Research ArticleMultifault Diagnosis of Rolling Element Bearings Usinga Wavelet Kurtogram and Vector Median-Based Feature Analysis

Phuong H Nguyen and Jong-Myon Kim

School of Electrical Electronics and Computer Engineering University of Ulsan Ulsan 680-749 Republic of Korea

Correspondence should be addressed to Jong-Myon Kim jongmyonkimgmailcom

Received 3 July 2015 Accepted 18 August 2015

Academic Editor Wahyu Caesarendra

Copyright copy 2015 P H Nguyen and J-M KimThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents a comprehensive multifault diagnosis methodology for incipient rolling element bearing failures This is doneby combining a wavelet packet transform- (WPT-) based kurtogram and a new vector median-based feature analysis techniqueThe proposed approach first extracts useful features that are characteristic of the bearing health condition from the time domainfrequency domain and envelope power spectrum of incoming acoustic emission (AE) signals by using a WPT-based kurtogramThen an enhanced feature analysis approach based on the linear discriminant analysis (LDA) technique is used to select the mostdiscriminant bearing fault features from the original feature setThese selected fault features are used by aNaıve Bayes (NB) classifierto classify the bearing fault conditionsThe performance of the proposedmethodology is tested and validated under various bearingfault conditions on an experimental test rig and compared with conventional state-of-the-art approaches The proposed bearingfault diagnosis methodology yields average classification accuracies of 9111 9667 9889 9944 and 9861 at rotationalspeeds of 300 350 400 450 and 500 rpm respectively

1 Introduction

For the past several decades the development of reliable faultdiagnosis systems to accurately detect and classify variousbearing faults has been at the heart of research in the field ofmachine condition monitoring for preventive and predictivemaintenanceThese fault diagnosis systems aim to accuratelydetect bearing faults at the early stages of their development inorder to prevent potential breakdown of industrial machinesthereby improving their reliability and reducingmaintenancecosts

Several signal processing-based methods have beendeveloped for fault diagnosis of rolling element bearingsThese methods extract characteristic fault features from theinherently nonstationary signals obtained from faulty bear-ings Antoni [1] presented the kurtogram which has provento be a powerful method for characterizing and extractinghidden nonstationary features in bearing fault signals [2ndash4]The kurtogrammethod relies on spectral kurtosis which wasoriginally proposed by Dwyer [5] to detect the presenceof nonstationary transients and accurately indicate their

location in the frequency bands of bearing signals Recentlyin attempts to enhance the performance of the kurtogrammethod for fault diagnosis many researchers have integratedthe kurtogram either with the short-time Fourier transform(STFT) [6] or with multirate filter banks (MRFB) [1] Theseapproaches however have yielded little improvement inextracting transient characteristics and have renderedkurtogram analysis more sensitive to irrelevant impulsivecomponents [7] These shortcomings have been addressedby introducing enhanced variations of the kurtogram suchas the one proposed by Shi et al [8] which uses the complexMorlet wavelet transform The complex Morlet wavelettransform however has its own limitationsThese include itshigh computational complexity and its inability to effectivelyseparate the high frequency components which usually carrythe characteristic fault information In this paper we proposea way to improve the kurtogram-based method by using theenvelope power spectrum and the wavelet packet transform(WPT)Thewavelet packet transform (WPT) is computation-allymore efficient andhighly effective in frequency decompo-sition The proposed kurtogram is performed by computing

Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 320508 14 pageshttpdxdoiorg1011552015320508

2 Shock and Vibration

kurtosis values from the envelope power spectrum of eachsubband signal at different levels of decomposition Thesubband signal that yields the highest spectral kurtosis valueis selected for extracting the features that are characteristicof the bearing fault conditions

In addition to feature extraction techniques feature anal-ysis methods have also been widely studied in machine faultdiagnosis in order to prevent the degradation of classificationperformance that is caused by redundant information in thefeature space [9ndash13] Dimensionality reduction techniqueshave been used to identify the features that effectivelyrepresent the high-dimensional data in a lower-dimensionalspace while retaining the intrinsic information of the bearingdefects these eventually lead to improvements in the classi-fication performance of the fault diagnosis system Amongvarious dimensionality reductionmethods principle compo-nent analysis (PCA) [14] independent component analysis(ICA) [15] and linear discriminant analysis (LDA) [16] arethe most popular methods that have been effectively utilizedin machinery fault diagnosis For instanceWidodo and Yang[11] applied the PCA technique to machine health prognos-tics to extract population characteristics from the availablecondition monitoring data Guo et al [12] investigated theperformance of an ICA algorithm in separating the envelopesof vibration signals to extract the weak impulsive featuresof incipient faults in rolling element bearings In their studylooking into fault diagnosis in ball bearings Harmouche et al[13] demonstrated the use of an LDA technique to effectivelydiscriminate the rather weak and otherwise difficult todetectidentify spectral features extracted from the envelopespectra of vibration signals The LDA feature space yieldsbetter separation between different classes of bearing faultsthan conventional feature analysismethods thereby resultingin improved classification performance PCA and ICA areunsupervised methods that ignore the label informationduring dimensionality reduction whereas LDA is a super-vised method that utilizes the class label information to findan optimal low-dimensional representation of the originalfeature set while also preserving discriminant informationbetween classes As a result LDA yields better classificationresults as compared to PCA and ICA [9 13 14] This paperpresents a new LDA-based feature analysis method thatuses a vector median-based discriminant criterion (VMDC)to characterize the intraclass compactness and interclassseparability of the feature space in order to select the mostdiscriminative subset of bearing fault features

This paper proposes a reliable multifault diagnosisscheme for rolling element bearings that combines animproved WPT-based kurtogram and the VMDC-basedfeature analysis methods The contributions discussed in thispaper can be summarized as follows

(1) An improved WPT-based kurtogram is proposed forextracting the most characteristic fault features fromnonstationary acoustic emission (AE) signals Thekurtogram is performed by computing the spectralkurtosis values for the envelope power spectrum ofeach subband signal at different levels of decompo-sition The subband signal that yields the highest

Naiumlve Bayes classifier

Unknown AE signals

Feature extraction

Feature selection

Fault classification

Waveletkurtogram

Bearing faults

Statistical parameters

Optimal features

Feature pool

Preprocessing ARprewhitening

Prewhitened signals

LDA VMDC

Figure 1 Flowchart of the proposed bearing fault diagnosismethodology

spectral kurtosis value is selected for extracting thefault features

(2) An efficient VMDC-based discriminative fault fea-ture analysis approach is proposed for selecting themost discriminative subset of fault features A vectormedian-based discriminant criterion is presented tominimize the intraclass compactness and maximizethe interclass separability of the feature space

(3) A comprehensive multiclass fault diagnosis method-ology for rolling element bearings is presented andits performance is validated using AE data for varioussingle and compound bearing defects acquired underdifferent simulated crack sizes and bearing rotationalspeeds

The remainder of the paper is structured as follows Sec-tion 2 describes the overall bearing fault diagnosis method-ology Section 3 introduces the self-designed fault simulator(including the data acquisition system and seeded bearingdefects for collecting fault signals) and Section 4 shows theexperimental results Finally Section 5 concludes this paper

2 Proposed Bearing FaultDiagnosis Methodology

The proposed comprehensive bearing fault diagnosis schemeconsists of four main processes including signal preprocess-ing feature extraction feature selection and fault classifica-tion Figure 1 illustrates the overall flowchart of the proposedmethodology

Shock and Vibration 3

21 Preprocessing The performance of wavelet kurtogramanalysis can be improved if the variations between the peaksand flanks of the spectral energy are minimized as shown inTable 6 this can be achieved by preprocessing the AE signalbefore feature extraction [17] In this study the prewhiteningtechnique is used to reduce the spectral energy variationsin the incoming AE fault signal To obtain the prewhitenedsignal an autoregressive (AR) model 119910(119899) is utilized whichis defined as follows

119910 (119899) =

119901

sum

119894=1

119886119894119909 (119894 + 119899) + 119890 (119899) (1)

where 119909(119899) is the incoming bearing signal 119886119894 are the ARcoefficients 119901 denotes the order of the AR model and 119890(119899) isthe residual signal representing a spectrum close to the whitenoise spectrum

22 Feature Extraction For the purpose of extracting thecharacteristic fault signatures from the AE signals this paperpresents a two-step feature extraction process that works asfollows

Step 1 In this step the proposed WPT-based kurtogrammethod is performed on the prewhitened AE signal to deter-mine its most informative subbandThe flowchart of the pro-posed WPT-based kurtogram is illustrated in Figure 2 andits details are provided below

First the prewhitened bearing signal is decomposed intoa series of subbands by performing the wavelet packet trans-form (WPT) with five decomposition levels (119899 = 5) using aDaubechies 2 (or db2) filter The five-level WPT decompo-sition results in a total of 63 subband signals The envelopespectrum of each subband signal is then calculated using thefast Fourier transform (FFT) to identify the characteristicbearing fault frequencies The envelope spectrum of an AEsignal obtained from a defective bearing is usually floodedwith the characteristic defect frequency and its harmonicsWe utilize kurtosis to measure the degree of protrusion ofthe envelope spectrum and then characterize the hiddenbearing defect signatures In order to do this effectively wefirst determine the bearing defect frequencies which includethe ball pass frequency of the bearing outer raceway (BPFO)the ball pass frequency of the bearing inner raceway (BPFI)the ball spin frequency of the bearing roller (BSF) and thefirst 119872 harmonics (119872 = 3 in this paper) of each of thesefrequencies These defect frequencies are defined as follows

BPFO =119873119903 sdot 119865119900

2(1 minus

119861119889

119875119889

cos120572)

BPFI =119873119903 sdot 119865119900

2(1 +

119861119889

119875119889

cos120572)

BSF =119875119889 sdot 119865119900

2 sdot 119861119889

(1 minus (119861119889

119875119889

cos120572)2

)

(2)

where 119873119903 denotes the number of cylindrical rollers 119865119900 isthe shaft speed 120572 is the contact angle and 119861119889 and 119875119889 are

Perform WPT on the signal

End

Generate the corresponding kurtograms based on the kurtosis values

For each kurtogram select the frequency band signal with the highest kurtosis

Calculate kurtosis of the bandwidths for each bearing fault characteristic frequency

