Neurocomputing 74 (2011) 1638–1645

Contents lists available at ScienceDirect

Neurocomputing

0925-23

doi:10.1

n Corr

E-m

sshmefm

journal homepage: www.elsevier.com/locate/neucom

Rolling element bearing fault diagnosis using wavelet transform

P.K. Kankar, Satish C. Sharma, S.P. Harsha n

Vibration and Noise Control Laboratory, Mechanical and Industrial Engineering Department, Indian Institute of Technology Roorkee, Roorkee 247667, India

a r t i c l e i n f o

Article history:

Received 16 August 2010

Received in revised form

13 January 2011

Accepted 21 January 2011

Communicated by J. Zhangwavelets are considered for the study and Complex Morlet wavelet is selected based on minimum

Available online 21 March 2011

Keywords:

Wavelets

Support vector machine (SVM)

Learning vector quantization (LVQ)

Self-organizing maps (SOM)

Shannon Entropy

12/$ - see front matter & 2011 Elsevier B.V. A

016/j.neucom.2011.01.021

esponding author. Tel.: þ91 1332 286602.

ail addresses: pavankankar@gmail.com (P.K. K

e@iitr.ernet.in (S.C. Sharma), spharsha@gma

a b s t r a c t

This paper is focused on fault diagnosis of ball bearings having localized defects (spalls) on the various

bearing components using wavelet-based feature extraction. The statistical features required for the

training and testing of artificial intelligence techniques are calculated by the implementation of a

wavelet based methodology developed using Minimum Shannon Entropy Criterion. Seven different base

Shannon Entropy Criterion to extract statistical features from wavelet coefficients of raw vibration

signals. In the methodology, firstly a wavelet theory based feature extraction methodology is developed

that demonstrates the information of fault from the raw signals and then the potential of various

artificial intelligence techniques to predict the type of defect in bearings is investigated. Three artificial

intelligence techniques are used for faults classifications, out of which two are supervised machine

learning techniques i.e. support vector machine, learning vector quantization and other one is an

unsupervised machine learning technique i.e. self-organizing maps. The fault classification results show

that the support vector machine identified the fault categories of rolling element bearing more

accurately and has a better diagnosis performance as compared to the learning vector quantization and

self-organizing maps.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Rolling element bearings are essential parts of rotatingmachinery from small hand held devices to heavy duty industrialsystems and are primary cause of breakdowns in machines. Amachine can be seriously damaged if faults occur in bearingsduring service. The importance of early detection of defects inbearings has led to continuous efforts due to the fact thatunpredictable occurrence of damage may cause disastrous failure.In order to ensure the normal operation of industry fault diag-nosis of bearings is essential. Fault diagnosis of rolling elementbearings using vibration signature analysis is the most commonlyused to prevent breakdowns in machinery.

Fault diagnosis is a type of classification problem, and artificialintelligence techniques based classifiers can be effectively used toclassify normal and faulty machine conditions. A machine faultclassification problem consists of two main steps. First step isfeature extraction from raw vibration signals to extract somefeatures that demonstrate the information of fault from the rawsignals and second step is to use these extracted features for faultdiagnosis using various artificial intelligence techniques like

ll rights reserved.

ankar),

il.com (S.P. Harsha).

artificial neural networks, support vector machines, etc. Toanalyze vibration signals and extract features, different techni-ques such as time domain [1–5], frequency domain [6–8] andtime–frequency domain [9–18] are extensively used. The complexand non-stationary vibration signals with a large amount of noisemake the bearing faults very difficult to detect by conventionaltime domain and frequency domain analysis, which assumes thatthe analyzed signal to be strictly periodic. Recently, wavelettransform, which is a time–frequency domain analysis method,has been widely used for fault diagnosis of rolling elementbearings. It has the local characteristic of time-domain as wellas frequency domain and its time–frequency window is change-able. In the processing of non-stationary signals it presents betterperformance than the traditional Fourier analysis.

