Measurement 46 (2013) 1551–1564

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Measurement

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Fault diagnosis of rotating machinery based on the statisticalparameters of wavelet packet paving and a generic supportvector regressive classifier

0263-2241/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.measurement.2012.12.011

⇑ Corresponding author at: Department of Precision Machinery andPrecision Instrumentation, University of Science and Technology of China,96 Jinzhai Road, Hefei 230026, China. Tel.: +86 551 3607074; fax: +86 5512565626.

E-mail address: kongfr@ustc.edu.cn (F. Kong).

Changqing Shen a,b,c, Dong Wang b, Fanrang Kong a,c,⇑, Peter W. Tse b,c

a Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, Chinab Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, Chinac USTC-CityU Joint Advanced Research Centre, Suzhou 215123, China

a r t i c l e i n f o

Article history:Received 5 August 2012Received in revised form 22 October 2012Accepted 4 December 2012Available online 5 January 2013

Keywords:Wavelet packet pavingStatistical parametersDistance evaluation techniqueSupport vector regressionMachine fault diagnosis

a b s t r a c t

The fault diagnosis of rotating machinery has attracted considerable research attention inrecent years because such components as bearings and gears frequently suffer failure,resulting in unexpected machine breakdowns. Signal processing-based condition monitor-ing and fault diagnosis methods have proved effective in fault identification, but the reve-lation of faults from the resulting signals requires a high degree of expertise. In addition, itis difficult to extract the fault-induced signatures in complex machinery via signal process-ing-based methods. In this paper, a new intelligent fault diagnosis scheme based on theextraction of statistical parameters from the paving of a wavelet packet transform(WPT), a distance evaluation technique (DET) and a support vector regression (SVR)-basedgeneric multi-class solver is proposed. The collected signals are first pre-processed by theWPT at different decomposition depths. In this paper, the wavelet packet coefficients at dif-ferent decomposition depths are referred to as WPT paving. Statistical parameters are thenextracted from the signals obtained via the WPT at different decomposition depths. Inselecting the sensitive fault features for fault pattern expression, a DET is employed toreduce the dimensionality of the feature space. Finally, a SVR-based generic multi-class sol-ver is proposed to identify the different fault patterns of rotating machinery. The effective-ness of the proposed intelligent fault diagnosis scheme is validated separately usingdatasets from bearing and gearbox test rigs. In addition, the effects of different waveletbasis functions on the performance of the proposed scheme are investigated experimen-tally. The results demonstrate that the proposed intelligent fault diagnosis scheme is highlyaccurate in differentiating the fault patterns of both bearings and gears.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Rotating machinery is widely used in a range ofmechanical transmission systems, including aircraft en-gines, automobile transmission systems and power plants.

Unexpected failures in such machinery can cause break-downs, leading to significant economic losses and, evenworse, human casualties. To avoid catastrophe and mini-mise defective machinery downtime, machine fault diag-nosis is of great industrial significance. Accordingly, thedevelopment of machine fault diagnosis methods has at-tracted considerable research attention in recent decades[1].

Such components as bearings and gearboxes are com-monly used in rotating machinery to support rotatingshafts and transmit torque, and statistical surveys suggest

1552 C. Shen et al. / Measurement 46 (2013) 1551–1564

that these components are the major causes of machinebreakdown. Although signal processing-based fault diag-nosis methods have been widely investigated, and demon-strated to be effective and powerful tools in machine faultdiagnosis [2–4], analysing the complex signals they pro-duce to allow judgment concerning diagnosis requires con-siderable expertise. Artificial intelligence-based faultdiagnosis methods, in contrast, have the potential to tacklethis problem.

These methods usually include three crucial steps: faultfeature extraction, sensitive fault feature selection andfault pattern recognition. Fault feature extraction is themost basic of these steps and involves the mapping ofthe original signals onto the statistical parameters con-cerned to reflect the health of the machine. These parame-ters are also referred to as health indices. Qiu et al. [5]employed a wavelet filter and self-organised mapping togenerate an index that assesses bearing health over time,and Wang et al. [6] used a discrete wavelet transform toconstruct a health index that describes the accumulateddeterioration of gears. Pan et al. [7] employed waveletpacket node energies as the input to fuzzy c-means to builda health index to track bearing heath, and Wang et al. [8]fused multiple health indicators extracted from the resid-ual error signals of gears for early gear fault diagnosisand prognosis. Yang and Makis [9] proposed a health indexbased on an autoregressive model with exogenous vari-ables to monitor gear health under varying load conditions.Bozchalooi and Liang [10] introduced a smoothness indexand discovered its upper bound in the absence of an abnor-mal bearing condition. They also employed this index toidentify the optimal wavelet transform for the extractionof a weak bearing fault signal. Raad et al. [11] introducednew and simple indicators of cyclostationarity for gearhealth evaluation, and Antoni and Randall [12] used spec-tral kurtosis to evaluate abnormal gearbox conditionscaused by excessive spall damage. Finally, Lei et al. [13] de-signed two new health indicators for the fault diagnosis ofplanetary gearboxes. The results obtained in all of thesecases indicate that (1) proper statistical parameters arecrucial for determining the actual health of a machine overtime, and (2) advanced signal processing methods arehelpful in boosting the performance of these parameters.