Calculate the envelope spectrum of the decomposed frequency band signal

Start

Identify the bandwidths of the bearing fault characteristic frequencies and of their first M harmonics

Figure 2 Flowchart of the wavelet kurtogram algorithm

the roller and pitch diameters respectively Each defect-related bandwidth BW119894 ranges from 119886119894 to 119887119894 (119894 = 1 2 119872)which can be calculated as follows

119886119894 =

(119894 minus ER) lowast BPFO if BPFO

(119894 minus ER) lowast BPFI minus 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 minus ER) lowast BSF minus 2 lowast (1 + ER) lowast 119865119862 otherwise

119887119894 =

(119894 + ER) lowast BPFO if BPFO

(119894 + ER) lowast BPFI + 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 + ER) lowast BSF + 2 lowast (1 + ER) lowast 119865119862 otherwise

(3)

Here ER is the error rate of the bearing test rig and 119865119862

is the cage frequency Once the bearing fault bandwidthsare identified three different kurtosis values are calculatedcorresponding to the three bearing defect frequencies (ieBPFO BPFI and BSF) After obtaining the kurtosis valuesfor the subband signals the wavelet kurtogram is generated(Figure 3) Figure 3(a) shows the frequency-scale paving ofthe proposed wavelet kurtogram while Figure 3(b) illustratesan example color kurtogram of the three bearing faultfrequencies (ie BPFO BPFI and BSF) which representsthe kurtosis values of all of the subbands

Finally for each kurtogram the subband signal withthe highest kurtosis value (ie the signal that has the mostdiscriminative fault features) is selected for extracting thebearing fault signatures In Figure 3(b) the selected subband

4 Shock and Vibration

12

14

18

116Δfk

Leve

ls

0

1

2

3

middot middot middot middot middot middot

0 18 1214 38

(a)

(b)

f

K0

K11

K12 K3

2 K32 K4

2

K83K7

3K63K5

3K43K3

3K23K1

3

K21

BPFI BPFO BSF

Leve

lk

0

1

2

3

4

5

Leve

lk

0

1

2

3

4

5Le

velk

0

1

2

3

4

5

Frequency (Hz)0 1 2 3 4 5

times104

Frequency (Hz)0 1 2 3 4 5

times104 Frequency (Hz)0 1 2 3 4 5

times104

07

065

06

055

05

16

155

15

145

14

135

13

16

15

1413

12

11

1

09

Wavelet kurtogram Wavelet kurtogram Wavelet kurtogram(Kmax = 07 level = 4 node = 14) (Kmax = 16 level = 5 node = 5) (Kmax = 17 level = 4 node = 14)

Figure 3The proposed wavelet kurtogram (a)The frequency-scale paving of the proposed wavelet kurtogram (b) An example of a proposedwavelet kurtogram

with the highest kurtosis value is highlighted using a dashedrectangle

Step 2 In this step 10 time domain (1198911 1198912 11989110) andthree frequency domain statistical features (11989111 11989112 11989113) areextracted from each of the selected subband signals as showninTables 1 and 2 respectively Furthermorewe calculate threeroot mean square (RMS) features (11989114ndash11989116) for the first threeharmonics of the corresponding defect frequencies in theenvelope spectrum of each of the selected subband signals asdescribed in Table 3This results in a feature pool that consistsof a total of119873119888 times119873119904 times119873119891 features where119873119888 is the number ofbearing fault classes119873119904 is the number of AE signals obtainedfor each fault type and119873119891 is the total number of features Inthis case119873119891 is 10 + 3+ 3= 16 and includes 10 time domain sta-tistical features three frequency domain statistical featuresand three envelope spectrum RMS features (calculated usingthe extractedwavelet kurtogram) for each of the three bearingdefect frequencies (ie BPFO BPFI and BSF)

23 Feature Selection In this paper we propose a featureanalysis method based on the linear discriminant analysis

(LDA) technique plus a vector median-based discriminantcriterion (VMDC) to find the most discriminative subsetof the extracted fault features for accurate fault diagnosisLDA is a supervised dimensionality reduction algorithmthat utilizes the class label information to find an opti-mal linear transformation matrix that projects the originalhigh-dimensional feature space onto the lower-dimensionalrepresentation while also preserving the information thatcan help discriminate among different classes Let 119883 =

1199091 1199092 119909119873 isin 119877119863times119873 be a dataset where 119863 is the original

dimensionality and 119873 is the number of samples in 119883 Eachsample 119909119894 belongs to a class 119888119894 = 1 2 119862 Let 119873119894 be thenumber of samples in class 119888119894 and let119873 be the total number ofsamples in all of the classesThen the intraclass scattermatrix119878119908 and the interclass scatter matrix 119878119887 can be evaluated with(4) and (5) respectively

119878119908 =

119862

sum

119894=1

sum

119909119896isin119862119894

(119909119896 minus 120583119894)119879(119909119896 minus 120583119894) (4)

119878119887 =

119862

sum

119894=1

(120583119894 minus 120583)119879(120583119894 minus 120583) (5)

Shock and Vibration 5

Table 1 Time domain statistical feature parameters

Parameter Definition

Root mean square (1198911) radic1

119873

119873

sum

119894=1

1199092

119894

Root mean square of the amplitude(1198912)

(1

119873

119873

sum

119894=1

radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Kurtosis (1198913)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

4

Skewness (1198914)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

3

Peak-to-peak (1198915) max (119909119894) minusmin (119909119894)

Crest factor (1198916)max (

10038161003816100381610038161199091198941003816100381610038161003816)

radic(1119873)sum119873

119894=11199092119894

Impulse factor (1198917)max (

10038161003816100381610038161199091198941003816100381610038161003816)

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Margin factor (1198918)max (

10038161003816100381610038161199091198941003816100381610038161003816)

((1119873)sum119873

119894=1radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Shape factor (1198919)radic(1119873)sum

119873

119894=11199092119894

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Kurtosis factor (11989110)(1119873)sum

119873

119894=1((119909119894 minus 119909) 120590)

4

((1119873)sum119873

119894=11199092119894)2

Table 2 Frequency domain statistical feature parameters

Parameter Definition

Frequency center (11989111)1

119873

119873

sum

119894=1

119891119894

Root mean square frequency (11989112) radic1

119873

119873

sum

119894=1

1198912

119894

Root variance frequency (11989113) radic1

119873

119873

sum

119894=1

(119891119894 minus 119883119891119888)2

Table 3 Envelope spectrum statistical feature parameters

Parameter Definition

RMS frequency of the first harmonic (11989114) radic1

(1198871 minus 1198861)

1198871

sum

119894=1198861

1198912

119894

RMS frequency of the second harmonic (11989115) radic1

(1198872 minus 1198862)

1198872

sum

119894=1198862

1198912

119894

RMS frequency of the third harmonic (11989116) radic1

(1198873 minus 1198863)

1198873

sum

119894=1198863

1198912

119894

Here 120583119894 = (1119873119894) sum119909119894isin119888119894119909119894 is the mean of the samples labelled

as class 119888119894 and 120583 = (1119873)sum119873

119894=1119909119894 is the mean of all of the

samples The LDA projects the space of the original variables

onto a (119862 minus 1)-dimensional space by maximizing the Fisherdiscriminant rule [18] which is defined as follows

119882lowast= argmax

119882119879119878119887119882

119882119879119878119908119882 (6)

This discriminant rule maximizes the ratio of inter-class separability to intraclass compactness by selecting areducednumber of themost discriminative components onlyHowever LDA-based feature analysis approaches are limitedin their ability to efficiently select the optimal number ofdiscriminative components to gain the highest classificationperformance In the existing literature there is no clearconsensus on the optimal number of LDA components thatyield the highest classification performance To address thisproblem we present a robust method based on the vectormedian approach to obtain the optimal number of LDA com-ponents that can maximize the classification performance Inorder to identify the vector median of each class this studyutilizes a cumulative distance criterion using the Euclideandistance The vector median VM119894 of class 119888119894 is defined as thedata point that yields the minimum accumulated distanceand is determined as follows

VM119894 = argmin119896isin119888119894

sum

119895isin119888119894 119895 =119896

10038171003817100381710038171003817119909119896 minus 119909119895

100381710038171003817100381710038172 (7)

Once the vectormedians of all classes are determined themodified intraclass compactness and interclass separabilityvalues are calculated using (8) and (9) respectively

119878119908 =1

119862

119862

sum

119894=1

1

119873119894

119873119894

sum

119895=1

10038171003817100381710038171003817VM119894 minus 119909119895

100381710038171003817100381710038172 (8)

119878119887 =1

119862

119862

sum

119894=1

argmin119895isin119862119895 =119894

10038171003817100381710038171003817VM119894 minus VM119895

100381710038171003817100381710038172 (9)

In (8) the intraclass compactness of a class is reflected by thedistance from its vectormedian to other samples in that classAlternatively in (9) the interclass separability of a class fromother classes is represented by the minimum distance of thevector median of that class to the vector medians of otherclassesThe effect of outliers in the feature space is minimizedby averaging these distance measurements which improvesthe discriminatory power of the proposed feature analysismethod The vector median-based discriminant criterionthat is used to select the optimal number of useful LDAcomponents is defined as follows

119870lowast= argmax

119878119887

119878119908

(10)

24 Fault Classification In this study a Naıve Bayes classifier[19] is used to classify various single and compound bearingfaults This classifier is selected due to its simplicity and highclassification performance at a relatively low computationalcost [19 20] The Naıve Bayes classifier has complexity119874(119873119889) where119873 is the total number of training samples and119889 is the number of conditional features Other classification

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 Shock and Vibration

kurtosis values from the envelope power spectrum of eachsubband signal at different levels of decomposition Thesubband signal that yields the highest spectral kurtosis valueis selected for extracting the features that are characteristicof the bearing fault conditions