Samantha and Al.-Balushi [4] have presented a procedure forfault diagnosis of rolling element bearings through artificialneural network (ANN). The characteristic features of time-domainvibration signals of the rotating machinery with normal anddefective bearings have been used as inputs to the ANN. Kankaret al. [5] have conducted a comparative experimental study forthe effectiveness of ANN and SVM in fault diagnosis of ballbearings and concluded that the classification accuracy forSVM is better than of ANN. Nikolaou and Antoniadis [10] haveused wavelet packet transform to identify the nature of rollingelement bearing faults. The wavelet packet transform is used forthe analysis of vibration signals resulting from bearings with

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–1645 1639

localized defects. Prabhakar et al. [11] and Purushotham et al. [12]have used discrete wavelet transform for detection of bearing racefaults. The effectiveness of wavelet-based features for faultdiagnosis of gears using support vector machines (SVM) andproximal support vector machines (PSVM) has been revealed bySaravanan et al. [13]. Methods for intelligent fault diagnosis ofrotating machinery based on wavelet packet transform (WPT),empirical mode decomposition (EMD), dimensionless parameters,a distance evaluation technique and radial basis function (RBF)network are proposed by Lei et al. [14].

Rafiee et al. [15] have developed a procedure which experi-mentally recognizes gears and bearings faults of a typical gearboxsystem using a multi-layer perceptron neural network. Rafiee andTse [16] have presented a time–frequency-based feature recogni-tion system for gear fault diagnosis using autocorrelation ofcontinuous wavelet coefficients (CWC). It has been shown thatthe size of vibration signals can be reduced with minimal loss ofsignificant frequency content. Rafiee et al. [17] have furtherproposed a technique for selecting mother wavelet function usingan intelligent fault diagnosis system. The type of gear failures of acomplex gearbox system are identified using genetic algorithmand artificial neural networks. Rafiee et al. [18] have shown thatthe Daubechies 44 wavelet is the most effective for both faultygears and bearings.

An extensive comparative study concerning the performanceof SVM against sixteen other popular classifiers, using twenty-onedifferent data sets, is carried out by Meyer et al. [19]. The resultsverify that SVM classifiers rank at the very top among theseclassifiers, although there are cases for which other classifiersgave lower error rates [19]. Based on the comparison andrecommendation of previous studies, authors have employedSVM and LVQ for bearing faults classification [19,20]. LVQ is asupervised machine learning technique and it is special case ofANN. In many situations, it is not easy to collect training data setbecause of routine maintenance and periodically repairs. To solvethis problem, authors have also used self-organizing maps (SOM)because unlike SVM and ANN, SOM-based approach has thepractical advantage of learning and producing fault classificationswithout any supervision.

In order to extract the fault feature of signals more effectively,an appropriate wavelet-base function should be selected. Pre-sently, in mechanical fault diagnosis, Daubechies and Morletwavelets are mostly applied to extract the fault feature [9–18].In present work, a methodology is proposed based on MinimumShannon Entropy Criterion for selection of most appropriatewavelet and to determine scale corresponding to characteristicdefect frequency. Seven different wavelets are considered eachwith 27 sub-signals i.e. 128 scales. In order to select the best basewavelet for rolling element bearings fault diagnosis, ShannonEntropy for each wavelet is calculated. Statistical features arecalculated from wavelet coefficients and fed as input to machinelearning techniques SVM, LVQ and SOM. The useful features canbe extracted from the original data and high dimensional oforiginal data can be reduced by removing irrelevant features withthe use of proposed methodology. Hence, the classifier canachieve a higher accuracy.

2. Machine learning techniques

Machine learning is an approach of using examples (data) tosynthesize programs. In the particular case when the examplesare input/output pairs, it is called Supervised Learning. In a case,where there are no output values and the learning task is to gainsome understanding of the process that generated the data,this type of learning is said to be unsupervised. In the present

study, the two supervised machine learning techniques i.e. SVMand LVQ are considered and the unsupervised machine learningtechnique like SOM is considered. Pattern recognition andclassification using machine learning techniques are describedin Ref. [21].