After the statistical parameters have been extracted, thedimensionality of the statistical features needs to be re-duced because there is no guarantee that all of these fea-tures are equally useful in reflecting machine health. Twostrategies for reducing the dimensionality of the fault fea-ture space have become popular. The first is to use thederivatives of principal component analysis (PCA) [14,15]and independent component analysis (ICA) [16]. Yuanet al. [17] employed PCA to reduce the dimensionality ofthe fault features extracted from a turbo-pump rotor sig-nal, and Widodo et al. [18] used ICA to reduce the dimen-sionality of those extracted from induction motors. Theirresults suggested that the nonlinear method was betterable to enhance the accuracy of fault diagnosis. The seconddimensionality reduction strategy is the distance evalua-tion technique (DET) [19–21], which has been reported tobe a successful and effective tool for the selection of usefulfault features. Following the original DET, Lei et al. [22]

proposed a modified DET that considers a compensationfactor to emphasise the weight of the sensitive faultfeatures.

Finally, after selection of the sensitive fault features un-der different machine health conditions, the accuracy ofthe identification of these conditions can be further en-hanced using classifiers that exhibit good performance.Artificial neural networks, which were developed in accor-dance with the way in which the human brain processesinformation, have proved to be a powerful tool in rotatingmachinery fault diagnosis, but they have a number ofdrawbacks, including generalisation ability and slow con-vergence. Moreover, they are unsuitable for handling prob-lems with few samples for training [23]. Vapnik [24]recently introduced a relatively new computational super-vised learning approach called the support vector machine(SVM), which is based on statistical learning theory. It hasa well-defined formulation and is consistent with mathe-matical theory. Different from other classification meth-ods, SVM does not require a large number of samples fortraining owing to its superior generalisation capability[23]. Qu and Zuo [25] used a trained SVM to identify thewear degree of slurry pump systems, and Cui and Wang[26] employed SVMs classifier to diagnose an analog cir-cuit. Unlike the traditional SVM, which can be used onlyto handle a binary problem, the target value of supportvector regression (SVR) is continuous. It has shown greatpotential in time series prediction, and thus can establisha stable nonlinear relationship between inputs and outputs[27]. Sun et al. [28] predicted the remaining life of a bear-ing by establishing a SVR-based model, and Hou and Li [29]optimised the parameters of SVR through an evolutionstrategy and formulated a SVR-based short-term fault pre-diction strategy. Most of the existing work based on SVRhas been aimed at time series prediction, whereas classifi-cation problems are usually handled by binary SVMclassifiers.

In this paper, a new intelligent machine fault diagnosisscheme is proposed. The signals are first processed bywavelet packet decomposition, and the statistical featuresare then extracted from the paving of wavelet packets atdifferent decomposition depths to characterise the ma-chine health status. To simplify the fault pattern of differ-ent machine health conditions and improve fault patternidentification accuracy, a DET is applied to select the sensi-tive fault features. For different types of fault pattern rec-ognition, a new generic multi-class solver, that is, asupport vector regressive classifier, is established througha proposed decision function. The proposed scheme is ap-plied to the fault diagnosis of both bearing and gear data-sets. Compared with the fault identification ratios obtainedusing conventional multi-classifiers constructed via binarySVMs, the method proposed herein achieves a higher de-gree of accuracy.

The rest of this paper is outlined as follows. Section 2briefly describes the fundamental theory of wavelet packetdecomposition, support vector machine and support vectorregression. The proposed new machine health status iden-tification method is presented in Section 3, followed by theexperimental verification tests using both bearing andgearbox datasets as stated in Section 4. A comparison study

C. Shen et al. / Measurement 46 (2013) 1551–1564 1553

between conventional SVM classifiers and the proposedscheme is conducted. In Section 5, the effect of differentwavelet basis functions on the performance of the pro-posed scheme is experimentally discussed. Conclusionsare drawn in Section 6.