In addition to feature extraction techniques feature anal-ysis methods have also been widely studied in machine faultdiagnosis in order to prevent the degradation of classificationperformance that is caused by redundant information in thefeature space [9ndash13] Dimensionality reduction techniqueshave been used to identify the features that effectivelyrepresent the high-dimensional data in a lower-dimensionalspace while retaining the intrinsic information of the bearingdefects these eventually lead to improvements in the classi-fication performance of the fault diagnosis system Amongvarious dimensionality reductionmethods principle compo-nent analysis (PCA) [14] independent component analysis(ICA) [15] and linear discriminant analysis (LDA) [16] arethe most popular methods that have been effectively utilizedin machinery fault diagnosis For instanceWidodo and Yang[11] applied the PCA technique to machine health prognos-tics to extract population characteristics from the availablecondition monitoring data Guo et al [12] investigated theperformance of an ICA algorithm in separating the envelopesof vibration signals to extract the weak impulsive featuresof incipient faults in rolling element bearings In their studylooking into fault diagnosis in ball bearings Harmouche et al[13] demonstrated the use of an LDA technique to effectivelydiscriminate the rather weak and otherwise difficult todetectidentify spectral features extracted from the envelopespectra of vibration signals The LDA feature space yieldsbetter separation between different classes of bearing faultsthan conventional feature analysismethods thereby resultingin improved classification performance PCA and ICA areunsupervised methods that ignore the label informationduring dimensionality reduction whereas LDA is a super-vised method that utilizes the class label information to findan optimal low-dimensional representation of the originalfeature set while also preserving discriminant informationbetween classes As a result LDA yields better classificationresults as compared to PCA and ICA [9 13 14] This paperpresents a new LDA-based feature analysis method thatuses a vector median-based discriminant criterion (VMDC)to characterize the intraclass compactness and interclassseparability of the feature space in order to select the mostdiscriminative subset of bearing fault features

This paper proposes a reliable multifault diagnosisscheme for rolling element bearings that combines animproved WPT-based kurtogram and the VMDC-basedfeature analysis methods The contributions discussed in thispaper can be summarized as follows

(1) An improved WPT-based kurtogram is proposed forextracting the most characteristic fault features fromnonstationary acoustic emission (AE) signals Thekurtogram is performed by computing the spectralkurtosis values for the envelope power spectrum ofeach subband signal at different levels of decompo-sition The subband signal that yields the highest

Naiumlve Bayes classifier

Unknown AE signals

Feature extraction

Feature selection

Fault classification

Waveletkurtogram

Bearing faults

Statistical parameters

Optimal features

Feature pool

Preprocessing ARprewhitening

Prewhitened signals

LDA VMDC

Figure 1 Flowchart of the proposed bearing fault diagnosismethodology

spectral kurtosis value is selected for extracting thefault features

(2) An efficient VMDC-based discriminative fault fea-ture analysis approach is proposed for selecting themost discriminative subset of fault features A vectormedian-based discriminant criterion is presented tominimize the intraclass compactness and maximizethe interclass separability of the feature space

(3) A comprehensive multiclass fault diagnosis method-ology for rolling element bearings is presented andits performance is validated using AE data for varioussingle and compound bearing defects acquired underdifferent simulated crack sizes and bearing rotationalspeeds

The remainder of the paper is structured as follows Sec-tion 2 describes the overall bearing fault diagnosis method-ology Section 3 introduces the self-designed fault simulator(including the data acquisition system and seeded bearingdefects for collecting fault signals) and Section 4 shows theexperimental results Finally Section 5 concludes this paper

2 Proposed Bearing FaultDiagnosis Methodology

The proposed comprehensive bearing fault diagnosis schemeconsists of four main processes including signal preprocess-ing feature extraction feature selection and fault classifica-tion Figure 1 illustrates the overall flowchart of the proposedmethodology

Shock and Vibration 3

21 Preprocessing The performance of wavelet kurtogramanalysis can be improved if the variations between the peaksand flanks of the spectral energy are minimized as shown inTable 6 this can be achieved by preprocessing the AE signalbefore feature extraction [17] In this study the prewhiteningtechnique is used to reduce the spectral energy variationsin the incoming AE fault signal To obtain the prewhitenedsignal an autoregressive (AR) model 119910(119899) is utilized whichis defined as follows

119910 (119899) =

119901

sum

119894=1

119886119894119909 (119894 + 119899) + 119890 (119899) (1)

where 119909(119899) is the incoming bearing signal 119886119894 are the ARcoefficients 119901 denotes the order of the AR model and 119890(119899) isthe residual signal representing a spectrum close to the whitenoise spectrum

22 Feature Extraction For the purpose of extracting thecharacteristic fault signatures from the AE signals this paperpresents a two-step feature extraction process that works asfollows

Step 1 In this step the proposed WPT-based kurtogrammethod is performed on the prewhitened AE signal to deter-mine its most informative subbandThe flowchart of the pro-posed WPT-based kurtogram is illustrated in Figure 2 andits details are provided below

First the prewhitened bearing signal is decomposed intoa series of subbands by performing the wavelet packet trans-form (WPT) with five decomposition levels (119899 = 5) using aDaubechies 2 (or db2) filter The five-level WPT decompo-sition results in a total of 63 subband signals The envelopespectrum of each subband signal is then calculated using thefast Fourier transform (FFT) to identify the characteristicbearing fault frequencies The envelope spectrum of an AEsignal obtained from a defective bearing is usually floodedwith the characteristic defect frequency and its harmonicsWe utilize kurtosis to measure the degree of protrusion ofthe envelope spectrum and then characterize the hiddenbearing defect signatures In order to do this effectively wefirst determine the bearing defect frequencies which includethe ball pass frequency of the bearing outer raceway (BPFO)the ball pass frequency of the bearing inner raceway (BPFI)the ball spin frequency of the bearing roller (BSF) and thefirst 119872 harmonics (119872 = 3 in this paper) of each of thesefrequencies These defect frequencies are defined as follows

BPFO =119873119903 sdot 119865119900

2(1 minus

119861119889

119875119889

cos120572)

BPFI =119873119903 sdot 119865119900

2(1 +

119861119889

119875119889

cos120572)

BSF =119875119889 sdot 119865119900

2 sdot 119861119889

(1 minus (119861119889

119875119889

cos120572)2

)

(2)

where 119873119903 denotes the number of cylindrical rollers 119865119900 isthe shaft speed 120572 is the contact angle and 119861119889 and 119875119889 are

Perform WPT on the signal

End

Generate the corresponding kurtograms based on the kurtosis values

For each kurtogram select the frequency band signal with the highest kurtosis

Calculate kurtosis of the bandwidths for each bearing fault characteristic frequency

Calculate the envelope spectrum of the decomposed frequency band signal

Start

Identify the bandwidths of the bearing fault characteristic frequencies and of their first M harmonics

Figure 2 Flowchart of the wavelet kurtogram algorithm

the roller and pitch diameters respectively Each defect-related bandwidth BW119894 ranges from 119886119894 to 119887119894 (119894 = 1 2 119872)which can be calculated as follows

119886119894 =

(119894 minus ER) lowast BPFO if BPFO

(119894 minus ER) lowast BPFI minus 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 minus ER) lowast BSF minus 2 lowast (1 + ER) lowast 119865119862 otherwise

119887119894 =

(119894 + ER) lowast BPFO if BPFO

(119894 + ER) lowast BPFI + 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 + ER) lowast BSF + 2 lowast (1 + ER) lowast 119865119862 otherwise

(3)

Here ER is the error rate of the bearing test rig and 119865119862

is the cage frequency Once the bearing fault bandwidthsare identified three different kurtosis values are calculatedcorresponding to the three bearing defect frequencies (ieBPFO BPFI and BSF) After obtaining the kurtosis valuesfor the subband signals the wavelet kurtogram is generated(Figure 3) Figure 3(a) shows the frequency-scale paving ofthe proposed wavelet kurtogram while Figure 3(b) illustratesan example color kurtogram of the three bearing faultfrequencies (ie BPFO BPFI and BSF) which representsthe kurtosis values of all of the subbands

Finally for each kurtogram the subband signal withthe highest kurtosis value (ie the signal that has the mostdiscriminative fault features) is selected for extracting thebearing fault signatures In Figure 3(b) the selected subband

4 Shock and Vibration

12

14

18

116Δfk

Leve

ls

0

1

2

3

middot middot middot middot middot middot

0 18 1214 38

(a)

(b)

f

K0

K11

K12 K3

2 K32 K4

2

K83K7

3K63K5

3K43K3

3K23K1

3

K21

BPFI BPFO BSF

Leve

lk

0

1

2

3

4

5

Leve

lk

0

1

2

3

4

5Le

velk

0

1

2

3

4

5

Frequency (Hz)0 1 2 3 4 5

times104

Frequency (Hz)0 1 2 3 4 5

times104 Frequency (Hz)0 1 2 3 4 5

times104

07

065

06

055

05

16

155

15

145

14

135

13

16

15

1413

12

11

1

09

Wavelet kurtogram Wavelet kurtogram Wavelet kurtogram(Kmax = 07 level = 4 node = 14) (Kmax = 16 level = 5 node = 5) (Kmax = 17 level = 4 node = 14)

Figure 3The proposed wavelet kurtogram (a)The frequency-scale paving of the proposed wavelet kurtogram (b) An example of a proposedwavelet kurtogram

with the highest kurtosis value is highlighted using a dashedrectangle

Step 2 In this step 10 time domain (1198911 1198912 11989110) andthree frequency domain statistical features (11989111 11989112 11989113) areextracted from each of the selected subband signals as showninTables 1 and 2 respectively Furthermorewe calculate threeroot mean square (RMS) features (11989114ndash11989116) for the first threeharmonics of the corresponding defect frequencies in theenvelope spectrum of each of the selected subband signals asdescribed in Table 3This results in a feature pool that consistsof a total of119873119888 times119873119904 times119873119891 features where119873119888 is the number ofbearing fault classes119873119904 is the number of AE signals obtainedfor each fault type and119873119891 is the total number of features Inthis case119873119891 is 10 + 3+ 3= 16 and includes 10 time domain sta-tistical features three frequency domain statistical featuresand three envelope spectrum RMS features (calculated usingthe extractedwavelet kurtogram) for each of the three bearingdefect frequencies (ie BPFO BPFI and BSF)

23 Feature Selection In this paper we propose a featureanalysis method based on the linear discriminant analysis

(LDA) technique plus a vector median-based discriminantcriterion (VMDC) to find the most discriminative subsetof the extracted fault features for accurate fault diagnosisLDA is a supervised dimensionality reduction algorithmthat utilizes the class label information to find an opti-mal linear transformation matrix that projects the originalhigh-dimensional feature space onto the lower-dimensionalrepresentation while also preserving the information thatcan help discriminate among different classes Let 119883 =