2.1. Self-organizing maps

Self-organizing maps are special class of ANN and are based oncompetitive learning. In self-organizing maps, the neurons areplaced at the nodes of a lattice that is usually one or twodimensional. The neurons become selectively tuned to variousinput patterns or classes of input patterns in the course of acompetitive learning process. The location of neuron is so tuned(winning neurons) that it becomes ordered with respect to eachother in such a way that a meaningful co-ordinate system fordifferent input features is created over the lattice.

A SOM is therefore characterized by the formation of atopographic map of the input patterns in which the spatiallocations of the neurons in the lattice are indicative of intrinsicstatistical features contained in the input patterns, hence self-organizing map.

2.2. Support vector machine

Support vector machine is a supervised machine learningmethod based on the statistical learning theory. It is a usefulmethod for classification and regression in small-sample casessuch as fault diagnosis. In this method, a boundary is placedbetween the two different classes and orients it, in such a waythat the margin is maximized, which results in the least general-ization error. The nearest data points that have been used todefine the margin are called Support Vectors. This is implementedby reducing it to a convex optimization problem: minimizing aquadratic function under linear inequality constraints [22]. Atraining sample set {(xi,yi)}; i¼1 to N is considered, where N istotal number of samples. The hyperplane f(x)¼0 that separatesthe given data can be obtained as a solution to the followingoptimization problem:

Minimize1

2:w:2

þCXN

i ¼ 1

xi ð1Þ

Subject toyiðw

T xiþbÞZ1�xi

xiZ0, i¼ 1,2,. . .,N

(ð2Þ

where C is a constant representing error penalty. Rewriting theabove optimization problem in terms of Lagrange multipliers,leads to the following problem:

MaximizeWðlÞ ¼XN

i ¼ 1

li�1

2

XN

i,j ¼ 1

yiyjliljðxi:xjÞ ð3Þ

Subject to

0rlirCXN

i ¼ 1

liyi ¼ 0, i¼ 1,2,. . .,N

8>><>>: ð4Þ

The Sequential Minimal Optimization (SMO) algorithm gives anefficient way of solving the dual problem arising from the deriva-tion of the SVM. SMO decomposes the overall quadratic program-ming problem into quadratic programming sub-problems.

2.3. Learning vector quantization

Learning vector quantization [21] is a supervised machinelearning technique in which the structure of the input space is

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–16451640

exploited so that the size of the input data can be reduced whichresults in less computational time. LVQ is based on vectorquantization in which an input space is divided into number ofdistinct regions and for each region a reconstruction vector isdefined. When a new vector is presented to the quantizer, theregion in which the vector lies is first determined, and is thenrepresented by the reproduction vector for that region. Thecollection of possible reproduction vectors is called the code bookof quantizer, and its members are called code words.

The SOM algorithm provides an approximate method forcomputing the Voronoi vectors in unsupervised manner, withthe approximation being specified by the synaptic weight vectorsof the neurons in the feature map. Therefore we can say thatfirstly SOM can be employed for the computation of the featuremap and secondly LVQ is applied which provides a mechanism forthe final tuning of a feature map. Hence LVQ is said to besupervised version of SOM.

3. Experimental setup

The problem of predicting the degradation of working condi-tions of bearings before they reach the alarm or failure thresholdis extremely important in industries to fully utilize the machineproduction capacity and to reduce the plant downtime. In thepresent study, an experimental test rig is used and vibrationresponse for healthy bearing and bearing with faults are obtained.The rig is connected to a data acquisition system through properinstrumentation. Data acquisition and analysis system consists ofVibraQuest software and data acquisition hardware. VibraQuestsoftware is designed in Lab VIEW for quick data acquisition,review, and storage. Hardware consists of 16 analog inputchannels, for simultaneous sampling. PCI bus ensures high-speeddata acquisition (102.4k samples/s). A remote optical sensor witha visible red LED light source is used to measure rotor speed.Piezo-electric accelerometers (IMI 603C01) are used for pickingup the vibration signals from various stations on the rig. Theseaccelerometers are having measurement range as 7490 m/s2.Table 1 shows dimensions of the ball bearings taken for the study.Piezo-electric accelerometers are used for picking up the vibra-tion signals from various stations on the rig.

