesian learning approach To generateoptimal decision threshold which can convert probability output obtained from classifiers into final simultaneous failure modesthis research proposes using samples containing both single and simultaneous failure modes and Grid search method which issuperior to traditional techniques in global optimization Compared with other frequently used diagnostic approaches based onsupport vector machine and probability neural networks experiment results based on F
1-measure value verify that the diagnostic
accuracy and efficiency of the proposed framework which are crucial for simultaneous failure diagnosis are superior to the existingapproach
1 Introduction
With sustained increase of work condition complexity simul-taneous failures occur more frequently in final drive which isthe pivotal part of car and seriously affect running status andcomfort and safety of car Final drive is mainly consisting ofa pair of gears which are meshing together when car runsOwing to the complex structure a certain function disorderin final drive usually stems frommore than one single failureat the same time which is called simultaneous failure Tra-ditional manual technology cannot accomplish simultaneousfailure diagnosis (SFD) This paper is focusing on final drivesimultaneous failure diagnosis which is essential for automanufacturer and maintenance industry
Failure diagnosis by using vibration signal is almost themost frequently used approach because vibration signal isrelatively precise and accurate against diagnosis based onsound It can be divided into three main steps featureextraction training diagnostic models and failure mode
identification The vibration signal collected from final drivehas the characteristics of being nonlinear and nonstationaryand it is enclosed with a lot of uncorrelated and superfluousinformation It is impossible to extract valid failure modeinformation from original vibration signal because of thenoise and interference embedded in it The frequently usedpreprocessed methods include wavelet analysis [1 2] waveletpackage transform (WPT) [3 4] and empiricalmode decom-position (EMD) [5]Wavelet package transform is suitable fornonstationary vibration signal by decomposing original sig-nal into several subfrequency bands which contains differentfailure information and effectively reduces noise interference
Data contained in preprocessed signal is high-dimen-sional so that it cannot be directly inputted into diagnosticsystem Feature extraction has a deep effect on accuracyand reliability of failure diagnosis Recently researchershave introduced entropy into the field of feature extractionincluding approximate entropy sample entropy [6] andfuzzy entropy [7] Compared with approximation entropy
Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2015 Article ID 427965 11 pageshttpdxdoiorg1011552015427965
2 Computational Intelligence and Neuroscience
and sample entropy which are based on Heaviside stepfunction which is mutational at the classification boundaryfuzzy entropy eliminates the influence of baseline drift ofdata and guarantees the entropy to vary smoothly andcontinuously with similarity tolerance [8] so that it isexcellent in measuring complexity and self-similarity of thepreprocessed vibration signal and fully reflecting changesof the vibration performance of mechanical equipment[9]
In recent years many machine learning methods areapplied in failure diagnosis including support vectormachine(SVM) [10] artificial neural networks (ANN) [11] extremelearningmachine (ELM) [12 13] and kernel extreme learningmachine (KELM) [14] ELM is single-hidden-layer feedfor-ward neural networks and without human intervention intuning parameters which differs from SVM and ANN andmakes it superior in high generalization and less learningtime KELM apply kernel function to ELM to improve gener-alization and nonlinear approximation ability [15] Howevercomputational cost and memory cost of KELM are high withregard to large scale problem Recently Bayesianmethods areemployed into ELM to learn the output weights by estimatingthe probability distribution of output with high generaliza-tion Soria-Olivas and Gomez-Sanchis proposed Bayesianextreme learning machine [16] for linear regression with-out solving classification problem Sparse Bayesian extremelearningmachine (SBELM) [17] is a novel method for findingthe sparse representatives of hidden layer output weights byimposing a hyperparameter on each weight During learningphase SBELM tunes some output weights into zero to obtaincompact model In summary SBELM has the advantagesof probability output high generalization sparsity and fasttraining speed To solve the problem of simultaneous failurediagnosis a proper classifier has to offer the probability of allpossible failures In this research the proposed frameworkconstructs classifiers based on paired SBELM in which eachclassifier based on SBELM is trained by a pair of singlefailure samples The paired SBELM effectively reflect theprobability distribution of failure modes In general onlysingle failure samples are used for constructing diagnosticmodels Since it is impossible to collect all combinationsof existing single failure modes for training the proposedframework can effectively solve the practical bottleneck insimultaneous failure diagnosis With the purpose of rec-ognizing simultaneous failure modes use both single andsimultaneous failure samples and Gird search method togenerate optimal decision threshold which could convertprobability result of classifier into final multiple failuremodes Considering that partial matching is valid and instru-mental in simultaneous failure diagnosis this research adoptsF1-measure to evaluate the performance of the proposedframework
This paper is organized as follows Section 2 presentsthe proposed framework Section 3 presents the experimentsetup data acquisition and preprocessing The results ofexperiment are discussed in Section 4 Finally a conclusionis given in Section 5
2 The Proposed Framework for Final DriveSimultaneous Failure Diagnosis
21 Feature Extraction Based on Wavelet PackageTransform and Fuzzy Entropy
211 Wavelet Package Transform In failure diagnosis one ofthe key points is extraction of features from original vibrationsignal which is nonstationary for mechanical equipmentWavelet package transform (WPT) is an extended form ofwavelet transform to analyse nonstationary and non-linearsignal and to supply better partition of frequency bandbecause the same frequency bandwidths can provide goodresolution regardless of high and low frequencies [18] As amultiresolution analysis method WPT can effectively pre-process nonstationary vibration signal in both time domainand frequency domain Two-scale equation ofWPT is shownbelow in which ℎ
0119896and ℎ1119896represent the filter coefficients
1199092119899(119905) = radic2sum
119896isin119885
ℎ0119896119909119899(2119905 minus 119896)
1199092119899+1
(119905) = radic2sum
119896isin119885
ℎ1119896119909119899(2119905 minus 119896)
(1)
The recursion formula of wavelet package coefficient is
119889119895+12119899
119896= sum
119897
ℎ0(2119897minus119896)
119889119895119899
119897 119889
119895+12119899+1
119896= sum
119897
ℎ1(2119897minus119896)
119889119895119899
119897 (2)
212 Fuzzy Entropy When failure occurred in final drive thecomplexity of oscillation feature will change hencewe shouldextract representative features containing in the signal Fuzzyentropy is an extension of Shannon entropy and fuzzy sets[19] The procedure of fuzzy entropy is described as follows
(1) Consider a time series with the length of119873 119909(119894) 1 le119894 le 119873 For given 119898 119899 and 119903 construct a vector set in theform of 119883119898
119894 119894 = 1 2 119873 minus 119898 + 1 in which each vector
contains119898 sequential elements starting from 119909(119894) shown as
119883119898
119894= 119909 (119894) 119909 (119894 + 1) 119909 (119909 + 119898 minus 1) minus 119909
0(119894)
119894 = 1 2 119873 minus 119898 + 1
(3)
where 1199090(119894) is the average of vector119883119898
119894
(2) Define the distance 119889119898119894119895between 119883119898
119894and 119883119898
119895where
119894 119895 = 1 2 119873 minus 119898 119894 = 119895 as follows
119889119898
119894119895= max119896isin(0119898minus1)
1003816100381610038161003816[119909 (119894 + 119896) minus 1199090 (119894)] minus [119909 (119895 + 119896) minus 1199090 (119895)]
1003816100381610038161003816
(4)
(3) Calculate similarity between 119883119898119894and 119883119898
119895using fuzzy
function
119863119898
119894119895= 120583 (119889
119898
119894119895 119899 119903) = 119890
minus In 2(119889119898119894119895119903)119899
(5)
(4) Define function 120601119898 as follows
120601119898(119899 119903) =
1
119873 minus 119898
119873minus119898
sum
119894=1
(1
119873 minus 119898 + 1
119873minus119898
sum
119895=1119895 =119894
119863119898
119894119895) (6)
Computational Intelligence and Neuroscience 3
(5) Change119898 to119898 + 1 and repeat step (1) to (4)
120601119898+1(119899 119903) =
1
119873 minus 119898
119873minus119898
sum
119894=1
(1
119873 minus 119898 + 1
119873minus119898
sum
119895=1119895 =119894
119863119898+1
119894119895) (7)
(6) Fuzzy entropy of sequence 119909(119894) 1 le 119894 le 119873 isdefined as follows
FuzzyEn (119898 119899 119903) = lim119873rarrinfin
[In120601119898 (119899 119903) minus In120601119898+1 (119899 119903)] (8)
(7) If the length 119873 is finite FuzzyEn(119898 119899 119903) can bechanged as follows
FuzzyEn (119898 119899 119903) = In120601119898 (119899 119903) minus In120601119898+1 (119899 119903) (9)
22 Sparse Bayesian Extreme Learning Machine (SBELM)Given a preprocessed data set 119863 = (119909
119894 119905119894) 119894 = 1 119873
119909119894isin 119877119899 119905119894isin 119877119898 The output function of ELM with 119871 hidden
nodes is shown as follows
119891 (119909) =
119871
sum
119894=1
120573119894ℎ119894(119909) = 120573 sdot 119867 (119909) (10)
where 120573 = [1205731 120573
119871]119879 is output weight connecting hidden
nodes and output nodes 119867(119909) = [ℎ1(119909) ℎ
119871(119909)] is the
hidden layer output matrix for input 119909 in which ℎ119894(119909) is the
hidden output of the 119894th hidden node Equation (10) can bewritten as follows
119867120573 = 119879 (11)
where 119879 is the training data target matrix SBELM learnsoutput weight by using Bayesian method instead of bycalculatingMoore-Penrose generalized inverse of119867 [17]Thehidden layer output 119867 becomes the input of SBELM Treateach training sample as an independent Bernoulli event sothat probability119901(119905 | 119909) satisfies Bernoulli distribution Applysigmoid function to convert the predicted output Y(ℎ 120573) asfollows
120590 (Y (ℎ 120573)) =1
(1 + exp (minusY (ℎ 120573))) (12)
The likelihood function of sample set is expressed asfollows
119901 (119905 | 119867 120573) =
119873
prod
119895=1
120590 (Y (ℎ 120573))119905119895
[1 minus 120590 (Y(ℎ 120573))]1minus119905119895
(13)
where 119905119895is the target of training sample 119909
119895Y(ℎ 120573) = ℎ120573 and
119905119895isin 0 1 Conditioned on a hyperparameter 120572
119895 zero-mean
Gaussian prior distribution over 120573119894is as follows
119901 (120573 | 120572) =
119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2) (14)
The typical step of SBELM is to establish the distributionof marginal likelihood over 119905 conditioned on 120572 and 119867 and