1199091 1199092 119909119873 isin 119877119863times119873 be a dataset where 119863 is the original

dimensionality and 119873 is the number of samples in 119883 Eachsample 119909119894 belongs to a class 119888119894 = 1 2 119862 Let 119873119894 be thenumber of samples in class 119888119894 and let119873 be the total number ofsamples in all of the classesThen the intraclass scattermatrix119878119908 and the interclass scatter matrix 119878119887 can be evaluated with(4) and (5) respectively

119878119908 =

119862

sum

119894=1

sum

119909119896isin119862119894

(119909119896 minus 120583119894)119879(119909119896 minus 120583119894) (4)

119878119887 =

119862

sum

119894=1

(120583119894 minus 120583)119879(120583119894 minus 120583) (5)

Shock and Vibration 5

Table 1 Time domain statistical feature parameters

Parameter Definition

Root mean square (1198911) radic1

119873

119873

sum

119894=1

1199092

119894

Root mean square of the amplitude(1198912)

(1

119873

119873

sum

119894=1

radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Kurtosis (1198913)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

4

Skewness (1198914)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

3

Peak-to-peak (1198915) max (119909119894) minusmin (119909119894)

Crest factor (1198916)max (

10038161003816100381610038161199091198941003816100381610038161003816)

radic(1119873)sum119873

119894=11199092119894

Impulse factor (1198917)max (

10038161003816100381610038161199091198941003816100381610038161003816)

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Margin factor (1198918)max (

10038161003816100381610038161199091198941003816100381610038161003816)

((1119873)sum119873

119894=1radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Shape factor (1198919)radic(1119873)sum

119873

119894=11199092119894

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Kurtosis factor (11989110)(1119873)sum

119873

119894=1((119909119894 minus 119909) 120590)

4

((1119873)sum119873

119894=11199092119894)2

Table 2 Frequency domain statistical feature parameters

Parameter Definition

Frequency center (11989111)1

119873

119873

sum

119894=1

119891119894

Root mean square frequency (11989112) radic1

119873

119873

sum

119894=1

1198912

119894

Root variance frequency (11989113) radic1

119873

119873

sum

119894=1

(119891119894 minus 119883119891119888)2

Table 3 Envelope spectrum statistical feature parameters

Parameter Definition

RMS frequency of the first harmonic (11989114) radic1

(1198871 minus 1198861)

1198871

sum

119894=1198861

1198912

119894

RMS frequency of the second harmonic (11989115) radic1

(1198872 minus 1198862)

1198872

sum

119894=1198862

1198912

119894

RMS frequency of the third harmonic (11989116) radic1

(1198873 minus 1198863)

1198873

sum

119894=1198863

1198912

119894

Here 120583119894 = (1119873119894) sum119909119894isin119888119894119909119894 is the mean of the samples labelled

as class 119888119894 and 120583 = (1119873)sum119873

119894=1119909119894 is the mean of all of the

samples The LDA projects the space of the original variables

onto a (119862 minus 1)-dimensional space by maximizing the Fisherdiscriminant rule [18] which is defined as follows

119882lowast= argmax

119882119879119878119887119882

119882119879119878119908119882 (6)

This discriminant rule maximizes the ratio of inter-class separability to intraclass compactness by selecting areducednumber of themost discriminative components onlyHowever LDA-based feature analysis approaches are limitedin their ability to efficiently select the optimal number ofdiscriminative components to gain the highest classificationperformance In the existing literature there is no clearconsensus on the optimal number of LDA components thatyield the highest classification performance To address thisproblem we present a robust method based on the vectormedian approach to obtain the optimal number of LDA com-ponents that can maximize the classification performance Inorder to identify the vector median of each class this studyutilizes a cumulative distance criterion using the Euclideandistance The vector median VM119894 of class 119888119894 is defined as thedata point that yields the minimum accumulated distanceand is determined as follows

VM119894 = argmin119896isin119888119894

sum

119895isin119888119894 119895 =119896

10038171003817100381710038171003817119909119896 minus 119909119895

100381710038171003817100381710038172 (7)

Once the vectormedians of all classes are determined themodified intraclass compactness and interclass separabilityvalues are calculated using (8) and (9) respectively

119878119908 =1

119862

119862

sum

119894=1

1

119873119894

119873119894

sum

119895=1

10038171003817100381710038171003817VM119894 minus 119909119895

100381710038171003817100381710038172 (8)

119878119887 =1

119862

119862

sum

119894=1

argmin119895isin119862119895 =119894

10038171003817100381710038171003817VM119894 minus VM119895

100381710038171003817100381710038172 (9)

In (8) the intraclass compactness of a class is reflected by thedistance from its vectormedian to other samples in that classAlternatively in (9) the interclass separability of a class fromother classes is represented by the minimum distance of thevector median of that class to the vector medians of otherclassesThe effect of outliers in the feature space is minimizedby averaging these distance measurements which improvesthe discriminatory power of the proposed feature analysismethod The vector median-based discriminant criterionthat is used to select the optimal number of useful LDAcomponents is defined as follows

119870lowast= argmax

119878119887

119878119908

(10)

24 Fault Classification In this study a Naıve Bayes classifier[19] is used to classify various single and compound bearingfaults This classifier is selected due to its simplicity and highclassification performance at a relatively low computationalcost [19 20] The Naıve Bayes classifier has complexity119874(119873119889) where119873 is the total number of training samples and119889 is the number of conditional features Other classification

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

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Shock and Vibration 3

21 Preprocessing The performance of wavelet kurtogramanalysis can be improved if the variations between the peaksand flanks of the spectral energy are minimized as shown inTable 6 this can be achieved by preprocessing the AE signalbefore feature extraction [17] In this study the prewhiteningtechnique is used to reduce the spectral energy variationsin the incoming AE fault signal To obtain the prewhitenedsignal an autoregressive (AR) model 119910(119899) is utilized whichis defined as follows

119910 (119899) =

119901

sum

119894=1

119886119894119909 (119894 + 119899) + 119890 (119899) (1)

where 119909(119899) is the incoming bearing signal 119886119894 are the ARcoefficients 119901 denotes the order of the AR model and 119890(119899) isthe residual signal representing a spectrum close to the whitenoise spectrum

22 Feature Extraction For the purpose of extracting thecharacteristic fault signatures from the AE signals this paperpresents a two-step feature extraction process that works asfollows

Step 1 In this step the proposed WPT-based kurtogrammethod is performed on the prewhitened AE signal to deter-mine its most informative subbandThe flowchart of the pro-posed WPT-based kurtogram is illustrated in Figure 2 andits details are provided below

First the prewhitened bearing signal is decomposed intoa series of subbands by performing the wavelet packet trans-form (WPT) with five decomposition levels (119899 = 5) using aDaubechies 2 (or db2) filter The five-level WPT decompo-sition results in a total of 63 subband signals The envelopespectrum of each subband signal is then calculated using thefast Fourier transform (FFT) to identify the characteristicbearing fault frequencies The envelope spectrum of an AEsignal obtained from a defective bearing is usually floodedwith the characteristic defect frequency and its harmonicsWe utilize kurtosis to measure the degree of protrusion ofthe envelope spectrum and then characterize the hiddenbearing defect signatures In order to do this effectively wefirst determine the bearing defect frequencies which includethe ball pass frequency of the bearing outer raceway (BPFO)the ball pass frequency of the bearing inner raceway (BPFI)the ball spin frequency of the bearing roller (BSF) and thefirst 119872 harmonics (119872 = 3 in this paper) of each of thesefrequencies These defect frequencies are defined as follows

BPFO =119873119903 sdot 119865119900

2(1 minus

119861119889

119875119889

cos120572)

BPFI =119873119903 sdot 119865119900

2(1 +

119861119889

119875119889

cos120572)

BSF =119875119889 sdot 119865119900

2 sdot 119861119889

(1 minus (119861119889

119875119889

cos120572)2

)

(2)

where 119873119903 denotes the number of cylindrical rollers 119865119900 isthe shaft speed 120572 is the contact angle and 119861119889 and 119875119889 are

Perform WPT on the signal

End

Generate the corresponding kurtograms based on the kurtosis values

For each kurtogram select the frequency band signal with the highest kurtosis

Calculate kurtosis of the bandwidths for each bearing fault characteristic frequency

Calculate the envelope spectrum of the decomposed frequency band signal

Start

Identify the bandwidths of the bearing fault characteristic frequencies and of their first M harmonics

Figure 2 Flowchart of the wavelet kurtogram algorithm

the roller and pitch diameters respectively Each defect-related bandwidth BW119894 ranges from 119886119894 to 119887119894 (119894 = 1 2 119872)which can be calculated as follows

119886119894 =

(119894 minus ER) lowast BPFO if BPFO

(119894 minus ER) lowast BPFI minus 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 minus ER) lowast BSF minus 2 lowast (1 + ER) lowast 119865119862 otherwise

119887119894 =

(119894 + ER) lowast BPFO if BPFO

(119894 + ER) lowast BPFI + 2 lowast (1 + ER) lowast 1198650 if BPFI

(119894 + ER) lowast BSF + 2 lowast (1 + ER) lowast 119865119862 otherwise

(3)

Here ER is the error rate of the bearing test rig and 119865119862

is the cage frequency Once the bearing fault bandwidthsare identified three different kurtosis values are calculatedcorresponding to the three bearing defect frequencies (ieBPFO BPFI and BSF) After obtaining the kurtosis valuesfor the subband signals the wavelet kurtogram is generated(Figure 3) Figure 3(a) shows the frequency-scale paving ofthe proposed wavelet kurtogram while Figure 3(b) illustratesan example color kurtogram of the three bearing faultfrequencies (ie BPFO BPFI and BSF) which representsthe kurtosis values of all of the subbands

Finally for each kurtogram the subband signal withthe highest kurtosis value (ie the signal that has the mostdiscriminative fault features) is selected for extracting thebearing fault signatures In Figure 3(b) the selected subband

4 Shock and Vibration

12

14

18

116Δfk

Leve

ls

0

1

2

3

middot middot middot middot middot middot

0 18 1214 38

(a)