As a first step, the machine was run with healthy bearing toestablish the base-line data. Then data are collected for different faultconditions. Various faults considered in bearing components are as

Table 1Parameters of bearing.

Parameter Value

Outer race diameter 28.262 mm

Inner race diameter 18.738 mm

Ball diameter 4.762 mm

Ball number 8

Radial clearance 10 mm

Spall

Fig. 1. Bearing components with faults induced in them. (a) Spall

shown in Fig. 1. A variety of faults on bearings are simulated on therig at different rotor speed i.e. 250, 500, 1000, 1500 and 2000 rpm.Following five bearing conditions are considered for the study:

1.

on

Healthy bearings (HB).

2. Bearing with spall on inner race (SIR). 3. Bearing with spall on outer race (SOR). 4. Bearing with spall on ball (BFB). 5. Combined bearing component defects (CBD).

4. Minimum Shannon Entropy Criterion (MEC)

Total of seven different wavelets have been considered for thepresent study. An appropriate wavelet is the base wavelet whichminimizes the Shannon Entropy of the corresponding waveletcoefficients. The Shannon Entropy of wavelet coefficients is given as

SentropyðnÞ ¼�Xm

i ¼ 1

pi log2pi ð5Þ

where pi is the energy probability distribution of the waveletcoefficients, defined as

pi ¼9Cn,i9

2

EðnÞð6Þ

withPm

i ¼ 1 pi ¼ 1, and in the case of pi¼0 for some i, the value ofpi log2pi is taken as zero.

The following steps explain the methodology developed forselecting a base wavelet based on the ‘‘Minimum ShannonEntropy Criterion’’ for the vibration signals under study:

(1)

o

Total 150 vibration signals are obtained by consideringhealthy and faulty bearing conditions.

(2)

To convert the complex vibration signals into simplifiedsignals with more resolution in time and frequency domain,these raw signals are divided into 27 sub-signals i.e. 128scales in seventh level of decomposition.

(3)

For healthy and faulty bearings, continuous wavelet coeffi-cients (CWC) of vibration signals are calculated using sevendifferent mother wavelets in which three from real valued asDaubechies 44, Meyer, Coiflet, Symlet wavelets and otherthree are complex valued as complex Gaussian, ComplexMorlet and Shannon wavelets.

(4)

The Shannon Entropy of CWC is calculated for each of 30segmented signals at different rotor speed 250, 500, 1000,1500 and 2000 rpm and loading conditions using healthy andfaulty bearings. The average of the Shannon Entropy in the 30segmented signals is calculated for five bearing conditions i.e.BFB, SIR, CBD, HB and SOR.

(5)

Sum of the mentioned average of the five bearing conditionsis determined for each scale (27).

(6)

The total Shannon Entropy for each wavelet is calculated byadding ‘‘sum of the mentioned average’’ of all the scales asshown in Table 2.

Spall

uter race, (b) spall on inner race and (c) ball with spall.

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–1645 1641

(7)

TablCom

W

Da

Me

Co

Sy

Co

Sh

Co

The wavelet having minimum Shannon Entropy is consideredfor fault diagnosis of rolling element bearing.

The flowchart for above mentioned methodology is shown inFig. 2. Shannon Entropy calculated for Complex Morlet wavelet isfound minimum. Hence, Complex Morlet wavelet is considered toextract features for fault diagnosis.