determine 120572 by maximizing the marginal likelihood 119901(119905 | 119867120572) by Laplace approximation method
argmax ln 119901 (119905 | 120573119867) 119901 (120573 | 120572)
= argmax[
[
ln
119873
prod
119895=1
119910119905119895
119895(1 minus 119910
119895)1minus119905119895
+ ln119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2)]
]
= argmax[
[
119873
sum
119895=1
119905119895ln119910119895+ (1 minus 119905
119895)
sdot ln (1 minus 119910119895) minus
120573119879119860120573
2+ const]
]
(15)
where 119910119895= 120590(Y(ℎ
119895 120573))119860 = diag(120572) and const =sum119871
119894=1ln120572119894minus
12 ln 2120587 Then make quadratic approximation for log ofposterior probability
nabla120573nabla120573 ln 119901 (119905 | 120573119867) 119901 (120573 | 120572) = minus (119867119879119870119867 + 119860) (16)
where 119870 is a diagonal matrix in which 119896119895= 119910119895(1 minus 119910
119895) with
119895 = 1 119873 Therefore the center and covariance matrix ofGauss distribution of 120573 expressed as 1205731015840 andΦ are obtained asfollows
1205731015840= Φ119867
1198791198701199051015840 Φ = (119867
119879119870119867 + 119860)
minus1
(17)
where 1199051015840 = 119867120573+119870minus1(119905minus119910) By obtainingGauss approximationof 120573 the log of marginal likelihood is represented as follows
L (120572) = ln119901 (119905 | 120572119867)
= minus1
2[119873 ln (2120587) + ln |119862| + (1199051015840)
119879
119862minus11199051015840]
(18)
where119862 = 119870+119867119860119867119879 By setting the differential ofL(120572)withrespect to 120572 as 0 update the hyperparameter 120572 as follows
120572119894=1 minus 120572119894Φ119894119894
(1205731198941015840)2 (19)
The main procedure of SBELM is described as follows
(1) Initialize 120572119894and 120573
119894randomly with 119894 = 1 119871
(2) By utilizing Laplace approximation approach obtainapproximated Gauss distribution of 120573 and update 1205731015840and Φ by using (17)
(3) Bymaximizing themarginal likelihood utilize (19) toupdate hyperparameter 120572 until reaching the termina-tion criteria
(4) By tuning some 120573119894into 0 obtain the sparse represen-
tation of hidden layer output weight(5) For an unknown sample 119909
119906 utilize (12) to predict
probability distribution 119901(119905 | 119909119906 1205731015840)
4 Computational Intelligence and Neuroscience
SBELM12
SBELMi1
SBELMm1
SBELM1m
SBELMim
SBELMm(mminus1)
PSBELM1
PSBELMi
PSBELMm
p1
pi
pm
middot middot middot
middot middot middot
middot middot middot
Figure 1 Structure of paired SBELM for simultaneous failure diag-nosis
23 Paired SBELM SBELM is excellent in solving binaryclassification by obtaining probability distribution of eachclass 119901(119905 | 119909 1205731015840) With the purpose of final drive simulta-neous failure diagnosis in which training samples of singlefailure are ample while training samples of simultaneousfailure are scarce this paper combines the state-of-the-artcoupling approach proposed in [20]with SBELM to constructa set of paired SBELM (PSBELM) classifiers expressed as[PSBELM
1 PSBELM
119898] for a 119898-label classification prob-
lem shown in Figure 1 and each paired classifier PSBELM119894=
[SBELM1198941 SBELM
119894119895 SBELM
119894119898] in which SBELM
119894119895is
trained by every pair of classes and its output is 119901119894119895(119905119894| 120573 119909)
for sample 119909 belonging to the 119894th against the 119895th class Thetotal number of classifiers is119898(119898 minus 1)2
In simultaneous failure diagnosis more than one failuremay occur at the same time that can infer the conceptsum119898
119894=1119901119894= 1 [21] By estimating each probability output of
binary classifiers SBELM119894119895to measure correlation between
various classes obtain the paired probability output 119901119894as
follows
119901119894=sum119889
119895=1119895 =119894119899119894119895119901119894119895
sum119889
119895=1119895 =119894119899119894119895
119894 = 1 119898 (20)
where 119899119894119895is the number of training sample belonging to the
119894th and the 119895th class
24 Optimization of DecisionThreshold for Simultaneous Fail-ure Mode Recognition For a 119898-class classification problemthe output of classifiers based on PSBELM is a probabilityvector 119875 = [119901
1 119901
119898] in which 119901
119895represents occur-
ring possibility of the 119895th failure In order to obtain finalsimultaneous failuremodes an appropriate threshold value isindispensable In general researchers usually use 05 to be thethreshold value [21] which is of generality but not suitable forspecific application This paper utilizes Grid Search methodand an independent sample set containing both single failureand simultaneous failure to generate an optimal decisionthreshold 120576lowast between 0 and 1 which can convert probabilityoutput vector into result vector 119865 = [119891
1 119891
119894 119891
119898]
effectively
119891119894= 1 119901119894ge 120576lowast
0 119901119894lt 120576lowast119894 = 1 119898 120576
lowastisin (0 1) (21)
The simultaneous failure modes are those single failuresthat their corresponding 119891
119894is equal to 1 Since the range of
searching is limited the time-consuming characteristic ofGrid Search method can not weaken its advantages of globaloptimization compared with GA and PSO [18]
25 Evaluation of Performance Based on F1-Measure Con-sidering that partial matching is valid and significant insimultaneous failure diagnosis [22] utilize an independenttesting set and F1-measure [23] which is commonly usedfor evaluation of information retrieval systems to evaluatediagnostic accuracy for the proposed simultaneous failurediagnostic framework Given a data set 119863 = (119909
119894 119905119894) 119894 =
1 119873 119909119894isin 119877119899 119905119894isin 119877119898 119905119894119895isin 0 1 119895 = 1 119898 define
two variables namely precision (119875) and recall (119877) amongwhich 119875 represents the ratio between correct identified singlefailure modes and the actual simultaneous failure modes and119877 represents the ratio between correct identified single failuremodes and the predicted simultaneous failure modes
119875 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119905119894119895
119877 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119891lowast119894119895
(22)
where 119891lowast119894= [119891
lowast
1198941 119891
lowast
119894119898] is the predicted simultaneous
failure modes by using the proposed framework and 119905119894=
[1199051198941 119905
119894119898] is the actual simultaneous failure modes of 119909
119894
The F1-measure value can be obtained as follows
119864 =2 lowast 119875 lowast 119877
119875 + 119877=
2sum119898
119895=1sum119873
119894=1119891lowast
119894119895119910119894119895
sum119898
119895=1sum119873
119894=1119910119894119895+ sum119898
119895=1sum119873
119894=1119891lowast119894119895
(23)
26 The Proposed Framework for Final Drive SimultaneousFailure Diagnosis The structure of the proposed frameworkis shown in Figure 2 and the procedure of the proposedframework is described as follows
(1) Divide sample set into four parts 119863training1 119863training2119863threshold and 119863testing All the sample should bepreprocessed by WPT and utilize fuzzy entropy tomeasure the feature of oscillatory
(2) Utilize 119863training1 containing only single failure modesto optimize parameters of WPT including number oflayer 119871 and mother wavelet in preprocessing by usingfailure diagnostic model of SBELM
(3) By using optimal parameters of WPT obtained fromstep 2 preprocess 119863training2 containing only singlefailure modes and train classifiers based on pairedSBELM
(4) The optimumdiagnostic model of PSBELMgeneratesa probability output vector [119901
1 119901
119898] in 119898-label
classification problem and uses 119863threshold containingboth single and simultaneous failure modes and GridSearch to confirm the decision threshold value 120576lowastwhich is used to obtain simultaneous failure modes
(5) Use119863testing and F1-measure to evaluate the diagnosticaccuracy of the proposed framework
Computational Intelligence and Neuroscience 5
Opt
imal
dia
gnos
tic m
odel
Evaluation of theproposed framework
Dtesting
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Decision threshold
Result vector
Evaluation
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Optimizingdecision threshold
Confirmation of thethreshold value
Optimalparametersof WPT
Optimal WPT andfuzzy entropy
Train diagnosticmodel based on paired SBELM
Training diagnosticmodel
Dtraining1
Determiningparameters of WPT
Standard SBELMdiagnostic model
Optimization of WPT
Dthreshold
Dtraining2
value 120576lowast
value 120576lowast
Optimal 120576lowast
Figure 2 The structure of the proposed framework
3 Experiment Setup and Preprocessing
31 Experiment Setup In order to obtain sample data withrepresentativeness for constructing diagnostic model andverify the efficiency of the proposed diagnostic platformimplement the experiments on a test bed containing a PC twosensors a signal amplifier and a simulation turntablewith thecomposition as shown in Figure 3 in quiet room to collectenough original vibration signal of final drive Two sensorsare laid on the final drive in horizontal and vertical directionas shown in Figure 4 to collect vibration signal when it is setinto running state Most failures of final drive such as gearerror gear hard point and tooth broken occurred in gear pairwhich is the hard core of final drive and consisted of a driving-gear and a driven-gear In this research simulate 9 commonfailures including 6 single failures and 3 simultaneous failureswhich are described in detail in Table 1 under the rotatingspeed of 1200 rm for driving motor As shown in Figure 5amplitudes of simultaneous failure are obviously greater thansingle failure because when simultaneous failure occurs thesesingle failures are coupled together severelyThewave profiles
between single and simultaneous failure patterns are similarso that it is difficult to distinguish them manually but thecharacteristics embedded in each vibration signal can beextracted and identified by using methods afore mentioned
Considering the universality of vibration signals whichare used to construct diagnostic models repeat simulatingeach failure mode for 100 times and record the most stable 2seconds in each time with the sampling rate of 12 kHz whichshould be higher than the gear meshing frequency so thateffective failure information may not be discarded duringthe sampling Eventually 1000 sample data are obtainedand prepared to be preprocessed All the simulations areimplemented in MATLAB 70 which is running in a PC withCPU of 34GHZ and RAM of 40GB
32 Feature Extraction Based on WPT and Fuzzy EntropyIn this paper fuzzy entropy is used to reflect the changeof complexity By calculating the average fuzzy entropy ofvibration signal corresponding to each failure mode which isshown in Table 2 we find out that the values of fuzzy entropyof these 10 failure modes are approximate so that it can not
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
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Industrial EngineeringJournal of
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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![Page 2: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/2.jpg)