(b)

f

K0

K11

K12 K3

2 K32 K4

2

K83K7

3K63K5

3K43K3

3K23K1

3

K21

BPFI BPFO BSF

Leve

lk

0

1

2

3

4

5

Leve

lk

0

1

2

3

4

5Le

velk

0

1

2

3

4

5

Frequency (Hz)0 1 2 3 4 5

times104

Frequency (Hz)0 1 2 3 4 5

times104 Frequency (Hz)0 1 2 3 4 5

times104

07

065

06

055

05

16

155

15

145

14

135

13

16

15

1413

12

11

1

09

Wavelet kurtogram Wavelet kurtogram Wavelet kurtogram(Kmax = 07 level = 4 node = 14) (Kmax = 16 level = 5 node = 5) (Kmax = 17 level = 4 node = 14)

Figure 3The proposed wavelet kurtogram (a)The frequency-scale paving of the proposed wavelet kurtogram (b) An example of a proposedwavelet kurtogram

with the highest kurtosis value is highlighted using a dashedrectangle

Step 2 In this step 10 time domain (1198911 1198912 11989110) andthree frequency domain statistical features (11989111 11989112 11989113) areextracted from each of the selected subband signals as showninTables 1 and 2 respectively Furthermorewe calculate threeroot mean square (RMS) features (11989114ndash11989116) for the first threeharmonics of the corresponding defect frequencies in theenvelope spectrum of each of the selected subband signals asdescribed in Table 3This results in a feature pool that consistsof a total of119873119888 times119873119904 times119873119891 features where119873119888 is the number ofbearing fault classes119873119904 is the number of AE signals obtainedfor each fault type and119873119891 is the total number of features Inthis case119873119891 is 10 + 3+ 3= 16 and includes 10 time domain sta-tistical features three frequency domain statistical featuresand three envelope spectrum RMS features (calculated usingthe extractedwavelet kurtogram) for each of the three bearingdefect frequencies (ie BPFO BPFI and BSF)

23 Feature Selection In this paper we propose a featureanalysis method based on the linear discriminant analysis

(LDA) technique plus a vector median-based discriminantcriterion (VMDC) to find the most discriminative subsetof the extracted fault features for accurate fault diagnosisLDA is a supervised dimensionality reduction algorithmthat utilizes the class label information to find an opti-mal linear transformation matrix that projects the originalhigh-dimensional feature space onto the lower-dimensionalrepresentation while also preserving the information thatcan help discriminate among different classes Let 119883 =

1199091 1199092 119909119873 isin 119877119863times119873 be a dataset where 119863 is the original

dimensionality and 119873 is the number of samples in 119883 Eachsample 119909119894 belongs to a class 119888119894 = 1 2 119862 Let 119873119894 be thenumber of samples in class 119888119894 and let119873 be the total number ofsamples in all of the classesThen the intraclass scattermatrix119878119908 and the interclass scatter matrix 119878119887 can be evaluated with(4) and (5) respectively

119878119908 =

119862

sum

119894=1

sum

119909119896isin119862119894

(119909119896 minus 120583119894)119879(119909119896 minus 120583119894) (4)

119878119887 =

119862

sum

119894=1

(120583119894 minus 120583)119879(120583119894 minus 120583) (5)

Shock and Vibration 5

Table 1 Time domain statistical feature parameters

Parameter Definition

Root mean square (1198911) radic1

119873

119873

sum

119894=1

1199092

119894

Root mean square of the amplitude(1198912)

(1

119873

119873

sum

119894=1

radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Kurtosis (1198913)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

4

Skewness (1198914)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

3

Peak-to-peak (1198915) max (119909119894) minusmin (119909119894)

Crest factor (1198916)max (

10038161003816100381610038161199091198941003816100381610038161003816)

radic(1119873)sum119873

119894=11199092119894

Impulse factor (1198917)max (

10038161003816100381610038161199091198941003816100381610038161003816)

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Margin factor (1198918)max (

10038161003816100381610038161199091198941003816100381610038161003816)

((1119873)sum119873

119894=1radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Shape factor (1198919)radic(1119873)sum

119873

119894=11199092119894

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Kurtosis factor (11989110)(1119873)sum

119873

119894=1((119909119894 minus 119909) 120590)

4

((1119873)sum119873

119894=11199092119894)2

Table 2 Frequency domain statistical feature parameters

Parameter Definition

Frequency center (11989111)1

119873

119873

sum

119894=1

119891119894

Root mean square frequency (11989112) radic1

119873

119873

sum

119894=1

1198912

119894

Root variance frequency (11989113) radic1

119873

119873

sum

119894=1

(119891119894 minus 119883119891119888)2

Table 3 Envelope spectrum statistical feature parameters

Parameter Definition

RMS frequency of the first harmonic (11989114) radic1

(1198871 minus 1198861)

1198871

sum

119894=1198861

1198912

119894

RMS frequency of the second harmonic (11989115) radic1

(1198872 minus 1198862)

1198872

sum

119894=1198862

1198912

119894

RMS frequency of the third harmonic (11989116) radic1

(1198873 minus 1198863)

1198873

sum

119894=1198863

1198912

119894

Here 120583119894 = (1119873119894) sum119909119894isin119888119894119909119894 is the mean of the samples labelled

as class 119888119894 and 120583 = (1119873)sum119873

119894=1119909119894 is the mean of all of the

samples The LDA projects the space of the original variables

onto a (119862 minus 1)-dimensional space by maximizing the Fisherdiscriminant rule [18] which is defined as follows

119882lowast= argmax

119882119879119878119887119882

119882119879119878119908119882 (6)

This discriminant rule maximizes the ratio of inter-class separability to intraclass compactness by selecting areducednumber of themost discriminative components onlyHowever LDA-based feature analysis approaches are limitedin their ability to efficiently select the optimal number ofdiscriminative components to gain the highest classificationperformance In the existing literature there is no clearconsensus on the optimal number of LDA components thatyield the highest classification performance To address thisproblem we present a robust method based on the vectormedian approach to obtain the optimal number of LDA com-ponents that can maximize the classification performance Inorder to identify the vector median of each class this studyutilizes a cumulative distance criterion using the Euclideandistance The vector median VM119894 of class 119888119894 is defined as thedata point that yields the minimum accumulated distanceand is determined as follows

VM119894 = argmin119896isin119888119894

sum

119895isin119888119894 119895 =119896

10038171003817100381710038171003817119909119896 minus 119909119895

100381710038171003817100381710038172 (7)

Once the vectormedians of all classes are determined themodified intraclass compactness and interclass separabilityvalues are calculated using (8) and (9) respectively

119878119908 =1

119862

119862

sum

119894=1

1

119873119894

119873119894

sum

119895=1

10038171003817100381710038171003817VM119894 minus 119909119895

100381710038171003817100381710038172 (8)

119878119887 =1

119862

119862

sum

119894=1

argmin119895isin119862119895 =119894

10038171003817100381710038171003817VM119894 minus VM119895

100381710038171003817100381710038172 (9)

In (8) the intraclass compactness of a class is reflected by thedistance from its vectormedian to other samples in that classAlternatively in (9) the interclass separability of a class fromother classes is represented by the minimum distance of thevector median of that class to the vector medians of otherclassesThe effect of outliers in the feature space is minimizedby averaging these distance measurements which improvesthe discriminatory power of the proposed feature analysismethod The vector median-based discriminant criterionthat is used to select the optimal number of useful LDAcomponents is defined as follows

119870lowast= argmax

119878119887

119878119908

(10)

24 Fault Classification In this study a Naıve Bayes classifier[19] is used to classify various single and compound bearingfaults This classifier is selected due to its simplicity and highclassification performance at a relatively low computationalcost [19 20] The Naıve Bayes classifier has complexity119874(119873119889) where119873 is the total number of training samples and119889 is the number of conditional features Other classification

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Shock and Vibration

12

14

18

116Δfk

Leve

ls

0

1

2

3

middot middot middot middot middot middot

0 18 1214 38

(a)

(b)

f

K0

K11

K12 K3

2 K32 K4

2

K83K7

3K63K5

3K43K3

3K23K1

3

K21

BPFI BPFO BSF

Leve

lk

0

1

2

3

4

5

Leve

lk

0

1

2

3

4

5Le

velk

0

1

2

3

4

5

Frequency (Hz)0 1 2 3 4 5

times104

Frequency (Hz)0 1 2 3 4 5

times104 Frequency (Hz)0 1 2 3 4 5

times104

07

065

06

055

05

16

155

15

145

14

135

13

16

15

1413

12

11

1

09

Wavelet kurtogram Wavelet kurtogram Wavelet kurtogram(Kmax = 07 level = 4 node = 14) (Kmax = 16 level = 5 node = 5) (Kmax = 17 level = 4 node = 14)

Figure 3The proposed wavelet kurtogram (a)The frequency-scale paving of the proposed wavelet kurtogram (b) An example of a proposedwavelet kurtogram

with the highest kurtosis value is highlighted using a dashedrectangle

Step 2 In this step 10 time domain (1198911 1198912 11989110) andthree frequency domain statistical features (11989111 11989112 11989113) areextracted from each of the selected subband signals as showninTables 1 and 2 respectively Furthermorewe calculate threeroot mean square (RMS) features (11989114ndash11989116) for the first threeharmonics of the corresponding defect frequencies in theenvelope spectrum of each of the selected subband signals asdescribed in Table 3This results in a feature pool that consistsof a total of119873119888 times119873119904 times119873119891 features where119873119888 is the number ofbearing fault classes119873119904 is the number of AE signals obtainedfor each fault type and119873119891 is the total number of features Inthis case119873119891 is 10 + 3+ 3= 16 and includes 10 time domain sta-tistical features three frequency domain statistical featuresand three envelope spectrum RMS features (calculated usingthe extractedwavelet kurtogram) for each of the three bearingdefect frequencies (ie BPFO BPFI and BSF)

23 Feature Selection In this paper we propose a featureanalysis method based on the linear discriminant analysis

(LDA) technique plus a vector median-based discriminantcriterion (VMDC) to find the most discriminative subsetof the extracted fault features for accurate fault diagnosisLDA is a supervised dimensionality reduction algorithmthat utilizes the class label information to find an opti-mal linear transformation matrix that projects the originalhigh-dimensional feature space onto the lower-dimensionalrepresentation while also preserving the information thatcan help discriminate among different classes Let 119883 =