For healthy and faulty bearings, Fig. 3 shows the plots betweenShannon Entropy and scale number at rotor speed 2000 rpm with noloader using Complex Morlet wavelet. Entropy plots for faults in ball,inner race and outer race are as shown in Fig. 3(a), (b) and (e),respectively. From this, it is concluded that fault in inner race givesminimum entropy as compare to fault in ball or outer race, whichindicates that inner race defect has more effect on machine vibra-tions. While for combined bearing component defects, Fig. 3(c) showsthat Shannon Entropy value is less. For healthy bearing, it is observedthat Shannon Entropy value is more as compare to bearing containingsome faults as shown in Fig. 3(d). Fig. 3 clearly indicates that

e 2parison of parameters for wavelet selection.

avelet type Shannon Entropy

ubechies 44 21.43

yer 21.59

iflet 39.49

mlet 28.88

mplex Gaussian 40.03

annon 21.26

mplex Morlet 19.79

Signal DecomWavelet

30 sample signals for BFB

30 sample signals for SIR

30 sample signals for CBD

30 sample signals for HB

30 sample signals for SOR

Raw Vibration Signals

4 Real Valued Wavelets

ShEntr

S = Sum of the calculated Average

Select wavelet w

T = total of S corre

Average ‘n’ of BFB

Average ‘n’ of SIR

AveraC

Fig. 2. Flowchart for wave

Minimum Shannon Entropy Criterion applied in this study can beeffectively used for fault diagnosis of rotor bearing system.

5. Feature extraction

Complex Morlet wavelet is selected as the best base waveletamong the other wavelets considered from the proposed methodol-ogy. The CWC of all the 150 signals with Complex Morlet as a basewavelet are calculated at seventh level of decomposition (27 scales).

When applying wavelet transform to a signal, if the ShannonEntropy measure of a particular scale is minimum then we can saythat a major defect frequency component exists in the scale. In thepresent study out of 27 scales considered, the scale having theminimum Shannon Entropy is selected, and the statistical featuresof the CWC corresponding to the selected scale are calculated.

Root mean square (RMS) value, crest factor, kurtosis, skewness,standard deviation, etc. are the most commonly used statisticalmeasures used for fault diagnosis of rolling element bearings.Statistical moments like kurtosis, skewness and standard deviationare descriptors of the shape of the amplitude distribution of vibrationdata collected from a bearing, and have some advantages overtraditional time and frequency analysis, such as its lower sensitivityto the variations of load and speed, the analysis of the conditionmonitoring results is easy and convenient, and no precious history ofthe bearing life is required for assessing the bearing condition [23].When selecting certain normalized statistical moments to monitorthe bearing condition, we usually need to consider two mostessential characteristics, i.e. sensitivity and robustness. By rectifyingthe signal, Honarvar and Martin [23] compared the third moment,skewness, of the rectified data to kurtosis, and found that this thirdmoment has better characteristics than kurtosis. In present paper,

position using Transform

3 Complex Valued Wavelets

annon opy (n)

in bearing conditions in each scale

hich minimizes “T”

sponding to all scales

ge ‘n’ of BD

Average ‘n’ of HB

Average ‘n’ of SOR

let selection criteria.

Fig. 3. Plots between Shannon Entropy and scale number at rotor speed 2000 rpm with no loader using Complex Morlet wavelet. (a) Bearing with spall on ball, (b) bearing

with spall on inner race, (c) combined bearing component defects, (d) healthy bearings and (e) bearing with spall on outer race.

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–16451642

authors’ use statistical moments like kurtosis, skewness and standarddeviation as features to effectively indicate early faults occurring inrolling element bearing. The statistical features that are considered inthe present study are:

(1)

Kurtosis: a statistical measure used to describe the distribu-tion of observed data around the mean. Kurtosis is defined asthe degree to which a statistical frequency curve is peaked.

Kurtosis¼nðnþ1Þ

ðn�1Þðn�2Þðn�3Þ

X xj�x

s

� �4( )

�3ðn�1Þ2

ðn�2Þðn�3Þð7Þ

(2)

Skewness: skewness characterizes the degree of asymmetry ofa distribution around its mean. Skewness can come in theform of negative or positive skewness.