2. Theoretical background

2.1. The review of wavelet packet transform

Wavelet packet transform (WPT), which is also calledwavelet packets, is an extension of discrete wavelet trans-form (DWT). WPT processes a signal by using more filtersthan those provided by DWT. It means that every detailsignal obtained by DWT is further decomposed into twosub-signals including an approximation signal and a detailsignal.

For the fast algorithm, wavelet packet coefficients arecalculated by [30,31]:

d2pjþ1½n� ¼ dp

j � hð�2nÞ; ð1Þ

d2pþ1jþ1 ½n� ¼ dp

j � gð�2nÞ; ð2Þ

where � is convolution operator; h(n) and g(n) are theconjugate mirror filters. wavelet packet children nodes(j + 1, 2p) and (j + 1, 2p + 1) are derived from their parentnode (j,p). Suppose the sampling frequency is equal to Fs.The covered frequency band of wavelet packetcoefficients at the node (j,p) is mostly concentratedin ½p� Fs=2jþ1; ðpþ 1Þ � Fs=2jþ1�; 1 6 j 6 J; 0 6 p 6 2J � 1,where J is the maximum decomposition depth. A decom-position tree of WPT of a signal at the maximum depthequal to 3 is plotted in Fig. 1.

2.2. Support vector machine

The SVM classifier is a supervised learning algorithmbased on statistical learning theory developed by Vapnik[24]. This learning algorithm maps the low dimensional

Fig. 1. A decomposition tree of wavelet packet transform for a signal atthe maximum depth of 3.

datasets to the high dimensional feature space, and aimsto solve a binary problem by searching an optimal hyperplane which can separate two datasets with the largestmargin in the high dimensional space. The optimal hyperplane is established through a set of support vectors fromthe original datasets and these subsets form the boundarybetween the two classes. Given fxi; yig

Ni¼1 be a training

dataset where xi is the input feature vector for each sam-ple; N is the sample number; and yi e { �1,+1} representsits label. As shown in Fig. 2, the optimal hyper plane is de-fined by w �x + b = 0, where x is the point lying in the hyperplane, w is the parameter for the orientation of hyperplane, and b is a scalar threshold which represents the biasfrom the margins.

For both classes, the input feature vectors satisfy thefollowing inequality:

yiðw � xi þ bÞP 1; i ¼ 1;2; . . . ;N: ð3Þ

To obtain the optimal hyper plane, the positive slackvariable ni is introduced to solve the following optimisationproblem given by:

min 12 kwk

2 þ CXN

i¼1

ni;

s:t: yiðw � xi þ bÞP 1� ni; i ¼ 1;2; . . . ;N;

ð4Þ

where C is a penalty parameter which controls the tradeoffbetween the margin maximisation and error minimisation.After solving the Lagrange equation of Eq. (4), a classifica-tion function can be defined as:

f ðxÞ ¼ signXn

i¼1

aiyiKðxi; xÞ þ b

( ); ð5Þ

where ai is the Lagrange multiplier; K(xi, x) = u(xi) � u(x) isa symmetric positive defined kernel function given by theMercer’s theorem, and the kernel function can map a lowdimensional vector to a high feature space through somenonlinear functions. In this paper, the popular radial basisfunction (RBF) is adopted and its mathematical formula isgiven as:

Kðxi; xÞ ¼ exp�kxi � xk2

2r2

!; ð6Þ

where r is a positive real number.

{ | 0}x w x b• + =

{ | 1}x w x b• + = +

{ | 1}x w x b• + = −

Support vectors

Fig. 2. Data classification by SVM.

1554 C. Shen et al. / Measurement 46 (2013) 1551–1564

As mentioned before, SVM is actually a binary classifier.However, rotating machinery may usually suffer morethan two faults. To tackle this problem, a variety of multi-class classification strategies, such as the one-against-one(OAO), the one-against-all (OAA) and the direct acyclicgraph (DAG) were proposed [23]. The OAO based strategyis a voting approach that is regarded as a more suitablestrategy to the actual application because of its compara-tively fast training speed and good classification accuracy[32]. As shown in Fig. 3 for a k class problem, the OAOmethod constructs k(k � 1)/2 binary classifiers. Simply, ifx is classified to class I, the vote for class I is increased byone. Finally, the class with highest votes is determined asthe class for x. As a result, the OAO based strategy is alsocalled max win strategy.