1199091 1199092 119909119873 isin 119877119863times119873 be a dataset where 119863 is the original

dimensionality and 119873 is the number of samples in 119883 Eachsample 119909119894 belongs to a class 119888119894 = 1 2 119862 Let 119873119894 be thenumber of samples in class 119888119894 and let119873 be the total number ofsamples in all of the classesThen the intraclass scattermatrix119878119908 and the interclass scatter matrix 119878119887 can be evaluated with(4) and (5) respectively

119878119908 =

119862

sum

119894=1

sum

119909119896isin119862119894

(119909119896 minus 120583119894)119879(119909119896 minus 120583119894) (4)

119878119887 =

119862

sum

119894=1

(120583119894 minus 120583)119879(120583119894 minus 120583) (5)

Shock and Vibration 5

Table 1 Time domain statistical feature parameters

Parameter Definition

Root mean square (1198911) radic1

119873

119873

sum

119894=1

1199092

119894

Root mean square of the amplitude(1198912)

(1

119873

119873

sum

119894=1

radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Kurtosis (1198913)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

4

Skewness (1198914)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

3

Peak-to-peak (1198915) max (119909119894) minusmin (119909119894)

Crest factor (1198916)max (

10038161003816100381610038161199091198941003816100381610038161003816)

radic(1119873)sum119873

119894=11199092119894

Impulse factor (1198917)max (

10038161003816100381610038161199091198941003816100381610038161003816)

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Margin factor (1198918)max (

10038161003816100381610038161199091198941003816100381610038161003816)

((1119873)sum119873

119894=1radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Shape factor (1198919)radic(1119873)sum

119873

119894=11199092119894

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Kurtosis factor (11989110)(1119873)sum

119873

119894=1((119909119894 minus 119909) 120590)

4

((1119873)sum119873

119894=11199092119894)2

Table 2 Frequency domain statistical feature parameters

Parameter Definition

Frequency center (11989111)1

119873

119873

sum

119894=1

119891119894

Root mean square frequency (11989112) radic1

119873

119873

sum

119894=1

1198912

119894

Root variance frequency (11989113) radic1

119873

119873

sum

119894=1

(119891119894 minus 119883119891119888)2

Table 3 Envelope spectrum statistical feature parameters

Parameter Definition

RMS frequency of the first harmonic (11989114) radic1

(1198871 minus 1198861)

1198871

sum

119894=1198861

1198912

119894

RMS frequency of the second harmonic (11989115) radic1

(1198872 minus 1198862)

1198872

sum

119894=1198862

1198912

119894

RMS frequency of the third harmonic (11989116) radic1

(1198873 minus 1198863)

1198873

sum

119894=1198863

1198912

119894

Here 120583119894 = (1119873119894) sum119909119894isin119888119894119909119894 is the mean of the samples labelled

as class 119888119894 and 120583 = (1119873)sum119873

119894=1119909119894 is the mean of all of the

samples The LDA projects the space of the original variables

onto a (119862 minus 1)-dimensional space by maximizing the Fisherdiscriminant rule [18] which is defined as follows

119882lowast= argmax

119882119879119878119887119882

119882119879119878119908119882 (6)

This discriminant rule maximizes the ratio of inter-class separability to intraclass compactness by selecting areducednumber of themost discriminative components onlyHowever LDA-based feature analysis approaches are limitedin their ability to efficiently select the optimal number ofdiscriminative components to gain the highest classificationperformance In the existing literature there is no clearconsensus on the optimal number of LDA components thatyield the highest classification performance To address thisproblem we present a robust method based on the vectormedian approach to obtain the optimal number of LDA com-ponents that can maximize the classification performance Inorder to identify the vector median of each class this studyutilizes a cumulative distance criterion using the Euclideandistance The vector median VM119894 of class 119888119894 is defined as thedata point that yields the minimum accumulated distanceand is determined as follows

VM119894 = argmin119896isin119888119894

sum

119895isin119888119894 119895 =119896

10038171003817100381710038171003817119909119896 minus 119909119895

100381710038171003817100381710038172 (7)

Once the vectormedians of all classes are determined themodified intraclass compactness and interclass separabilityvalues are calculated using (8) and (9) respectively

119878119908 =1

119862

119862

sum

119894=1

1

119873119894

119873119894

sum

119895=1

10038171003817100381710038171003817VM119894 minus 119909119895

100381710038171003817100381710038172 (8)

119878119887 =1

119862

119862

sum

119894=1

argmin119895isin119862119895 =119894

10038171003817100381710038171003817VM119894 minus VM119895

100381710038171003817100381710038172 (9)

In (8) the intraclass compactness of a class is reflected by thedistance from its vectormedian to other samples in that classAlternatively in (9) the interclass separability of a class fromother classes is represented by the minimum distance of thevector median of that class to the vector medians of otherclassesThe effect of outliers in the feature space is minimizedby averaging these distance measurements which improvesthe discriminatory power of the proposed feature analysismethod The vector median-based discriminant criterionthat is used to select the optimal number of useful LDAcomponents is defined as follows

119870lowast= argmax

119878119887

119878119908

(10)

24 Fault Classification In this study a Naıve Bayes classifier[19] is used to classify various single and compound bearingfaults This classifier is selected due to its simplicity and highclassification performance at a relatively low computationalcost [19 20] The Naıve Bayes classifier has complexity119874(119873119889) where119873 is the total number of training samples and119889 is the number of conditional features Other classification

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Shock and Vibration 5

Table 1 Time domain statistical feature parameters

Parameter Definition

Root mean square (1198911) radic1

119873

119873

sum

119894=1

1199092

119894

Root mean square of the amplitude(1198912)

(1

119873

119873

sum

119894=1

radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Kurtosis (1198913)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

4

Skewness (1198914)1

119873

119873

sum

119894=1

(119909119894 minus 119909

120590)

3

Peak-to-peak (1198915) max (119909119894) minusmin (119909119894)

Crest factor (1198916)max (

10038161003816100381610038161199091198941003816100381610038161003816)

radic(1119873)sum119873

119894=11199092119894

Impulse factor (1198917)max (

10038161003816100381610038161199091198941003816100381610038161003816)

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Margin factor (1198918)max (

10038161003816100381610038161199091198941003816100381610038161003816)

((1119873)sum119873

119894=1radic1003816100381610038161003816119909119894

1003816100381610038161003816)

2

Shape factor (1198919)radic(1119873)sum

119873

119894=11199092119894

(1119873)sum119873

119894=1

10038161003816100381610038161199091198941003816100381610038161003816

Kurtosis factor (11989110)(1119873)sum

119873

119894=1((119909119894 minus 119909) 120590)

4

((1119873)sum119873

119894=11199092119894)2

Table 2 Frequency domain statistical feature parameters

Parameter Definition

Frequency center (11989111)1

119873

119873

sum

119894=1

119891119894

Root mean square frequency (11989112) radic1

119873

119873

sum

119894=1

1198912

119894

Root variance frequency (11989113) radic1

119873

119873

sum

119894=1

(119891119894 minus 119883119891119888)2

Table 3 Envelope spectrum statistical feature parameters

Parameter Definition

RMS frequency of the first harmonic (11989114) radic1

(1198871 minus 1198861)

1198871

sum

119894=1198861

1198912

119894

RMS frequency of the second harmonic (11989115) radic1

(1198872 minus 1198862)

1198872

sum

119894=1198862

1198912

119894

RMS frequency of the third harmonic (11989116) radic1

(1198873 minus 1198863)

1198873

sum

119894=1198863

1198912

119894

Here 120583119894 = (1119873119894) sum119909119894isin119888119894119909119894 is the mean of the samples labelled

as class 119888119894 and 120583 = (1119873)sum119873

119894=1119909119894 is the mean of all of the

samples The LDA projects the space of the original variables

onto a (119862 minus 1)-dimensional space by maximizing the Fisherdiscriminant rule [18] which is defined as follows

119882lowast= argmax

119882119879119878119887119882

119882119879119878119908119882 (6)

This discriminant rule maximizes the ratio of inter-class separability to intraclass compactness by selecting areducednumber of themost discriminative components onlyHowever LDA-based feature analysis approaches are limitedin their ability to efficiently select the optimal number ofdiscriminative components to gain the highest classificationperformance In the existing literature there is no clearconsensus on the optimal number of LDA components thatyield the highest classification performance To address thisproblem we present a robust method based on the vectormedian approach to obtain the optimal number of LDA com-ponents that can maximize the classification performance Inorder to identify the vector median of each class this studyutilizes a cumulative distance criterion using the Euclideandistance The vector median VM119894 of class 119888119894 is defined as thedata point that yields the minimum accumulated distanceand is determined as follows

VM119894 = argmin119896isin119888119894

sum

119895isin119888119894 119895 =119896

10038171003817100381710038171003817119909119896 minus 119909119895

100381710038171003817100381710038172 (7)

Once the vectormedians of all classes are determined themodified intraclass compactness and interclass separabilityvalues are calculated using (8) and (9) respectively

119878119908 =1

119862

119862

sum

119894=1

1

119873119894

119873119894

sum

119895=1

10038171003817100381710038171003817VM119894 minus 119909119895

100381710038171003817100381710038172 (8)

119878119887 =1

119862

119862

sum

119894=1

argmin119895isin119862119895 =119894

10038171003817100381710038171003817VM119894 minus VM119895

100381710038171003817100381710038172 (9)

In (8) the intraclass compactness of a class is reflected by thedistance from its vectormedian to other samples in that classAlternatively in (9) the interclass separability of a class fromother classes is represented by the minimum distance of thevector median of that class to the vector medians of otherclassesThe effect of outliers in the feature space is minimizedby averaging these distance measurements which improvesthe discriminatory power of the proposed feature analysismethod The vector median-based discriminant criterionthat is used to select the optimal number of useful LDAcomponents is defined as follows

119870lowast= argmax

119878119887

119878119908

(10)

24 Fault Classification In this study a Naıve Bayes classifier[19] is used to classify various single and compound bearingfaults This classifier is selected due to its simplicity and highclassification performance at a relatively low computationalcost [19 20] The Naıve Bayes classifier has complexity119874(119873119889) where119873 is the total number of training samples and119889 is the number of conditional features Other classification

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

Adjustable bladesA cylindrical roller bearing

PCI-2 based AE system

AE sensors

Figure 4 Experimental test rig for fault diagnosis of rolling element bearings [10]

algorithms such as KNN ANN and SVM have complexities119874(1198732) 119874(119873