Skewness¼n

ðn�1Þðn�2Þ

X xj�x

s

� �3

ð8Þ

(3)

Standard deviation: standard deviation is measure of energycontent in the vibration signal.

Standard deviation¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinP

x2�ðP

xÞ2

nðn�1Þ

sð9Þ

These statistical features are fed as input to the artificialintelligence techniques for faults classification. The following

steps give an overview of the methodology presented in thisstudy for bearing faults diagnosis:

(1)

In this study, healthy bearings, bearing with spall in outerrace, inner race, ball and bearing with combined compo-nent defects are considered. Vibration signals in timedomain are obtained both in horizontal and vertical directionsfor each bearing condition at different rotor speed 250,500, 1000, 1500 and 2000 rpm under loader and no loadercondition.

(2)

Continuous wavelet coefficients of the vibration signals arecalculated at the seventh level of decomposition (27 scales foreach sample). These coefficients are calculated for all sevenmother wavelets, considered in this study.

(3)

Shannon Entropy of CWC can be calculated thereafter. (4) Complex Morlet wavelet is considered for the fault diagnosis

among the seven mother wavelets based on minimum Shan-non Entropy Criterion.

(5)

Statistical features like kurtosis, skewness and standarddeviation are calculated from the wavelet coefficientscorresponding to scales having the minimum ShannonEntropy.

These statistical features are fed as input to the machinelearning algorithms SVM, LVQ and SOM for faults classifi-cation.

Table 6Confusion matrix for SVM.

BFB SIR CBD HB SOR Classified as

15 0 0 0 0 BFB0 15 0 0 0 SIR0 0 15 0 0 CBD0 0 0 15 0 HB0 0 0 0 15 SOR

Table 7Confusion matrix for LVQ.

BFB SIR CBD HB SOR Classified as

12 0 1 0 2 BFB0 12 1 2 0 SIR

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–1645 1643

6. Results and discussions

In the present study, classification of bearing faults is carriedout using SVM, LVQ and SOM. The number of code book vectorsfixed before the training of the LVQ algorithm is 20. Out of this 20code book vectors the class distribution among the five differentfault classes is given in Table 3. Four different code book vectorsare selected by the LVQ algorithm to represent each of BFB andSIR cases and this corresponds to 20% each. Whereas 2(10%),7(35%), 3(15%) for CBD, HB, SOR, respectively. The class distribu-tion among the five different bearing cases for SOM is given inTable 4.

The results on a test set in a multi-class prediction aredisplayed as a two dimensional confusion matrix with a rowand column for each class [24]. Each matrix element shows thenumber of test examples for which the actual class is the row andthe predicted class is the column. A sample training/testing vectoris shown in Table 5. Total 75 instances and 8 features are used forthe study including statistical features for each of the horizontaland vertical response, number of loader and rotor speed used.Tables 6–8 show the test results as confusion matrices for each ofthe two techniques i.e. SVM, LVQ and SOM. Total 75 numbers of

Table 3Class distribution for LVQ.

S. no. Type of bearing No. of code book vectors

1 BFB 4(20%)

2 SIR 4(20%)

3 CBD 2(10%)

4 HB 7(35%)

5 SOR 3(15%)

Table 4Class distribution for SOM.

S. no. Type of bearing % Class

1 BFB 10(21%)

2 SIR 9(19%)

3 CBD 8(17%)

4 HB 10(21%)

5 SOR 11(23%)

Table 5Sample input vector for SVM, LVQ and SOM.

Features

Horizontal response Ver

Kurtosis Skewness Standard deviation Kur

Amplitude of features 10.83371 2.219912 0.00022 44.

11.07509 2.328135 0.002189 22.

6.465513 1.50172 0.000543 16.

5.105068 1.251012 9.59E�05 54.

6.461471 1.54027 0.000284 5.

11.52051 2.097072 0.000249 7.

11.93591 2.410487 0.000198 7.