2 Computational Intelligence and Neuroscience
and sample entropy which are based on Heaviside stepfunction which is mutational at the classification boundaryfuzzy entropy eliminates the influence of baseline drift ofdata and guarantees the entropy to vary smoothly andcontinuously with similarity tolerance [8] so that it isexcellent in measuring complexity and self-similarity of thepreprocessed vibration signal and fully reflecting changesof the vibration performance of mechanical equipment[9]
In recent years many machine learning methods areapplied in failure diagnosis including support vectormachine(SVM) [10] artificial neural networks (ANN) [11] extremelearningmachine (ELM) [12 13] and kernel extreme learningmachine (KELM) [14] ELM is single-hidden-layer feedfor-ward neural networks and without human intervention intuning parameters which differs from SVM and ANN andmakes it superior in high generalization and less learningtime KELM apply kernel function to ELM to improve gener-alization and nonlinear approximation ability [15] Howevercomputational cost and memory cost of KELM are high withregard to large scale problem Recently Bayesianmethods areemployed into ELM to learn the output weights by estimatingthe probability distribution of output with high generaliza-tion Soria-Olivas and Gomez-Sanchis proposed Bayesianextreme learning machine [16] for linear regression with-out solving classification problem Sparse Bayesian extremelearningmachine (SBELM) [17] is a novel method for findingthe sparse representatives of hidden layer output weights byimposing a hyperparameter on each weight During learningphase SBELM tunes some output weights into zero to obtaincompact model In summary SBELM has the advantagesof probability output high generalization sparsity and fasttraining speed To solve the problem of simultaneous failurediagnosis a proper classifier has to offer the probability of allpossible failures In this research the proposed frameworkconstructs classifiers based on paired SBELM in which eachclassifier based on SBELM is trained by a pair of singlefailure samples The paired SBELM effectively reflect theprobability distribution of failure modes In general onlysingle failure samples are used for constructing diagnosticmodels Since it is impossible to collect all combinationsof existing single failure modes for training the proposedframework can effectively solve the practical bottleneck insimultaneous failure diagnosis With the purpose of rec-ognizing simultaneous failure modes use both single andsimultaneous failure samples and Gird search method togenerate optimal decision threshold which could convertprobability result of classifier into final multiple failuremodes Considering that partial matching is valid and instru-mental in simultaneous failure diagnosis this research adoptsF1-measure to evaluate the performance of the proposedframework
This paper is organized as follows Section 2 presentsthe proposed framework Section 3 presents the experimentsetup data acquisition and preprocessing The results ofexperiment are discussed in Section 4 Finally a conclusionis given in Section 5
2 The Proposed Framework for Final DriveSimultaneous Failure Diagnosis
21 Feature Extraction Based on Wavelet PackageTransform and Fuzzy Entropy
211 Wavelet Package Transform In failure diagnosis one ofthe key points is extraction of features from original vibrationsignal which is nonstationary for mechanical equipmentWavelet package transform (WPT) is an extended form ofwavelet transform to analyse nonstationary and non-linearsignal and to supply better partition of frequency bandbecause the same frequency bandwidths can provide goodresolution regardless of high and low frequencies [18] As amultiresolution analysis method WPT can effectively pre-process nonstationary vibration signal in both time domainand frequency domain Two-scale equation ofWPT is shownbelow in which ℎ
0119896and ℎ1119896represent the filter coefficients
1199092119899(119905) = radic2sum
119896isin119885
ℎ0119896119909119899(2119905 minus 119896)
1199092119899+1
(119905) = radic2sum
119896isin119885
ℎ1119896119909119899(2119905 minus 119896)
(1)
The recursion formula of wavelet package coefficient is
119889119895+12119899
119896= sum
119897
ℎ0(2119897minus119896)
119889119895119899
119897 119889
119895+12119899+1
119896= sum
119897
ℎ1(2119897minus119896)
119889119895119899
119897 (2)
212 Fuzzy Entropy When failure occurred in final drive thecomplexity of oscillation feature will change hencewe shouldextract representative features containing in the signal Fuzzyentropy is an extension of Shannon entropy and fuzzy sets[19] The procedure of fuzzy entropy is described as follows
(1) Consider a time series with the length of119873 119909(119894) 1 le119894 le 119873 For given 119898 119899 and 119903 construct a vector set in theform of 119883119898
119894 119894 = 1 2 119873 minus 119898 + 1 in which each vector
contains119898 sequential elements starting from 119909(119894) shown as
119883119898
119894= 119909 (119894) 119909 (119894 + 1) 119909 (119909 + 119898 minus 1) minus 119909
0(119894)
119894 = 1 2 119873 minus 119898 + 1
(3)
where 1199090(119894) is the average of vector119883119898
119894
(2) Define the distance 119889119898119894119895between 119883119898
119894and 119883119898
119895where
119894 119895 = 1 2 119873 minus 119898 119894 = 119895 as follows
119889119898
119894119895= max119896isin(0119898minus1)
1003816100381610038161003816[119909 (119894 + 119896) minus 1199090 (119894)] minus [119909 (119895 + 119896) minus 1199090 (119895)]
1003816100381610038161003816
(4)
(3) Calculate similarity between 119883119898119894and 119883119898
119895using fuzzy
function
119863119898
119894119895= 120583 (119889
119898
119894119895 119899 119903) = 119890
minus In 2(119889119898119894119895119903)119899
(5)
(4) Define function 120601119898 as follows
120601119898(119899 119903) =
1
119873 minus 119898
119873minus119898
sum
119894=1
(1
119873 minus 119898 + 1
119873minus119898
sum
119895=1119895 =119894
119863119898
119894119895) (6)
Computational Intelligence and Neuroscience 3
(5) Change119898 to119898 + 1 and repeat step (1) to (4)
120601119898+1(119899 119903) =
1
119873 minus 119898
119873minus119898
sum
119894=1
(1
119873 minus 119898 + 1
119873minus119898
sum
119895=1119895 =119894
119863119898+1
119894119895) (7)
(6) Fuzzy entropy of sequence 119909(119894) 1 le 119894 le 119873 isdefined as follows
FuzzyEn (119898 119899 119903) = lim119873rarrinfin
[In120601119898 (119899 119903) minus In120601119898+1 (119899 119903)] (8)
(7) If the length 119873 is finite FuzzyEn(119898 119899 119903) can bechanged as follows
FuzzyEn (119898 119899 119903) = In120601119898 (119899 119903) minus In120601119898+1 (119899 119903) (9)
22 Sparse Bayesian Extreme Learning Machine (SBELM)Given a preprocessed data set 119863 = (119909
119894 119905119894) 119894 = 1 119873
119909119894isin 119877119899 119905119894isin 119877119898 The output function of ELM with 119871 hidden
nodes is shown as follows
119891 (119909) =
119871
sum
119894=1
120573119894ℎ119894(119909) = 120573 sdot 119867 (119909) (10)
where 120573 = [1205731 120573
119871]119879 is output weight connecting hidden
nodes and output nodes 119867(119909) = [ℎ1(119909) ℎ
119871(119909)] is the
hidden layer output matrix for input 119909 in which ℎ119894(119909) is the
hidden output of the 119894th hidden node Equation (10) can bewritten as follows
119867120573 = 119879 (11)
where 119879 is the training data target matrix SBELM learnsoutput weight by using Bayesian method instead of bycalculatingMoore-Penrose generalized inverse of119867 [17]Thehidden layer output 119867 becomes the input of SBELM Treateach training sample as an independent Bernoulli event sothat probability119901(119905 | 119909) satisfies Bernoulli distribution Applysigmoid function to convert the predicted output Y(ℎ 120573) asfollows
120590 (Y (ℎ 120573)) =1
(1 + exp (minusY (ℎ 120573))) (12)
The likelihood function of sample set is expressed asfollows
119901 (119905 | 119867 120573) =
119873
prod
119895=1
120590 (Y (ℎ 120573))119905119895
[1 minus 120590 (Y(ℎ 120573))]1minus119905119895
(13)
where 119905119895is the target of training sample 119909
119895Y(ℎ 120573) = ℎ120573 and
119905119895isin 0 1 Conditioned on a hyperparameter 120572
119895 zero-mean
Gaussian prior distribution over 120573119894is as follows
119901 (120573 | 120572) =
119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2) (14)
The typical step of SBELM is to establish the distributionof marginal likelihood over 119905 conditioned on 120572 and 119867 and
determine 120572 by maximizing the marginal likelihood 119901(119905 | 119867120572) by Laplace approximation method
argmax ln 119901 (119905 | 120573119867) 119901 (120573 | 120572)
= argmax[
[
ln
119873
prod
119895=1
119910119905119895
119895(1 minus 119910
119895)1minus119905119895
+ ln119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2)]
]
= argmax[
[
119873
sum
119895=1
119905119895ln119910119895+ (1 minus 119905
119895)
sdot ln (1 minus 119910119895) minus
120573119879119860120573
2+ const]
]
(15)
where 119910119895= 120590(Y(ℎ
119895 120573))119860 = diag(120572) and const =sum119871
119894=1ln120572119894minus
12 ln 2120587 Then make quadratic approximation for log ofposterior probability
nabla120573nabla120573 ln 119901 (119905 | 120573119867) 119901 (120573 | 120572) = minus (119867119879119870119867 + 119860) (16)
where 119870 is a diagonal matrix in which 119896119895= 119910119895(1 minus 119910
119895) with
119895 = 1 119873 Therefore the center and covariance matrix ofGauss distribution of 120573 expressed as 1205731015840 andΦ are obtained asfollows
1205731015840= Φ119867
1198791198701199051015840 Φ = (119867
119879119870119867 + 119860)
minus1
(17)
where 1199051015840 = 119867120573+119870minus1(119905minus119910) By obtainingGauss approximationof 120573 the log of marginal likelihood is represented as follows
L (120572) = ln119901 (119905 | 120572119867)
= minus1
2[119873 ln (2120587) + ln |119862| + (1199051015840)
119879
119862minus11199051015840]
(18)
where119862 = 119870+119867119860119867119879 By setting the differential ofL(120572)withrespect to 120572 as 0 update the hyperparameter 120572 as follows
120572119894=1 minus 120572119894Φ119894119894
(1205731198941015840)2 (19)
The main procedure of SBELM is described as follows
(1) Initialize 120572119894and 120573
119894randomly with 119894 = 1 119871
(2) By utilizing Laplace approximation approach obtainapproximated Gauss distribution of 120573 and update 1205731015840and Φ by using (17)
(3) Bymaximizing themarginal likelihood utilize (19) toupdate hyperparameter 120572 until reaching the termina-tion criteria
(4) By tuning some 120573119894into 0 obtain the sparse represen-
tation of hidden layer output weight(5) For an unknown sample 119909
119906 utilize (12) to predict
probability distribution 119901(119905 | 119909119906 1205731015840)
4 Computational Intelligence and Neuroscience
SBELM12
SBELMi1
SBELMm1
SBELM1m
SBELMim
SBELMm(mminus1)
PSBELM1
PSBELMi
PSBELMm
p1
pi
pm
middot middot middot
middot middot middot
middot middot middot
Figure 1 Structure of paired SBELM for simultaneous failure diag-nosis