2) and 119874(119873

3) respectively [20] Furthermore

the Naıve Bayes classifier is adaptive in nature and doesnot require any fixed parameters (unlike other classificationalgorithms)

In this study in order to evaluate the generalized classifi-cation performance of the proposed comprehensive bearingfault diagnosis method 119896-fold cross validation (119896-cv) [21] isemployed In 119896-cv the feature pool is randomly partitionedinto 119896 mutual subsets (119896 = 3 in this study) Then at the119894th iteration of 119896-cv one of the subsets is used as the testingdataset and the other (119896 minus 1) subsets are employed to trainthe Naıve Bayes classifier The classification performance isaveraged over 119896 trials of 119896-cvThe advantage of this techniqueis that no matter how we divide the data every data sampleis in the testing set once and is included in the trainingset (119896 minus 1) times Thus variance in the classification resultsis minimized To validate the classification performanceof the proposed method this paper utilizes the averageclassification accuracy (ACA) and the true positive rate (TPR)as performance measures These are defined in (11) and (12)respectively

ACA =1

119896

119896

sum

119894=1

1

119873

119862

sum

119895=1

119873119894119895

TP times 100 () (11)

TPR119895 =1

119896

119896

sum

119894=1

119873119894119895

TP

119873119894119895

TP + 119873119894119895

FN

times 100 () (12)

where 119896 is the number of cross validation folds and 119873119894119895

TP and119873119894119895

FN are the number of true positives and false negatives ofclass 119888119895 resulting in the 119894th iteration of 119896-cv respectively Inaddition the number of true positives is defined as the totalnumber of samples in class 119888119895 that are accurately classified as

class 119888119895 Alternatively the number of false negatives indicatesthe number of samples in class 119888119895 that are not classified as 119888119895

3 Experimental Setup

In this study we used an experimental test rig developedby Intelligence Dynamics Lab (Gyeongsang National Uni-versity Korea) to validate the performance of the proposedfault diagnosis methodology as shown in Figure 4 Anacoustic emission (AE) sensor (WS120572 type from PhysicalAcoustic Cooperation) was employed to capture continuousAE signals Table 3 describes the specifications of the dataacquisition system used in this study

The bearings used in this study were cylindrical rollingelement type (FAG NJ206-3-TVP2) These bearings wereengrained with different bearing defects which are shownin Figure 5 and listed as follows bearing-crack-on-outer-raceway (BCO) bearing-crack-on-inner-raceway (BCI) bear-ing-crack-on-roller (BCR) bearing-crack-on-outer-and-inner-raceways (BCOI) bearing-crack-on-outer-raceway-and-roller (BCOR) bearing-crack-on-inner-race-and-roller(BCIR) and bearing-crack-on-outer-and-inner-raceways-and-roller (BCOIR) A healthy or defect-free bearing (DFB)was used as a reference for baseline measurements In totaleight types of bearing fault signals including a normaldefect-free bearing (as a baseline) were acquired underdifferent rotational speeds (300 350 400 450 and 500 rpm)A total of 360 AE fault signals each 10 seconds in durationwere collected at a sampling rate of 250KHz for each bearingdefect in this study

4 Experimental Results

41 Data Preprocessing In this subsection we investigateand justify the preprocessing of the AE fault signals to

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Shock and Vibration 7

(a) (b)

(c) (d)

(e) (f)

(g)

Figure 5 Single and multiple-combined bearing defects (a) BCO (b) BCI (c) BCR (d) BCOI (e) BCOR (f) BCIR and (g) BCOIR

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

minus2 minus1 0 1 2minus0002

00002

Com

pone

nt n

umbe

r 7

Component number 1minus0020002004

minus002

0002

Com

pone

nt nu

mbe

r 5

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 2

minus4

minus2

0

2

4

6

Com

pone

nt n

umbe

r 2

Original signal (3mm-500 rpm) Original signal (3mm-300 rpm)

times10minus3

times10minus3

(a)

minus0050005

minus002

0002

Compo

nent

numbe

r 5

Component number 1minus002 0 002

minus002

0002

Com

pone

nt n

umbe

r 7

Component number 1

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 2

minus002

minus001

0

001

002

003

Com

pone

nt n

umbe

r 2

Prewhitened signal (3mm-300 rpm)Prewhitened signal (3mm-500 rpm)

(b)

Figure 6 Feature distribution spaces with a bearing crack size of 3mm (a) Before prewhitening and (b) after prewhitening

improve the classification performance of our methodologyAs mentioned earlier a total of eight single and compoundbearing defects were investigated in this study Figures 6and 7 show the feature distribution of the optimal LDAdiscriminant components for four datasets These datasetswere acquired at two different rotational speeds (ie 500 rpmand 300 rpm) and for two different bearing crack sizes(ie 3mm and 12mm) From Figure 6 it is clear thatthe fault features are not well separated and discriminationbetween different classes is poor without preprocessing Forinstance the class clusters of the 3mm crack length and300 rpm rotational speed datasets are heavily overlapped

which leads to higher error rate in classification Converselypreprocessing the original signals to obtain the prewhitenedsignals reduces overlapping between clusters and improvesseparation between their boundaries

Likewise Figure 7 shows that the boundaries betweensome class clusters of the original signals are blurred andunclear whereas the prewhitened signals have clearer andmore distinct boundaries These results strongly suggest thatprewhitened signals are able to strongly project the discrim-inative information that is hidden in the bearing signals Thevariation between the peaks and flanks of the spectral energyin spectral kurtosis analysis is one reason why each class of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus002 0 002 004minus008

0006

Compo

nent

num

ber 2

Component number 1minus002 0 002

minus0050

005

Compon

ent n

umber 2

Component number 1

minus0015

minus001

minus0005

0

0005

001

Com

pone

nt n

umbe

r 3Original signal (12mm-300 rpm)Original signal (12mm-500 rpm)

minus002

minus001

0

001

002

Com

pone

nt n

umbe

r 3(a)

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

DFBBCIBCOBCR

BCOIBCORBCIRBCOIR

minus005 0 005minus01

001

Compon

ent n

umber 2

Component number 1

minus004 minus002 0 002minus004

0004

Component number 2

Component number 1

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

minus004

minus002

0

002

004

Com

pone

nt n

umbe

r 3

Prewhitened signal (12mm-300 rpm)Prewhitened signal (12mm-500 rpm)

(b)

Figure 7 Feature distribution spaces with a bearing crack size of 12mm (a) Before prewhitening and (b) after prewhitening

the original signals cannot be clustered accurately Thereforea prewhitening process is required to improve separationbetween different clusters which makes classification easierand more accurate even with a Naıve Bayes classifier

42 Proposed VMDC-Based Feature Analysis Method Inorder to validate the effectiveness of the proposed featureanalysis method this study compares the feature selectionperformance (in terms of the classification accuracy) of theproposed method and the original LDA for 10 differentdatasets as shown in Figures 8 and 9 The vertical axis

represents the average classification accuracy calculated forthe classification results of different fault types through 119896

trials of 119896-cv and the horizontal axis represents the numberof LDA discriminant components that are selected There isno general consensus about the appropriate number of LDAcomponents that always guarantees the highest classificationaccuracy As evident in Figures 8 and 9 the LDA methodachieves its highest classification accuracy when the numberof LDA discriminant components reaches seven Neverthe-less there are some exceptions For example in Figure 8 (forthe dataset of a 3mm length crack and a rotational speed of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

3mm-450 rpm3mm-400 rpm

3mm-350 rpm3mm-300 rpm

3mm-500 rpm

Figure 8 Performance of the proposed feature analysis at a bearing crack size of 3mm

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

LDAProposed

LDAProposed

LDAProposed

LDAProposed

LDAProposed

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120Cl

assifi

catio

n ac

cura

cy (

)

2 3 4 5 6 71Number of components

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

12mm-500 rpm

12mm-450 rpm12mm-400 rpm

12mm-350 rpm12mm-300 rpm

0

20

40

60

80

100

120

Clas

sifica

tion

accu

racy

()

2 3 4 5 6 71Number of components

Figure 9 Performance of the proposed feature analysis at a bearing crack size of 12mm

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

Table 4 Specifications of the data acquisition system

PCI-2 based AE system(i) ADC 18-bit 40MSs per channel maximum(ii) Frequency response 1 kHzndash3MHz (at minus3 dB points)(iii) Sample rate 100 kSs 200 kSs 500 kSs 1MSs 2MSs 5MSs 10MSs 20MSs and40MSs are selectable

WS120572 sensor(i) Peak sensitivity (V120583bar) minus62 dB(ii) Operating frequency range 100ndash900 kHz(iii) Resonant frequency 650 kHz

kSs kSamples per second MSs MSamples per second

Table 5 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 3mm (unit )

Shaft speed TPR per bearing fault condition under 3mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 4000 6222 6222 6667 5333 6222 6667 7556 6111350 RPM 5778 5556 2889 9111 4444 6889 3111 5556 5417400 RPM 6667 7111 1556 8667 7556 5111 9778 6000 6556450 RPM 8667 8667 2667 9111 3333 7556 9556 8000 7194500 RPM 8222 8222 3333 9111 4889 7111 9333 4667 6861

ICA

300RPM 4889 6000 6222 7111 4000 5778 7111 7778 6111350 RPM 4222 5111 1333 8667 3556 7333 5778 4000 5000400 RPM 8889 8000 4222 8000 6667 3556 10000 6222 6944450 RPM 8889 8222 2889 8889 5333 8222 9556 7333 7417500 RPM 8889 8444 3556 9111 3111 7556 9333 4444 6806

LDA

300RPM 5333 9333 7333 10000 7778 8444 8222 7778 8028350 RPM 8222 9111 7111 8667 7778 8667 8000 8889 8306400 RPM 9333 9111 5778 9333 9111 7778 9778 8000 8528450 RPM 8889 9111 7778 10000 8667 9556 10000 7111 8889500 RPM 8889 9778 6889 9111 7333 8667 10000 8000 8583

Proposed

300 RPM 5333 8000 6222 10000 7556 8000 8222 8000 7667350 RPM 8000 8889 7333 8889 8000 8667 8222 9111 8389400 RPM 9111 9111 6000 9333 9333 8222 10000 8222 8667450 RPM 8889 9778 8667 9778 8889 9778 9556 8444 9222500 RPM 8889 9778 6444 9111 7556 9111 10000 8000 8611