4.630504 1.210162 0.000193 13.

5.553487 1.400872 0.000348 10.

7.704414 1.519889 0.000105 6.

6.118728 1.480516 0.000204 4.

4.282953 1.093893 0.000264 5.

14.40096 2.558341 0.0002 31.

6.202332 1.447155 0.000246 25.

5.107758 1.28273 0.000466 8.

instances are obtained in which 15 cases are considered with eachof BFB, SIR, CBD, HB and SOR, respectively. SVM has correctlypredicted all instances for BFB, SIR, CBD, HB and SOR, respectively,as shown in Table 6. From Table 7, it is inferred that LVQ hascorrectly predicted 12, 12, 15, 14 and 14 instances, while Table 8

tical response Loader Speed Class

tosis Skewness Standard deviation

70497 4.753333 0.000702 0 1000 BFB

66564 3.398547 0.001975 0 1500 BFB

52251 2.751154 0.00444 0 2000 BFB

83589 4.1949 0.000118 1 1000 SIR

805013 1.464965 0.000217 1 1500 SIR

707975 1.741795 0.000371 1 2000 SIR

281817 1.735277 0.000209 1 1000 CBD

42329 2.375881 0.000467 1 1500 CBD

68352 2.191045 0.001183 1 2000 CBD

478991 1.578542 0.000399 2 1000 HB

864674 1.254669 0.000205 2 1500 HB

511267 1.36593 0.000297 2 2000 HB

59812 4.54973 0.001268 2 1000 SOR

01716 3.508182 0.00568 2 1500 SOR

521063 2.24933 0.030608 2 2000 SOR

Table 9Evaluation of the success of numeric prediction.

Parameters SVM LVQ SOM

Correctly classified instances 75(100%) 67(89.3333%) 56(74.6667%)

Incorrectly classified instances Nil 8(10.6667%) 19(25.3333%)

Total number of instances 75 75 75

Table 8Confusion matrix for SOM.

BFB SIR CBD HB SOR Classified as

13 0 0 0 2 BFB3 10 0 1 1 SIR1 0 12 0 2 CBD3 1 0 8 3 HB0 1 1 0 13 SOR

0 0 15 0 0 CBD0 0 0 14 1 HB0 1 0 0 14 SOR

Table 10A compressive study between the present work and some recent publications.

References Objects Defects considered Techniques usedfor vibrationsignatureanalysis

Featuresconsidered

Classifier used Classifierefficiencies

Paya et al. [9] Bearings and

gears

Defects on inner race of bearing

and gear tooth irregularity.

Daubechies 4 10 wavelet

numbers

indicating both

time and

frequency and

their 10

corresponding

amplitudes

Artificial neural

networks

96%

Nikolaou andAntoniadis [10]

Rolling element

bearings

Inner race and outer race fault Daubechies 12 Mean and

standard deviation

of wavelet packet

coefficients

NA NA

Prabhakaret al. [11]

Rolling element

bearings

One scratch mark each on inner

race (on the track) and outer

race (on the track), two scratch

marks on outer race (1801 apart

on the track), one scratch mark

on each of inner race and outer

race (on the track)

Daubechies 4 RMS, Kurtosis NA NA

Purushothamet al. [12]

Rolling element

bearings

Single and multiple point

defects on inner race, outer

race, ball fault and combination

of these faults

Daubechies Mel Frequency

Complex

Cepstrum (MFCC)

coefficients

Hidden Markov

model classifiers

Best efficiency

obtained as 99%

Saravananet al. [13]

Gears Gear tooth breakage, gear with

crack at root and with face wear

Morlet wavelet Statistical features

namely, standard

error, sample

variance, kurtosis

and minimum

value

Support vector

machines (SVM)

and proximal

support vector

machines (PSVM)

Best efficiency

obtained as

100%

Rafiee et al. [15] Gears and

bearings

Three different fault conditions

on gears (slight-worn, medium-

worn and broken tooth), faulty

bearings

Daubechies 4

(wavelet packet)

Standard

deviation of

wavelet packet

coefficients

Artificial neural

networks

Best efficiency

obtained as

100%

Rafiee et al. [18] Gears and

bearings

Ball, cage, inner race, outer race

defects on bearings and three

different fault conditions on

gears (slight-worn, medium-

worn and broken tooth)

324 mother

wavelets from

various wavelet

families like Haar,

Daubechies,

Coiflet, Morlet, etc.