23 Paired SBELM SBELM is excellent in solving binaryclassification by obtaining probability distribution of eachclass 119901(119905 | 119909 1205731015840) With the purpose of final drive simulta-neous failure diagnosis in which training samples of singlefailure are ample while training samples of simultaneousfailure are scarce this paper combines the state-of-the-artcoupling approach proposed in [20]with SBELM to constructa set of paired SBELM (PSBELM) classifiers expressed as[PSBELM
1 PSBELM
119898] for a 119898-label classification prob-
lem shown in Figure 1 and each paired classifier PSBELM119894=
[SBELM1198941 SBELM
119894119895 SBELM
119894119898] in which SBELM
119894119895is
trained by every pair of classes and its output is 119901119894119895(119905119894| 120573 119909)
for sample 119909 belonging to the 119894th against the 119895th class Thetotal number of classifiers is119898(119898 minus 1)2
In simultaneous failure diagnosis more than one failuremay occur at the same time that can infer the conceptsum119898
119894=1119901119894= 1 [21] By estimating each probability output of
binary classifiers SBELM119894119895to measure correlation between
various classes obtain the paired probability output 119901119894as
follows
119901119894=sum119889
119895=1119895 =119894119899119894119895119901119894119895
sum119889
119895=1119895 =119894119899119894119895
119894 = 1 119898 (20)
where 119899119894119895is the number of training sample belonging to the
119894th and the 119895th class
24 Optimization of DecisionThreshold for Simultaneous Fail-ure Mode Recognition For a 119898-class classification problemthe output of classifiers based on PSBELM is a probabilityvector 119875 = [119901
1 119901
119898] in which 119901
119895represents occur-
ring possibility of the 119895th failure In order to obtain finalsimultaneous failuremodes an appropriate threshold value isindispensable In general researchers usually use 05 to be thethreshold value [21] which is of generality but not suitable forspecific application This paper utilizes Grid Search methodand an independent sample set containing both single failureand simultaneous failure to generate an optimal decisionthreshold 120576lowast between 0 and 1 which can convert probabilityoutput vector into result vector 119865 = [119891
1 119891
119894 119891
119898]
effectively
119891119894= 1 119901119894ge 120576lowast
0 119901119894lt 120576lowast119894 = 1 119898 120576
lowastisin (0 1) (21)
The simultaneous failure modes are those single failuresthat their corresponding 119891
119894is equal to 1 Since the range of
searching is limited the time-consuming characteristic ofGrid Search method can not weaken its advantages of globaloptimization compared with GA and PSO [18]
25 Evaluation of Performance Based on F1-Measure Con-sidering that partial matching is valid and significant insimultaneous failure diagnosis [22] utilize an independenttesting set and F1-measure [23] which is commonly usedfor evaluation of information retrieval systems to evaluatediagnostic accuracy for the proposed simultaneous failurediagnostic framework Given a data set 119863 = (119909
119894 119905119894) 119894 =
1 119873 119909119894isin 119877119899 119905119894isin 119877119898 119905119894119895isin 0 1 119895 = 1 119898 define
two variables namely precision (119875) and recall (119877) amongwhich 119875 represents the ratio between correct identified singlefailure modes and the actual simultaneous failure modes and119877 represents the ratio between correct identified single failuremodes and the predicted simultaneous failure modes
119875 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119905119894119895
119877 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119891lowast119894119895
(22)
where 119891lowast119894= [119891
lowast
1198941 119891
lowast
119894119898] is the predicted simultaneous
failure modes by using the proposed framework and 119905119894=
[1199051198941 119905
119894119898] is the actual simultaneous failure modes of 119909
119894
The F1-measure value can be obtained as follows
119864 =2 lowast 119875 lowast 119877
119875 + 119877=
2sum119898
119895=1sum119873
119894=1119891lowast
119894119895119910119894119895
sum119898
119895=1sum119873
119894=1119910119894119895+ sum119898
119895=1sum119873
119894=1119891lowast119894119895
(23)
26 The Proposed Framework for Final Drive SimultaneousFailure Diagnosis The structure of the proposed frameworkis shown in Figure 2 and the procedure of the proposedframework is described as follows
(1) Divide sample set into four parts 119863training1 119863training2119863threshold and 119863testing All the sample should bepreprocessed by WPT and utilize fuzzy entropy tomeasure the feature of oscillatory
(2) Utilize 119863training1 containing only single failure modesto optimize parameters of WPT including number oflayer 119871 and mother wavelet in preprocessing by usingfailure diagnostic model of SBELM
(3) By using optimal parameters of WPT obtained fromstep 2 preprocess 119863training2 containing only singlefailure modes and train classifiers based on pairedSBELM
(4) The optimumdiagnostic model of PSBELMgeneratesa probability output vector [119901
1 119901
119898] in 119898-label
classification problem and uses 119863threshold containingboth single and simultaneous failure modes and GridSearch to confirm the decision threshold value 120576lowastwhich is used to obtain simultaneous failure modes
(5) Use119863testing and F1-measure to evaluate the diagnosticaccuracy of the proposed framework
Computational Intelligence and Neuroscience 5
Opt
imal
dia
gnos
tic m
odel
Evaluation of theproposed framework
Dtesting
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Decision threshold
Result vector
Evaluation
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Optimizingdecision threshold
Confirmation of thethreshold value
Optimalparametersof WPT
Optimal WPT andfuzzy entropy
Train diagnosticmodel based on paired SBELM
Training diagnosticmodel
Dtraining1
Determiningparameters of WPT
Standard SBELMdiagnostic model
Optimization of WPT
Dthreshold
Dtraining2
value 120576lowast
value 120576lowast
Optimal 120576lowast
Figure 2 The structure of the proposed framework
3 Experiment Setup and Preprocessing
31 Experiment Setup In order to obtain sample data withrepresentativeness for constructing diagnostic model andverify the efficiency of the proposed diagnostic platformimplement the experiments on a test bed containing a PC twosensors a signal amplifier and a simulation turntablewith thecomposition as shown in Figure 3 in quiet room to collectenough original vibration signal of final drive Two sensorsare laid on the final drive in horizontal and vertical directionas shown in Figure 4 to collect vibration signal when it is setinto running state Most failures of final drive such as gearerror gear hard point and tooth broken occurred in gear pairwhich is the hard core of final drive and consisted of a driving-gear and a driven-gear In this research simulate 9 commonfailures including 6 single failures and 3 simultaneous failureswhich are described in detail in Table 1 under the rotatingspeed of 1200 rm for driving motor As shown in Figure 5amplitudes of simultaneous failure are obviously greater thansingle failure because when simultaneous failure occurs thesesingle failures are coupled together severelyThewave profiles
between single and simultaneous failure patterns are similarso that it is difficult to distinguish them manually but thecharacteristics embedded in each vibration signal can beextracted and identified by using methods afore mentioned
Considering the universality of vibration signals whichare used to construct diagnostic models repeat simulatingeach failure mode for 100 times and record the most stable 2seconds in each time with the sampling rate of 12 kHz whichshould be higher than the gear meshing frequency so thateffective failure information may not be discarded duringthe sampling Eventually 1000 sample data are obtainedand prepared to be preprocessed All the simulations areimplemented in MATLAB 70 which is running in a PC withCPU of 34GHZ and RAM of 40GB
32 Feature Extraction Based on WPT and Fuzzy EntropyIn this paper fuzzy entropy is used to reflect the changeof complexity By calculating the average fuzzy entropy ofvibration signal corresponding to each failure mode which isshown in Table 2 we find out that the values of fuzzy entropyof these 10 failure modes are approximate so that it can not
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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![Page 3: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/3.jpg)
Computational Intelligence and Neuroscience 3
(5) Change119898 to119898 + 1 and repeat step (1) to (4)
120601119898+1(119899 119903) =
1
119873 minus 119898
119873minus119898
sum
119894=1
(1
119873 minus 119898 + 1
119873minus119898
sum
119895=1119895 =119894
119863119898+1
119894119895) (7)
(6) Fuzzy entropy of sequence 119909(119894) 1 le 119894 le 119873 isdefined as follows
FuzzyEn (119898 119899 119903) = lim119873rarrinfin
[In120601119898 (119899 119903) minus In120601119898+1 (119899 119903)] (8)
(7) If the length 119873 is finite FuzzyEn(119898 119899 119903) can bechanged as follows
FuzzyEn (119898 119899 119903) = In120601119898 (119899 119903) minus In120601119898+1 (119899 119903) (9)
22 Sparse Bayesian Extreme Learning Machine (SBELM)Given a preprocessed data set 119863 = (119909
119894 119905119894) 119894 = 1 119873
119909119894isin 119877119899 119905119894isin 119877119898 The output function of ELM with 119871 hidden
nodes is shown as follows
119891 (119909) =
119871
sum
119894=1
120573119894ℎ119894(119909) = 120573 sdot 119867 (119909) (10)
where 120573 = [1205731 120573
119871]119879 is output weight connecting hidden
nodes and output nodes 119867(119909) = [ℎ1(119909) ℎ
119871(119909)] is the
hidden layer output matrix for input 119909 in which ℎ119894(119909) is the
hidden output of the 119894th hidden node Equation (10) can bewritten as follows
119867120573 = 119879 (11)
where 119879 is the training data target matrix SBELM learnsoutput weight by using Bayesian method instead of bycalculatingMoore-Penrose generalized inverse of119867 [17]Thehidden layer output 119867 becomes the input of SBELM Treateach training sample as an independent Bernoulli event sothat probability119901(119905 | 119909) satisfies Bernoulli distribution Applysigmoid function to convert the predicted output Y(ℎ 120573) asfollows
120590 (Y (ℎ 120573)) =1
(1 + exp (minusY (ℎ 120573))) (12)
The likelihood function of sample set is expressed asfollows
119901 (119905 | 119867 120573) =
119873
prod
119895=1
120590 (Y (ℎ 120573))119905119895
[1 minus 120590 (Y(ℎ 120573))]1minus119905119895
(13)
where 119905119895is the target of training sample 119909
119895Y(ℎ 120573) = ℎ120573 and
119905119895isin 0 1 Conditioned on a hyperparameter 120572
119895 zero-mean
Gaussian prior distribution over 120573119894is as follows
119901 (120573 | 120572) =
119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2) (14)
The typical step of SBELM is to establish the distributionof marginal likelihood over 119905 conditioned on 120572 and 119867 and
determine 120572 by maximizing the marginal likelihood 119901(119905 | 119867120572) by Laplace approximation method
argmax ln 119901 (119905 | 120573119867) 119901 (120573 | 120572)
= argmax[
[
ln
119873
prod
119895=1
119910119905119895
119895(1 minus 119910
119895)1minus119905119895
+ ln119871
prod
119894=1
120572119894
radic2120587exp(minus
1205721198941205732
119894
2)]
]
= argmax[
[