450 rpm) the highest accuracy that can be achieved is 9167(with six LDA components) the highest accuracy obtainedwith seven LDA components is only 9083 Thus thenumber of LDA components that can achieve the maximumclassification accuracy must be determined empirically foreach study On the contrary the proposed feature analysisapproach always shows better average classification accura-cies when compared with the original LDA algorithm Forinstance in Figure 9 (for the dataset of a 12mm lengthcrack and a rotational speed of 300 rpm) the proposedmethod yields a classification accuracy of up to 928clearly outperforming the LDA method with any numberof components This can be explained by the fact that ourproposed method utilizes the vector-median discriminantcriterion which can adaptively select the optimal numberof LDA components to maximize the ratio of interclassseparability and intraclass compactness thereby achievingthe maximum discriminatory power in a low-dimensionalfeature space This enables the proposed approach to alwaysachieve the best classification performance The analysis of

these results highlights themain contributions of this study inanalyzing and selecting the optimal features from the originalfeature pool to achieve superior classification performance ascompared to conventional feature analysis algorithms Usingthe LDAmethod the number of LDA components that yieldthe best classification results must be determined empiricallyon a dataset to dataset basis whereas the proposed VMDC-based approach does this adaptively

43 Classification Performance In this section we comparethe classification performance of the proposed methodologywith other state-of-the-art feature analysis approaches (iePCA ICA and LDA) The optimal number of componentsfor PCA ICA and LDA was determined by utilizing thetraining set of 119896-cv fold at each iteration and finding thenumber of components that yielded the highest accuracy foreach of these methods The final classification results whichhave been calculated through 119896 folds of 119896-cv are summarizedin Tables 4 and 5 We used two evaluation indexes the truepositive rate (TPR) and the average classification accuracy

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

Table 6 Performance comparison between conventional feature analysis approaches and the proposed feature analysis method in terms ofthe average classification accuracy and the true positive rate at a bearing crack size of 12mm (unit )

Shaft speed TPR per bearing fault condition under 12mm crack size ACADFB BCI BCO BCR BCOI BCOR BCIR BCOIR

PCA

300RPM 8444 7556 6444 6667 8667 9556 7111 7556 7750350 RPM 9556 5333 7556 7111 7778 8889 8000 9556 7972400 RPM 9333 7333 8667 8222 7556 9111 9556 9778 8694450 RPM 9111 7778 8889 7333 9111 9556 9111 9111 8750500 RPM 8889 9556 9111 8667 9556 9333 9111 9333 9194

ICA

300RPM 5111 4889 8667 6667 7111 9333 7111 6444 6917350 RPM 6444 4222 8889 7111 8667 9111 7778 9111 7667400 RPM 8889 6222 8889 7556 7556 8889 9111 9778 8361450 RPM 10000 4889 9333 6889 8889 9778 9333 8889 8500500 RPM 9111 8889 9111 8444 9778 9333 8889 9556 9139

LDA

300RPM 7778 8889 8222 9333 9556 10000 9778 8889 9056350 RPM 9111 10000 9111 9333 10000 10000 9778 10000 9667400 RPM 9556 10000 9778 9556 10000 10000 9778 9778 9806450 RPM 10000 10000 9778 9333 9778 10000 10000 9778 9833500 RPM 9111 10000 10000 9778 10000 9778 10000 10000 9833

Proposed

300 RPM 8000 8667 8889 9333 9333 10000 9778 8889 9111350 RPM 9111 10000 8889 9333 10000 10000 10000 10000 9667400 RPM 9556 10000 9778 9778 10000 10000 10000 10000 9889450 RPM 10000 10000 10000 9778 9778 10000 10000 10000 9944500 RPM 9333 10000 10000 9778 10000 9778 10000 10000 9861

(ACA) From the figures in Tables 4 and 5 it is clear that theproposed feature analysis scheme consistently outperformsthe conventional approaches of PCA ICA and LDA forall of the datasets that were analyzed in this study Forinstance Table 5 reveals that the TPR of the proposedmethod is around 100 for almost all bearing faults (exceptfor the BCR fault condition where it ranges between 93and 97 but is still higher than that of PCA and ICA)In Table 4 it can be observed that the proposed methodachieves good classification performance even though thefeature clustering of the 3mm length crack datasets was poorand not well separated as compared to the 12mm length crackdatasets This comparatively high classification performancedemonstrates that the proposed approach is more effective infeature analysis as compared to other conventional methodsOur approach is also able to yield maximum discriminationin a lower-dimensional feature space

5 Conclusion

This paper proposed a comprehensive multifault diagno-sis methodology based on AE analysis to detect multiplelocalized bearing faults of a rolling element bearing Themethod comprises a prewhitening step a feature extractionbased on wavelet kurtogram a useful feature selection withthe proposed VMDC-based feature analysis and a faultclassification by employing the NB classifier One of themain advantages of the proposed methodology is that thesubband of the nonstationary AE signal which carries themost sensitive information related to fault characteristic

is adaptively identified without any prior knowledge ofthe bearing fault type by using an enhanced WPT-basedkurtogram algorithm In addition the proposed VMDC-based discriminative feature analysis approach efficientlyidentifies optimal features where their discriminatory poweris maximized The proposed methodology was evaluated byan experimental setup using a healthy bearing and sevendamaged ones under different rotational speeds and differentsimulated crack sizes Experimental results indicated thatthe proposed multifault diagnosis methodology achieves thehighest classification accuracy up to 9111 9667 98899944 and 9861 under bearing rotational speeds of 300rpm 350 rpm 400 rpm 450 rpm and 500 rpm respectively

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government(MSIP) (no NRF-2013R1A2A2A05004566)

References

[1] J Antoni ldquoFast computation of the kurtogram for the detectionof transient faultsrdquo Mechanical Systems and Signal Processingvol 21 no 1 pp 108ndash124 2007

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Shock and Vibration

[2] N Sawalhi R B Randall and H Endo ldquoThe enhancementof fault detection and diagnosis in rolling element bearingsusingminimum entropy deconvolution combinedwith spectralkurtosisrdquoMechanical Systems and Signal Processing vol 21 no6 pp 2616ndash2633 2007

[3] T Barszcz and R B Randall ldquoApplication of spectral kurtosisfor detection of a tooth crack in the planetary gear of a windturbinerdquo Mechanical Systems and Signal Processing vol 23 no4 pp 1352ndash1365 2009

[4] P Boskoski J Petrovicic BMusizza andD Juriicic ldquoDetectionof lubrication starved bearings in electrical motors by meansof vibration analysisrdquo Tribology International vol 43 no 9 pp1683ndash1692 2010

[5] R F Dwyer ldquoDetection of non-Gaussian signals by frequencydomain kurtosis estimationrdquo in Proceedings of the IEEE Inter-national Conference on Acoustics Speech and Signal Processing(ICASSP rsquo83) pp 607ndash610 Boston Mass USA 1984

[6] J Antoni and R B Randall ldquoThe spectral kurtosis applica-tion to the vibratory surveillance and diagnostics of rotatingmachinesrdquo Mechanical Systems and Signal Processing vol 20no 2 pp 308ndash331 2006

[7] B Chen Z Zhang Y Zi Z He and C Sun ldquoDetecting oftransient vibration signatures using an improved fast spatial-spectral ensemble kurtosis kurtogram and its applications tomechanical signature analysis of short duration data fromrotating machineryrdquoMechanical Systems and Signal Processingvol 40 no 1 pp 1ndash37 2013

[8] L Shi R B Randall and J Antoni ldquoRolling element bearingfault detection using improved envelope analysisrdquo in Proceed-ings of the Eighth International Conference on Vibrations inRotating Machinery pp 301ndash311 Swansea Wales September2004

[9] M Kang J Kim J-M Kim A C C Tan E Y Kim andB-K Choi ldquoReliable fault diagnosis for low-speed bearingsusing individually trained support vector machines with kerneldiscriminative feature analysisrdquo IEEE Transactions on PowerElectronics vol 30 no 5 pp 2786ndash2797 2015

[10] M Kang J Kim B-K Choi and J-M Kim ldquoEnvelop analysiswith a genetic algorithm-based adaptive filter bank for bearingfault detectionrdquoThe Journal of the Acoustical Society of Americavol 138 no 1 article EL65 6 pages 2015

[11] A Widodo and B-S Yang ldquoMachine health prognostics usingsurvival probability and support vector machinerdquo Expert Sys-tems with Applications vol 38 no 7 pp 8430ndash8437 2011

[12] Y Guo J Na B Li and R-F Fung ldquoEnvelope extraction baseddimension reduction for independent component analysis infault diagnosis of rolling element bearingrdquo Journal of Sound andVibration vol 333 no 13 pp 2983ndash2994 2014

[13] J Harmouche C Delpha and D Diallo ldquoImproved faultdiagnosis of ball bearings based on the global spectrum ofvibration signalsrdquo IEEE Transactions on Energy Conversion vol30 no 1 pp 376ndash383 2015

[14] K Fukunaga Introduction to Statistical Pattern RecognitionComputer Science and Scientific Computing Academic PressBoston Mass USA 1990

[15] P Comon ldquoIndependent component analysis a new conceptrdquoSignal Processing vol 36 no 3 pp 287ndash314 1994

[16] G J McLachlan Discriminant Analysis and Statistical PatternRecognition Wiley New York NY USA 1992

[17] F Cong J Chen and G Dong ldquoSpectral kurtosis based on ARmodel for fault diagnosis and condition monitoring of rolling

bearingrdquo Journal of Mechanical Science and Technology vol 26no 2 pp 301ndash306 2012

[18] KMardia J Kent and J BibbyMultivariate Analysis AcademicPress London UK 1979

[19] J Vaidya M Kantarcıoglu and C Clifton ldquoPrivacy-preservingNaıve Bayes classificationrdquoThe VLDB Journal vol 17 no 4 pp879ndash898 2008

[20] Y-L He R Wang S Kwong and X-Z Wang ldquoBayesianclassifiers based on probability density estimation and theirapplications to simultaneous fault diagnosisrdquo Information Sci-ences vol 259 pp 252ndash268 2014

[21] J Rodriguez A J Perez and J Lozano ldquoSensitivity analysisof k-fold cross validation in prediction error estimationrdquo IEEETransactions on Pattern Analysis and Machine Intelligence vol32 no 3 pp 569ndash575 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of