Variance, standard

deviation, kurtosis

and 4th central

moment of CWC-

SVS

Artificial neural

networks

Recommended

that the best

efficiency can be

achieved using

db 44 for gear

and bearing

fault diagnosis

Present work Rolling element

bearings

Spall in inner race, outer race,

rolling element and combined

component defects

Daubechies 44,

Meyer, Coiflet5,

Symlet2, Gaussian,

Complex Morlet

and Shannon

wavelets

Statistical features

namely, kurtosis,

skewness and

standard deviation

from wavelet

coefficients

corresponding to

scale maximizing

energy to Shannon

Entropy ratio

Support vector

machines,

artificial neural

networks, self-

organizing maps

The best

efficiency

obtained using

complex Morlet

wavelet and

SVM classifier as

100%

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–16451644

shows that SOM has classified 13, 10, 12, 8 and 13 instances.Table 9 shows accuracy associated with each technique for faultsclassification. For this study, classification accuracy shows thatSVM is a better classifier than LVQ and SOM. The predictionperformance of SVM is coming out to be superior mainly due toits good generalization capability, which is also reported byMeyer et al. [19]. The correctly classified instances for SVM, LVQand SOM are 100%, 89.3333% and 74.6667%, respectively. To showthe efficiency of the selected features and the methodology, acomparison between the current work and some publishedliteratures has been shown in Table 10. In this table, comparisonhas been made on the basis of the objects used, defects consid-ered for the study, techniques used for vibration signatureanalysis, features considered, classifier used and the classifierefficiencies in each paper.

7. Conclusion

Aiming at the characteristics of the vibration signal of rollingbearing with fault, the Complex Morlet wavelet is selected based onMinimum Shannon Entropy Criterion to extract the fault feature inthis paper. Rafiee et al. [18] have also shown that among a widevariety of mother wavelets, Complex Morlet wavelet have satisfactoryperformances for both bearing and gear fault identification, which isverified by obtained results. This study presents a methodology fordetection of bearing faults by classifying them using three artificialintelligence techniques. The responses observed for different faultcondition of bearing shows that minimum Shannon Entropy isobtained for bearings with inner race fault. The results of faultsclassification with SVM (100%) are superior to LVQ and SOM. LVQbeing the supervised version of SOM the classification accuracy

P.K. Kankar et al. / Neurocomputing 74 (2011) 1638–1645 1645

obtained 89.3333%, which is better than SOM (74.6667%). The resultsshow the potential application of these artificial intelligence techni-ques for developing effective maintenance strategies to preventcatastrophic failure and reduce operating cost.

Acknowledgement

This work was financially supported by the Department of Scienceand Technology, Government of India [Grant number DST/457/MID].

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Mr. P.K. Kankar has done his B.E. (Mechanical Engi-neering), M.E. (Manufacturing System Engineering)and pursuing Ph.D. (Vibration). His research areas aremachine design, vibration, controls and non-lineardynamics. He has published more than 10 papers invarious refereed journals.

Prof. Satish C. Sharma has done his B.E. (MechanicalEngineering), M.E. (Machine Design) and Ph.D. (Tribol-ogy). His research areas are machine design, tribologyand measurement. He has published more than 70papers in various refereed journals.

Dr. S.P. Harsha has done his B.E. (Mechanical Engineer-ing), M.E. (Machine Design) and Ph.D. (Vibration). Hisresearch areas are machine design, vibration, controlsand non-linear dynamics. He has published more than60 papers in various refereed journals.