119873
sum
119895=1
119905119895ln119910119895+ (1 minus 119905
119895)
sdot ln (1 minus 119910119895) minus
120573119879119860120573
2+ const]
]
(15)
where 119910119895= 120590(Y(ℎ
119895 120573))119860 = diag(120572) and const =sum119871
119894=1ln120572119894minus
12 ln 2120587 Then make quadratic approximation for log ofposterior probability
nabla120573nabla120573 ln 119901 (119905 | 120573119867) 119901 (120573 | 120572) = minus (119867119879119870119867 + 119860) (16)
where 119870 is a diagonal matrix in which 119896119895= 119910119895(1 minus 119910
119895) with
119895 = 1 119873 Therefore the center and covariance matrix ofGauss distribution of 120573 expressed as 1205731015840 andΦ are obtained asfollows
1205731015840= Φ119867
1198791198701199051015840 Φ = (119867
119879119870119867 + 119860)
minus1
(17)
where 1199051015840 = 119867120573+119870minus1(119905minus119910) By obtainingGauss approximationof 120573 the log of marginal likelihood is represented as follows
L (120572) = ln119901 (119905 | 120572119867)
= minus1
2[119873 ln (2120587) + ln |119862| + (1199051015840)
119879
119862minus11199051015840]
(18)
where119862 = 119870+119867119860119867119879 By setting the differential ofL(120572)withrespect to 120572 as 0 update the hyperparameter 120572 as follows
120572119894=1 minus 120572119894Φ119894119894
(1205731198941015840)2 (19)
The main procedure of SBELM is described as follows
(1) Initialize 120572119894and 120573
119894randomly with 119894 = 1 119871
(2) By utilizing Laplace approximation approach obtainapproximated Gauss distribution of 120573 and update 1205731015840and Φ by using (17)
(3) Bymaximizing themarginal likelihood utilize (19) toupdate hyperparameter 120572 until reaching the termina-tion criteria
(4) By tuning some 120573119894into 0 obtain the sparse represen-
tation of hidden layer output weight(5) For an unknown sample 119909
119906 utilize (12) to predict
probability distribution 119901(119905 | 119909119906 1205731015840)
4 Computational Intelligence and Neuroscience
SBELM12
SBELMi1
SBELMm1
SBELM1m
SBELMim
SBELMm(mminus1)
PSBELM1
PSBELMi
PSBELMm
p1
pi
pm
middot middot middot
middot middot middot
middot middot middot
Figure 1 Structure of paired SBELM for simultaneous failure diag-nosis
23 Paired SBELM SBELM is excellent in solving binaryclassification by obtaining probability distribution of eachclass 119901(119905 | 119909 1205731015840) With the purpose of final drive simulta-neous failure diagnosis in which training samples of singlefailure are ample while training samples of simultaneousfailure are scarce this paper combines the state-of-the-artcoupling approach proposed in [20]with SBELM to constructa set of paired SBELM (PSBELM) classifiers expressed as[PSBELM
1 PSBELM
119898] for a 119898-label classification prob-
lem shown in Figure 1 and each paired classifier PSBELM119894=
[SBELM1198941 SBELM
119894119895 SBELM
119894119898] in which SBELM
119894119895is
trained by every pair of classes and its output is 119901119894119895(119905119894| 120573 119909)
for sample 119909 belonging to the 119894th against the 119895th class Thetotal number of classifiers is119898(119898 minus 1)2
In simultaneous failure diagnosis more than one failuremay occur at the same time that can infer the conceptsum119898
119894=1119901119894= 1 [21] By estimating each probability output of
binary classifiers SBELM119894119895to measure correlation between
various classes obtain the paired probability output 119901119894as
follows
119901119894=sum119889
119895=1119895 =119894119899119894119895119901119894119895
sum119889
119895=1119895 =119894119899119894119895
119894 = 1 119898 (20)
where 119899119894119895is the number of training sample belonging to the
119894th and the 119895th class
24 Optimization of DecisionThreshold for Simultaneous Fail-ure Mode Recognition For a 119898-class classification problemthe output of classifiers based on PSBELM is a probabilityvector 119875 = [119901
1 119901
119898] in which 119901
119895represents occur-
ring possibility of the 119895th failure In order to obtain finalsimultaneous failuremodes an appropriate threshold value isindispensable In general researchers usually use 05 to be thethreshold value [21] which is of generality but not suitable forspecific application This paper utilizes Grid Search methodand an independent sample set containing both single failureand simultaneous failure to generate an optimal decisionthreshold 120576lowast between 0 and 1 which can convert probabilityoutput vector into result vector 119865 = [119891
1 119891
119894 119891
119898]
effectively
119891119894= 1 119901119894ge 120576lowast
0 119901119894lt 120576lowast119894 = 1 119898 120576
lowastisin (0 1) (21)
The simultaneous failure modes are those single failuresthat their corresponding 119891
119894is equal to 1 Since the range of
searching is limited the time-consuming characteristic ofGrid Search method can not weaken its advantages of globaloptimization compared with GA and PSO [18]
25 Evaluation of Performance Based on F1-Measure Con-sidering that partial matching is valid and significant insimultaneous failure diagnosis [22] utilize an independenttesting set and F1-measure [23] which is commonly usedfor evaluation of information retrieval systems to evaluatediagnostic accuracy for the proposed simultaneous failurediagnostic framework Given a data set 119863 = (119909
119894 119905119894) 119894 =
1 119873 119909119894isin 119877119899 119905119894isin 119877119898 119905119894119895isin 0 1 119895 = 1 119898 define
two variables namely precision (119875) and recall (119877) amongwhich 119875 represents the ratio between correct identified singlefailure modes and the actual simultaneous failure modes and119877 represents the ratio between correct identified single failuremodes and the predicted simultaneous failure modes
119875 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119905119894119895
119877 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119891lowast119894119895
(22)
where 119891lowast119894= [119891
lowast
1198941 119891
lowast
119894119898] is the predicted simultaneous
failure modes by using the proposed framework and 119905119894=
[1199051198941 119905
119894119898] is the actual simultaneous failure modes of 119909
119894
The F1-measure value can be obtained as follows
119864 =2 lowast 119875 lowast 119877
119875 + 119877=
2sum119898
119895=1sum119873
119894=1119891lowast
119894119895119910119894119895
sum119898
119895=1sum119873
119894=1119910119894119895+ sum119898
119895=1sum119873
119894=1119891lowast119894119895
(23)
26 The Proposed Framework for Final Drive SimultaneousFailure Diagnosis The structure of the proposed frameworkis shown in Figure 2 and the procedure of the proposedframework is described as follows
(1) Divide sample set into four parts 119863training1 119863training2119863threshold and 119863testing All the sample should bepreprocessed by WPT and utilize fuzzy entropy tomeasure the feature of oscillatory
(2) Utilize 119863training1 containing only single failure modesto optimize parameters of WPT including number oflayer 119871 and mother wavelet in preprocessing by usingfailure diagnostic model of SBELM
(3) By using optimal parameters of WPT obtained fromstep 2 preprocess 119863training2 containing only singlefailure modes and train classifiers based on pairedSBELM
(4) The optimumdiagnostic model of PSBELMgeneratesa probability output vector [119901
1 119901
119898] in 119898-label
classification problem and uses 119863threshold containingboth single and simultaneous failure modes and GridSearch to confirm the decision threshold value 120576lowastwhich is used to obtain simultaneous failure modes
(5) Use119863testing and F1-measure to evaluate the diagnosticaccuracy of the proposed framework
Computational Intelligence and Neuroscience 5
Opt
imal
dia
gnos
tic m
odel
Evaluation of theproposed framework
Dtesting
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Decision threshold
Result vector
Evaluation
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Optimizingdecision threshold
Confirmation of thethreshold value
Optimalparametersof WPT
Optimal WPT andfuzzy entropy
Train diagnosticmodel based on paired SBELM
Training diagnosticmodel
Dtraining1
Determiningparameters of WPT
Standard SBELMdiagnostic model
Optimization of WPT
Dthreshold
Dtraining2
value 120576lowast
value 120576lowast
Optimal 120576lowast
Figure 2 The structure of the proposed framework
3 Experiment Setup and Preprocessing
31 Experiment Setup In order to obtain sample data withrepresentativeness for constructing diagnostic model andverify the efficiency of the proposed diagnostic platformimplement the experiments on a test bed containing a PC twosensors a signal amplifier and a simulation turntablewith thecomposition as shown in Figure 3 in quiet room to collectenough original vibration signal of final drive Two sensorsare laid on the final drive in horizontal and vertical directionas shown in Figure 4 to collect vibration signal when it is setinto running state Most failures of final drive such as gearerror gear hard point and tooth broken occurred in gear pairwhich is the hard core of final drive and consisted of a driving-gear and a driven-gear In this research simulate 9 commonfailures including 6 single failures and 3 simultaneous failureswhich are described in detail in Table 1 under the rotatingspeed of 1200 rm for driving motor As shown in Figure 5amplitudes of simultaneous failure are obviously greater thansingle failure because when simultaneous failure occurs thesesingle failures are coupled together severelyThewave profiles
between single and simultaneous failure patterns are similarso that it is difficult to distinguish them manually but thecharacteristics embedded in each vibration signal can beextracted and identified by using methods afore mentioned
Considering the universality of vibration signals whichare used to construct diagnostic models repeat simulatingeach failure mode for 100 times and record the most stable 2seconds in each time with the sampling rate of 12 kHz whichshould be higher than the gear meshing frequency so thateffective failure information may not be discarded duringthe sampling Eventually 1000 sample data are obtainedand prepared to be preprocessed All the simulations areimplemented in MATLAB 70 which is running in a PC withCPU of 34GHZ and RAM of 40GB
32 Feature Extraction Based on WPT and Fuzzy EntropyIn this paper fuzzy entropy is used to reflect the changeof complexity By calculating the average fuzzy entropy ofvibration signal corresponding to each failure mode which isshown in Table 2 we find out that the values of fuzzy entropyof these 10 failure modes are approximate so that it can not
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
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![Page 4: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/4.jpg)
4 Computational Intelligence and Neuroscience
SBELM12
SBELMi1
SBELMm1
SBELM1m
SBELMim
SBELMm(mminus1)
PSBELM1
PSBELMi
PSBELMm
p1
pi
pm
middot middot middot
middot middot middot
middot middot middot
Figure 1 Structure of paired SBELM for simultaneous failure diag-nosis
23 Paired SBELM SBELM is excellent in solving binaryclassification by obtaining probability distribution of eachclass 119901(119905 | 119909 1205731015840) With the purpose of final drive simulta-neous failure diagnosis in which training samples of singlefailure are ample while training samples of simultaneousfailure are scarce this paper combines the state-of-the-artcoupling approach proposed in [20]with SBELM to constructa set of paired SBELM (PSBELM) classifiers expressed as[PSBELM
1 PSBELM
119898] for a 119898-label classification prob-
lem shown in Figure 1 and each paired classifier PSBELM119894=
[SBELM1198941 SBELM
119894119895 SBELM
119894119898] in which SBELM
119894119895is
trained by every pair of classes and its output is 119901119894119895(119905119894| 120573 119909)
for sample 119909 belonging to the 119894th against the 119895th class Thetotal number of classifiers is119898(119898 minus 1)2
In simultaneous failure diagnosis more than one failuremay occur at the same time that can infer the conceptsum119898
119894=1119901119894= 1 [21] By estimating each probability output of
binary classifiers SBELM119894119895to measure correlation between
various classes obtain the paired probability output 119901119894as
follows
119901119894=sum119889
119895=1119895 =119894119899119894119895119901119894119895
sum119889
119895=1119895 =119894119899119894119895
119894 = 1 119898 (20)
where 119899119894119895is the number of training sample belonging to the
119894th and the 119895th class
24 Optimization of DecisionThreshold for Simultaneous Fail-ure Mode Recognition For a 119898-class classification problemthe output of classifiers based on PSBELM is a probabilityvector 119875 = [119901
1 119901
119898] in which 119901
119895represents occur-
ring possibility of the 119895th failure In order to obtain finalsimultaneous failuremodes an appropriate threshold value isindispensable In general researchers usually use 05 to be thethreshold value [21] which is of generality but not suitable forspecific application This paper utilizes Grid Search methodand an independent sample set containing both single failureand simultaneous failure to generate an optimal decisionthreshold 120576lowast between 0 and 1 which can convert probabilityoutput vector into result vector 119865 = [119891
1 119891
119894 119891
119898]
effectively
119891119894= 1 119901119894ge 120576lowast
0 119901119894lt 120576lowast119894 = 1 119898 120576
lowastisin (0 1) (21)
The simultaneous failure modes are those single failuresthat their corresponding 119891
119894is equal to 1 Since the range of
searching is limited the time-consuming characteristic ofGrid Search method can not weaken its advantages of globaloptimization compared with GA and PSO [18]
25 Evaluation of Performance Based on F1-Measure Con-sidering that partial matching is valid and significant insimultaneous failure diagnosis [22] utilize an independenttesting set and F1-measure [23] which is commonly usedfor evaluation of information retrieval systems to evaluatediagnostic accuracy for the proposed simultaneous failurediagnostic framework Given a data set 119863 = (119909
119894 119905119894) 119894 =
1 119873 119909119894isin 119877119899 119905119894isin 119877119898 119905119894119895isin 0 1 119895 = 1 119898 define
two variables namely precision (119875) and recall (119877) amongwhich 119875 represents the ratio between correct identified singlefailure modes and the actual simultaneous failure modes and119877 represents the ratio between correct identified single failuremodes and the predicted simultaneous failure modes
119875 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119905119894119895
119877 =sum119898
119895=1sum119873
119894=1119891lowast
119894119895119905119894119895
sum119898
119895=1sum119873
119894=1119891lowast119894119895
(22)
where 119891lowast119894= [119891
lowast
1198941 119891
lowast
119894119898] is the predicted simultaneous
failure modes by using the proposed framework and 119905119894=
[1199051198941 119905
119894119898] is the actual simultaneous failure modes of 119909
119894
The F1-measure value can be obtained as follows
119864 =2 lowast 119875 lowast 119877
119875 + 119877=
2sum119898
119895=1sum119873
119894=1119891lowast
119894119895119910119894119895
sum119898
119895=1sum119873
119894=1119910119894119895+ sum119898
119895=1sum119873
119894=1119891lowast119894119895
(23)
26 The Proposed Framework for Final Drive SimultaneousFailure Diagnosis The structure of the proposed frameworkis shown in Figure 2 and the procedure of the proposedframework is described as follows
(1) Divide sample set into four parts 119863training1 119863training2119863threshold and 119863testing All the sample should bepreprocessed by WPT and utilize fuzzy entropy tomeasure the feature of oscillatory
(2) Utilize 119863training1 containing only single failure modesto optimize parameters of WPT including number oflayer 119871 and mother wavelet in preprocessing by usingfailure diagnostic model of SBELM
(3) By using optimal parameters of WPT obtained fromstep 2 preprocess 119863training2 containing only singlefailure modes and train classifiers based on pairedSBELM
(4) The optimumdiagnostic model of PSBELMgeneratesa probability output vector [119901
1 119901
119898] in 119898-label
classification problem and uses 119863threshold containingboth single and simultaneous failure modes and GridSearch to confirm the decision threshold value 120576lowastwhich is used to obtain simultaneous failure modes
(5) Use119863testing and F1-measure to evaluate the diagnosticaccuracy of the proposed framework
Computational Intelligence and Neuroscience 5
Opt
imal
dia
gnos
tic m
odel
Evaluation of theproposed framework
Dtesting
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Decision threshold
Result vector
Evaluation
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Optimizingdecision threshold
Confirmation of thethreshold value
Optimalparametersof WPT
Optimal WPT andfuzzy entropy
Train diagnosticmodel based on paired SBELM
Training diagnosticmodel
Dtraining1
Determiningparameters of WPT
Standard SBELMdiagnostic model
Optimization of WPT
Dthreshold
Dtraining2
value 120576lowast
value 120576lowast
Optimal 120576lowast
Figure 2 The structure of the proposed framework
3 Experiment Setup and Preprocessing
31 Experiment Setup In order to obtain sample data withrepresentativeness for constructing diagnostic model andverify the efficiency of the proposed diagnostic platformimplement the experiments on a test bed containing a PC twosensors a signal amplifier and a simulation turntablewith thecomposition as shown in Figure 3 in quiet room to collectenough original vibration signal of final drive Two sensorsare laid on the final drive in horizontal and vertical directionas shown in Figure 4 to collect vibration signal when it is setinto running state Most failures of final drive such as gearerror gear hard point and tooth broken occurred in gear pairwhich is the hard core of final drive and consisted of a driving-gear and a driven-gear In this research simulate 9 commonfailures including 6 single failures and 3 simultaneous failureswhich are described in detail in Table 1 under the rotatingspeed of 1200 rm for driving motor As shown in Figure 5amplitudes of simultaneous failure are obviously greater thansingle failure because when simultaneous failure occurs thesesingle failures are coupled together severelyThewave profiles
between single and simultaneous failure patterns are similarso that it is difficult to distinguish them manually but thecharacteristics embedded in each vibration signal can beextracted and identified by using methods afore mentioned
Considering the universality of vibration signals whichare used to construct diagnostic models repeat simulatingeach failure mode for 100 times and record the most stable 2seconds in each time with the sampling rate of 12 kHz whichshould be higher than the gear meshing frequency so thateffective failure information may not be discarded duringthe sampling Eventually 1000 sample data are obtainedand prepared to be preprocessed All the simulations areimplemented in MATLAB 70 which is running in a PC withCPU of 34GHZ and RAM of 40GB
32 Feature Extraction Based on WPT and Fuzzy EntropyIn this paper fuzzy entropy is used to reflect the changeof complexity By calculating the average fuzzy entropy ofvibration signal corresponding to each failure mode which isshown in Table 2 we find out that the values of fuzzy entropyof these 10 failure modes are approximate so that it can not
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 5: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/5.jpg)
Computational Intelligence and Neuroscience 5
Opt
imal
dia
gnos
tic m
odel
Evaluation of theproposed framework
Dtesting
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Decision threshold
Result vector
Evaluation
Optimal WPT andfuzzy entropy
Optimal diagnosticmodel based onpaired SBELM
Optimizingdecision threshold
Confirmation of thethreshold value
Optimalparametersof WPT
Optimal WPT andfuzzy entropy
Train diagnosticmodel based on paired SBELM
Training diagnosticmodel
Dtraining1
Determiningparameters of WPT
Standard SBELMdiagnostic model
Optimization of WPT
Dthreshold
Dtraining2
value 120576lowast
value 120576lowast
Optimal 120576lowast
Figure 2 The structure of the proposed framework
3 Experiment Setup and Preprocessing
31 Experiment Setup In order to obtain sample data withrepresentativeness for constructing diagnostic model andverify the efficiency of the proposed diagnostic platformimplement the experiments on a test bed containing a PC twosensors a signal amplifier and a simulation turntablewith thecomposition as shown in Figure 3 in quiet room to collectenough original vibration signal of final drive Two sensorsare laid on the final drive in horizontal and vertical directionas shown in Figure 4 to collect vibration signal when it is setinto running state Most failures of final drive such as gearerror gear hard point and tooth broken occurred in gear pairwhich is the hard core of final drive and consisted of a driving-gear and a driven-gear In this research simulate 9 commonfailures including 6 single failures and 3 simultaneous failureswhich are described in detail in Table 1 under the rotatingspeed of 1200 rm for driving motor As shown in Figure 5amplitudes of simultaneous failure are obviously greater thansingle failure because when simultaneous failure occurs thesesingle failures are coupled together severelyThewave profiles
between single and simultaneous failure patterns are similarso that it is difficult to distinguish them manually but thecharacteristics embedded in each vibration signal can beextracted and identified by using methods afore mentioned
Considering the universality of vibration signals whichare used to construct diagnostic models repeat simulatingeach failure mode for 100 times and record the most stable 2seconds in each time with the sampling rate of 12 kHz whichshould be higher than the gear meshing frequency so thateffective failure information may not be discarded duringthe sampling Eventually 1000 sample data are obtainedand prepared to be preprocessed All the simulations areimplemented in MATLAB 70 which is running in a PC withCPU of 34GHZ and RAM of 40GB
32 Feature Extraction Based on WPT and Fuzzy EntropyIn this paper fuzzy entropy is used to reflect the changeof complexity By calculating the average fuzzy entropy ofvibration signal corresponding to each failure mode which isshown in Table 2 we find out that the values of fuzzy entropyof these 10 failure modes are approximate so that it can not
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 6: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/6.jpg)
6 Computational Intelligence and Neuroscience
Table 1 Simple and simultaneous failure modes description
Failurelabel Failure mode description
C1 Single failures Normal statusC2
Single failures
Gear errorC3 Gear burrC4 Gear hard pointC5 MisalignmentC6 Gear tooth brokenC7 Gear crackC8
Simultaneousfailures
Gear tooth broken and gear crack
C9 Gear tooth broken and gear hardpoint
C10 Misalignment and gear crack
Turntable part
Drive part
Figure 3 The test bed
correctly distinguish failures of final drive The reason is thatinformation supplied by fuzzy entropy of original signal islimited and unable to reflect the deep-seated information ofeach failure situation Therefore we employ the frequentlyused mother wavelet function called Daubechies waveletwhich has orthogonal characteristic and effectiveness infiltering signal of vibrating machinery to implement waveletpackage transform and decompose original vibration signalinto several subfrequency bands By calculating fuzzy entropyof each frequency band obtained from 119871-level wavelet pack-age transform decomposition construct a feature vectorwith the dimension of 2119871 which can effectively reflect thecomplexity and self-similarity of oscillation characteristic offailure modes occurring in final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn2119871] (24)
33 Distribution Plan of Samples There are 1000 sample datacontaining 100 normal samples 600 single failure samples
Horizontaldirection
Verticaldirection
Figure 4 Two sensors on final drive
and 300 simultaneous failure samples In each trial ran-domly divide the whole sample set into four parts 119863training1119863training2 119863threshold and 119863testing 119863training1 and 119863training2 whichare consisting of only single failure modes are used for opti-mizing parameters of WPT and training optimal diagnosticmodel based on paired SBELM119863threshold which contains bothsingle and simultaneous failure modes is used to generateoptimal decision threshold which convert probability resultof diagnostic model based on paired SBELM into final simul-taneous failure modes119863testing is used to test and evaluate theproposed framework by using F1-measure Ensure that thewhole sample set be preprocessed and the size of trainingsamples should be more than testing samples to ensure thegeneralization of the proposed framework The distributionplan is shown in Table 3
4 Result and Discussion
41 Optimization of Preprocessing and Feature Extraction Indata preprocessing optimum combination of decompositionlevel and mother wavelet of WPT and parameters of fuzzyentropy can achieve better performance in classification Weuse119863training1 containing random 250 single samples to obtainthe optimal combination of level number andmother waveletwhich is suitable for preprocessing samples collected fromfinal drive In order to simplify experiment and on the basisof previous research result focus on three wavelets Db3 Db4and Db5 and three decomposition levels from 3 to 5 Threeparameters of fuzzy entropy including119898 119899 and 119903 are definedempirically in advance Parameter 119898 is usually set to be 2Related to the boundary of fuzzy function parameters 119903 and119899 are setting as 02 and 2 STD where STD is the standarddeviation of original data [8]
By using single failure samples contained in 119863training1and standard diagnostic model based on SBELM with failureparameters find out appropriate parameters of WPT toachieve best performance of preprocessing The standarddiagnostic model based on SBELM is only used for selectingoptimal parameters of WPT that exist in the best failureidentification model in which the accuracy of classificationis highest The comparison result is shown in Figure 6 whichindicates that classification accuracy of the preprocessing by
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
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Distributed Sensor Networks
International Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 7: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/7.jpg)
Computational Intelligence and Neuroscience 7
Table 2 Average fuzzy entropy of 10 failure modes
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10Average fuzzy entropy 17761 18695 18855 17904 18734 19018 18080 18653 18107 19268
0 500 1000 1500 2000 2500minus02
0
02 C1
0 500 1000 1500 2000 2500
C2
minus02
0
02
C4
minus02
0
02
0 500 1000 1500 2000 2500
C6
minus02
0
02
0 500 1000 1500 2000 2500
C8
minus05
0
05
0 500 1000 1500 2000 2500
C10
minus05
0
05
0 500 1000 1500 2000 2500
C3
minus02
0
02
0 500 1000 1500 2000 2500
C5
minus02
0
02
0 500 1000 1500 2000 2500
C7
minus02
0
02
0 500 1000 1500 2000 2500
C9
minus05
0
05
0 500 1000 1500 2000 2500
Figure 5 Vibration waveforms of 9 failure modes and normal status
Table 3 Division of the whole sample dataset
Single failure Simultaneous failure Total number119863training1 250 250119863training2 250 250119863threshold 100 200 300119863testing 100 100 200Total 700 300 1000
using 3 level decomposition and Db4 as mother wavelet andstandard diagnostic model based on SBELM is highest withthe accuracy of 952 This parameter combination of WPTis suitable for preprocessing the dataset in this application
After decomposing vibration signal by using three-levelwavelet package decomposition calculate the correspondingvalue of fuzzy entropy as shown in Figure 7 In Figure 7horizontal ordinate represents eight subfrequency bands ofthree-level wavelet package decomposition and longitudinalcoordinate represents the fuzzy entropy value The FuzzyEnof the oscillation from final drive with simultaneous failuresis larger than that of single failures and normal status Whensimultaneous failures occur under rotation of gear pairdifferent failure points are coupling together to make the
9270
9520
9240
94809450
9250
93909420
92
9000
9100
9200
9300
9400
9500
9600
9700
L3D
b3
()
L3D
b4
L3D
b5
L4D
b3
L4D
b4
L4D
b5
L5D
b3
L5D
b4
L5D
b5
Diagnostic accuracy
Combination of parameters
Figure 6 The diagnostic accuracy of different parameters
oscillation complex and stronger Furthermore the values offuzzy entropy vary from one failure pattern to another Thischaracteristic denotes fuzzy entropy can be used as feature offailure diagnosis
By calculating fuzzy entropy of each frequency bandobtained from three-levelwavelet package decompositionwe
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 8: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/8.jpg)
8 Computational Intelligence and Neuroscience
05075
1125
15175
2225
1 2 3 4 5 6 7 8
12345
678910
Number of feature vectors
Figure 7 Mean value of fuzzy entropy for failure modes
construct a feature vector with the dimension of 8 which caneffectively reflect the failure modes of final drive
Feature = [FuzzyEn1 FuzzyEn2 FuzzyEn8] (25)
42 Effectiveness of Optimal Decision Threshold After con-structing optimal diagnostic model based on paired SBELMwith optimal parameters of WPT in preprocessing by usingonly single failure modes generation of optimal decisionthreshold is the pivotal point which affects final diagnosticaccuracy of simultaneous failure Traditional machine learn-ingmethods usually adopt 05 as general threshold value (GT)[24]This research uses119863threshold containing 100 single failuremodes and 200 simultaneous failure modes and Grid Searchmethodwith interval of 001 to search final decision threshold120576lowast in range of 0 to 1 AlthoughGrid Search is time consumingit can obtain global optimum
With the purpose of verifying effectiveness of optimaldecision threshold utilize 5-fold cross validation method toimplement a set of experiments by using 119863threshold for bothsingle and simultaneous failure modes recognition Resultsare shown in Figure 8
After optimizing threshold the accuracy of diagnosticmodel improves by an average of 6 FixedGeneral thresholdis generated by experience so that it has generalization butwithout optimization [25] Even using the same diagnosticmodel to diagnose different sample set would require differ-ent threshold Therefore this research uses an independentsample set to generate optimal decision threshold
43 Sensitivity Analysis of SBELM For diagnosis based onELM diagnostic accuracy and training speed are sensitiveto the initial number of hidden nodes To analyze thesensitivity of SBELM on the number of hidden nodes in thisapplication use 500 single failure samples in 119863training1 and119863training2 to train classifier based on SBELM and the bestaverage accuracy along with the increase of hidden nodesis shown in Figure 9 As shown in Figure 9 the averageaccuracies of ELM with increment of hidden nodes are inlarger variation The reason for this fluctuation is that ELM
9020
8450
8860
9780
91309450
7000
7500
8000
8500
9000
9500
10000
Single fault
()
Simultaneous fault Total fault
General thresholdOptimal decision threshold
Figure 8 Diagnostic accuracies of models with general thresholdand optimal decision threshold
80
85
90
95
100
10 20 30 40 50 60 70 80 90 100
Accu
racy
()
ELMSBELM
Figure 9 Variation of accuracy of ELM and SBELM
is in poor generalization because of data overfitting [17]However the average accuracies are stable and are obviouslyhigher than ELMThe result verifies that SBELM is relativelyinsensitive to the initial number of hidden nodes MoreoverSBELM can obtain an excellent accuracy with a small hiddenlayer which reduces the computational cost effectively
44 Evaluation of the Proposed Framework In order to effec-tively confirm the availability of the proposed simultaneousfailure diagnosis framework we use 119863testing containing 100single failure modes and 100 simultaneous failure modes andF1-measuremethod tomeasure performance of the proposedframework and diagnostic model based on PNN and SVM indiagnostic accuracy and diagnostic speed Firstly use sampleset which are consisting of119863training1 and119863training2 to constructand tune parameters of diagnostic model based on PNN andSVM separately and then use 119863threshold to generate optimalthreshold value Since SVM is essentially used for binary-classclassification [26] with the purpose of simultaneous failurediagnosis we combine SVM with multiclass classificationstrategy to construct a set of classifiers in which each classifier
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 9: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/9.jpg)
Computational Intelligence and Neuroscience 9
Table 4 Comparison of paired strategy and one-to-all strategy
Classifier Decision threshold isin [0 1] Multiclass classification strategy Accuracy ()Single failures Simultaneous failures Entire sample
PNN 069 One-to-all 9154 (plusmn102) 8822 (plusmn155) 8942 (plusmn167)paired strategy 9321 (plusmn125) 8914 (plusmn176) 9233 (plusmn205)
SVM 069 One-to-all 9202 (plusmn235) 8090 (plusmn162) 8470 (plusmn187)paired strategy 9484 (plusmn175) 8432 (plusmn135) 8892 (plusmn214)
SBELM 072 One-to-all 9513 (plusmn122) 9054 (plusmn205) 9294 (plusmn173)paired strategy 9842 (plusmn141) 9281 (plusmn235) 9623 (plusmn159)
is only focusing on two failure modes Trying to ensurethe excellent performance of classifiers based on SVM setthe value of regularization parameter 119862 of SVM to be 10120572where 120572 is between 0 and 2 Radial basis kernel functionis employed in SVM with 119862 = 10 and 119903 = 2 whichshow the best accuracy of classification As a probabilityclassifier the crucial hyperparameter of PNN is spread 119904 Inthis research the value of s is chosen from 1 to 3 with intervalof 05 according to conclusion of references Finally the besthyperparameters 119904 and threshold value 120576 for PNN are 1 and069
To verify the effectiveness of the paired strategy inthe proposed framework implement a set of experimentswith one-to-all strategy The experimental results are shownin Table 4 Comparing different classifiers with one-to-allstrategy and paired strategy the accuracies of classifiers withpaired strategy are generally 2 to 4 higher than that ofclassifiers with one-to-all strategyThe primary reason is thatpaired strategy which is used in the proposed frameworkfully considers the correlation between each single failureHowever one-to-all strategy may cause some indecisionregions between different classes The indecision region isprone to sinking into misclassification
To verify the performance of the proposed frameworkimplement a set of experiments about different classifierswith the same testing set and best parameters The decisionthreshold values training time testing time and testingaccuracy of diagnosticmodels based on paired SBELM SVMand PNN are shown in Table 5 The diagnostic accuracy ofpaired SBELM for single failure simultaneous failure andentire sample is 984 928 and 962 which are higherthan that of the SVM and PNN The reason is that SBELMestimates the probability distribution of output values insteadof fitting data to improve generalization [17] Moreover thetraining time and testing time of paired SBELM are 1454msand 487ms that are much fewer than SVMs The reason forthis disparity is that even though paired SBELM builds aset of binary classifiers the sparse characteristic of SBELMreduces the computational cost Consequently the disparitywill become more obvious if the size of sample is big
In practical application of auto manufacturer repre-sentative and valid samples are continuously collected andadded to the training sample database to improve trainingaccuracy Based on this learning speed becomes a crucialfactor for evaluating the efficiency of diagnostic platform Ingeneral considering both diagnostic accuracy and diagnosticefficiency the proposed platform is superior in simultaneous
Table 5 Performance of three classifiers
PNN SVM SBELMDecision threshold[0 1] 069 069 076
Accuracy of singlefailure () 9324 (plusmn186) 9481 (plusmn219) 9842 (plusmn155)
Accuracy ofsimultaneousfailure ()
8912 (plusmn241) 8734 (plusmn196) 9281 (plusmn185)
Accuracy of entiresample () 9230 (plusmn255) 9143 (plusmn232) 9623 (plusmn206)
Training time(ms) 2682 493 1454
Testing time(ms) 865 1194 487
9300
()
9400
9500
9600
9700
9800
10 20 30 40 50 60 70 80 90 100Number of trials
Figure 10 Testing result of 100 trials
failure diagnosis and it is not only suitable for final drive ofcar but also it can be porting to other research fields
In order to verify the stability of the proposed diagnosticframework based on paired SBELM implement 100 trials andin each trial thewhole sample data is reshuffled and randomlydistributed into119863testing afresh andmake sure there are enoughsingle failure samples and simultaneous failure samples in119863testing The testing result is shown in Figure 10 in which thetesting accuracy is stable in the range between 95 and 97and there is no dramatic variation in 100 simulation trials
5 Conclusion
This paper proposes a novel framework based on SBELMand fuzzy entropy for simultaneous failure diagnosis offinal drive which is hardcore to affect the performance
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 10: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/10.jpg)
10 Computational Intelligence and Neuroscience
and safety of car The proposed framework contains foursections preprocessing and feature extraction based onWPT and fuzzy entropy construction of diagnostic modelbased on paired SBELM generation of decision thresholdvalue and recognition of simultaneous failure modes Byusing single failure samples obtain optimal parameters ofWPT which are perfectly adequate for the data in thisapplication Diagnostic model based on paired SBELM inwhich each binary classifier is trained by only single failuresamplesWith an independent sample subset containing bothsingle and simultaneous failure samples use Grid Searchmethod to generate optimal decision threshold by whichprobability result obtained from diagnostic model can beconverted into final result of simultaneous failure modesCompared with frequently used diagnostic model based onSVM and PNN there are three superiorities of the proposedframework (1) The proposed framework based on SBELMinherits the advantages of ELM (efficient approximation andlearning speed) and sparse Bayesian learning (high sparsityand generalization) (2) Fully considering the difficulty andimpossibility of assembling all possible simultaneous failuremodes the proposed framework trains paired classifiersbased on SBELM by using only single failure samples andmoreover the paired strategy can effectively avoid indecisionregions between different classes which can result in misclas-sification (3) With the average testing accuracy of 962 andtesting time of 487ms the proposed framework outperformsother diagnostic models in diagnostic accuracy and learningspeedThe proposed framework is general and transplantablefor simultaneous failure diagnosis so it can be applied toother applications in industrial area in which accuracy andtime cost of failure identification are key factors
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work is supported by the National Natural ScienceFoundation of China under Grant no 70701013 the Scien-tific Research and Technology Development Plan Project ofGuangxi Province under Grant no 2013F020202 and theResearch Project of Liuzhou GM-Wuling Limited LiabilityCompany under Grant no 20132h0261 The authors alsogratefully acknowledge the helpful comments and sugges-tions of the reviewers which have improved the paper
References
[1] X Chiementin B Kilundu L Rasolofondraibe S Crequyand B Pottier ldquoPerformance of wavelet denoising in vibrationanalysis highlightingrdquo Journal of Vibration and Control vol 18no 6 pp 850ndash858 2012
[2] J Rafiee M A Rafiee and P W Tse ldquoApplication of motherwavelet functions for automatic gear and bearing fault diagno-sisrdquo Expert Systems with Applications vol 37 no 6 pp 4568ndash4579 2010
[3] J-DWu and J-J Chan ldquoFaulted gear identification of a rotatingmachinery based on wavelet Transform and artificial neuralnetworkrdquo Expert Systems with Applications vol 36 no 5 pp8862ndash8875 2009
[4] M Vannucci and V Colla ldquoNovel classificationmethod for sen-sitive problems and uneven datasets based on neural networksand fuzzy logicrdquo Applied Soft Computing Journal vol 11 no 2pp 2383ndash2390 2011
[5] A Janusauskas V Marozas and A Lukosevicius ldquoEnsembleempirical mode decomposition based feature enhancement ofcardio signalsrdquo Medical Engineering and Physics vol 35 no 8pp 1059ndash1069 2013
[6] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007
[7] J S Richman and J R Moorman ldquoPhysiological time-seriesanalysis using approximate and sample entropyrdquoThe AmericanJournal of PhysiologymdashHeart and Circulatory Physiology vol278 no 6 pp H2039ndashH2049 2000
[8] J Zheng J Cheng and Y Yang ldquoA rolling bearing fault diagno-sis approach based on LCD and fuzzy entropyrdquoMechanism andMachine Theory vol 70 pp 441ndash453 2013
[9] G L Xiong L Zhang H S Liu H J Zou and W-ZGuo ldquoA comparative study on ApEn SampEn and their fuzzycounterparts in a multiscale framework for feature extractionrdquoJournal of Zhejiang University Science A vol 11 no 4 pp 270ndash279 2010
[10] S Deng S Y Lin and W L Chang ldquoApplication of multiclasssupport vector machines for fault diagnosis of field air defensegunrdquo Expert Systems with Applications vol 38 no 5 pp 6007ndash6013 2011
[11] W Jatmiko W P Nulad M I Elly I M A Setiawan and PMursanto ldquoHeart beat classification using wavelet feature basedon neural networkrdquoWSEASTransactions on Systems vol 10 no1 pp 17ndash26 2011
[12] G-B Huang Q-Y Zhu and C-K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006
[13] E Cambria G-B Huang L L C Kasun et al ldquoExtremelearning machinesrdquo IEEE Intelligent Systems vol 28 no 6 pp30ndash59 2013
[14] Q YuanWZhou S Li andDCai ldquoEpileptic EEG classificationbased on extreme learning machine and nonlinear featuresrdquoEpilepsy Research vol 96 no 1-2 pp 29ndash38 2011
[15] G-B Huang H Zhou X Ding and R Zhang ldquoExtremelearning machine for regression and multiclass classificationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 513ndash529 2012
[16] E Soria-Olivas and J Gomez-Sanchis ldquoBELM bayesianextreme learning machinerdquo IEEE Transaction on Neural Net-works vol 22 no 3 pp 505ndash509 2011
[17] J Luo C-M Vong and P-K Wong ldquoSparse bayesian extremelearningmachine formulti-classificationrdquo IEEETransactions onNeural Networks and Learning Systems vol 25 no 4 pp 836ndash843 2014
[18] Z Yang P K Wong C M Vong J Zhong and J LiangldquoSimultaneous-fault diagnosis of gas turbine generator systemsusing a pairwise-coupled probabilistic classifierrdquoMathematicalProblems in Engineering vol 2013 Article ID 827128 14 pages2013
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 11: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/11.jpg)
Computational Intelligence and Neuroscience 11
[19] D Karaboga and B Basturk ldquoA powerful and efficientalgorithm for numerical function optimization artificial beecolony(ABC)algorithmrdquo Journal of Global Optimization vol 39no 3 pp 459ndash471 2007
[20] T-F Wu C-J Lin and R C Weng ldquoProbability estimatesfor multi-class classification by pairwise couplingrdquo Journal ofMachine Learning Research vol 5 pp 975ndash1005 2004
[21] F Schwenker ldquoHierarchical support vector machines for multi-class pattern recognitionrdquo in Proceedings of the 4th Interna-tional Conference on Knowledge-Based Intellingent EngineeringSystems amp Allied Technologies pp 561ndash565 Brighton UKSeptember 2000
[22] T Yingthawornsuk ldquoClassification of cardiac arrhythmia viaSVMrdquo in Proceedings of the 2nd International Conference onBiomedical Engineering and Technology vol 34 IPCBEE 2012
[23] R Baeza-Yates and B Ribeiro-Neto Modern InformationRetrieval ACMPress Addision-WesleyWokingham UK 1999
[24] J Cheng K Zhang and Y Yang ldquoAn order tracking techniquefor the gear fault diagnosis using local mean decompositionmethodrdquo Mechanism and Machine Theory vol 55 pp 67ndash762012
[25] D Karaboga B Akay and C Ozturk ldquoArtificial bee colony(ABC) optimization algorithm for training feed-forward neuralnetworksrdquo Modeling Decisions for Artificial Intelligence vol4617 pp 318ndash329 2007
[26] C M Vong P K Wong and W F Ip ldquoA new frameworkof simultaneous-fault diagnosis using pairwise probabilisticmulti-label classification for time-dependent patternsrdquo IEEETransactions on Industrial Electronics vol 60 no 8 pp 3372ndash3385 2013
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
![Page 12: Research Article A Framework for Final Drive Simultaneous ...downloads.hindawi.com/journals/cin/2015/427965.pdf · framework can e ectively solve the practical bottleneck in simultaneous](https://reader035.vdocuments.us/reader035/viewer/2022063011/5fc58f111d795255265b0130/html5/thumbnails/12.jpg)
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014