2.3. Support Vector Regression (SVR)

SVR theory is developed based on the principle of SVMand suitable for time series prediction [27]. Given a datasetfxi; yig

Ni¼1, where xi is an input feature vector, yi is the target

value, and N is the total number of training samples. In e –insensitive support vector regression, it aims to obtain afunction f(x) which can predict the output yi within the er-ror limit of e. Besides, the estimation function f(x) can be asflat as possible to ensure a good generalisation propertyand variance. This function is presented as follow:

f ðxÞ ¼ w � xþ b; ð7Þ

where w is the weight vector and b is a constant. The func-tion can be obtained by solving the following optimisationproblem:

min 12 jwj

2 þ CXn

i¼1

ðni þ n�i Þ;

s:t:yi �w � xi � b 6 eþ ni

w � xi þ b� yi 6 eþ n�ini; n

�i P 0

8><>:

ð8Þ

In Eq. (8), ni and n�i denote the slack variable, C is a po-sitive constant which penalises the errors larger than ±eusing e – insensitive loss function given as follow:

jnje ¼0; if jnj < ejnj � e; otherwise;

�ð9Þ

Fig. 4a shows the regression line, the upper and lowerboundary lines. Fig. 4b shows the e – insensitive lossfunction.

After solving the optimisation problem described in Eq.(8), a linear regression function is presented as follows:

A-B A-C B-C

A B C

Fig. 3. Illustration of the OAO approach.

f ðxÞ ¼Xn

i¼1

ðai � a�i Þðxi � xÞ þ b; ð10Þ

where ai and a�i are the Lagrange multipliers. The linearregression function is not sufficient enough to processthe non-linear problem. The kernel function is applied hereto map the input vector into high dimensional featurespace and thus the regressive function is derived as follow:

f ðxÞ ¼Xn

i¼1

ðai � a�i ÞKðxi; xÞ þ b: ð11Þ

Similar to the SVM, the RBF kernel function written inEq. (6) is adopted in this paper.

3. Proposed health status identification scheme

The proposed new intelligent machine fault diagnosisscheme includes three steps: fault feature extraction, sen-sitive fault feature selection and fault pattern recognition.Each step in details is illustrated in the following subsec-tions. The framework of the proposed scheme is depictedin Fig. 5.

3.1. Fault feature extraction

The vibration signals collected by accelerometers arefirst processed by a wavelet packet transform (WPT) at dif-ferent decomposition depths to enhance the signal-to-noise ratio. The wavelet packet coefficients at differentdecomposition depths are referred to as the WPT pavingin this paper. The paving of wavelet packets at a maximumdepth of 3 is plotted in Fig. 6. All wavelet packet coeffi-cients at different depths are considered because it is diffi-cult to declare definitively that those at a certain depth arebetter than those at another. The typical example is thekurtosis of wavelet packet coefficient paving, which Leiet al. [33] referred to as an improved kurtogram. Their re-sults showed that the maximum kurtosis of the coefficientsof wavelet packets could be obtained at different depths.Hence, it is more reasonable to extract the fault featuresfrom the paving of wavelet packets (the wavelet packetcoefficients at different depths). The nine statistical param-eters listed in Table 1 are extracted from the paving ofwavelet packets at different decomposition depths. In gen-eral, the maximum wavelet packet decomposition level of3 is effective for features extraction purpose [20,21]. As aresult, a feature set containing 126 features for each sam-ple is obtained.

3.2. Fault feature selection

The nine statistical fault features based on waveletpacket coefficients have their own particular meanings indescribing the different aspects of a machine’s health sta-tus. The wavelet packets at a maximum depth of 3 produce126 fault features. It should be noted that the packets havedifferent sensitivity contributions for classification [19]. Inother words, too many input parameters for a classifier cangreatly decrease its identification accuracy and greatly in-crease the computational burden. Hence, it is necessary to

(a) (b)

Fig. 4. The regression line of SVR is shown in (a) and the loss function of SVR is shown in (b).

Start

Wavelet packet decomposition at different decomposition depths

Extract statistical features from the paving of wavelet packets at different depths

Training samples

Testing samples

Construction of the generic support vector regressive classifier

Rotating machinery health status evaluation

Sensitive feature selection with DET

Fault feature extraction

Sensitive fault feature selection

Fault pattern recognition

Fig. 5. Framework of the proposed intelligent machine fault diagnosisscheme.

Node

(1,0)

Node

(1,1)

Node

(2,0)

Node

(2,1)

Node

(2,2)

Node

(2,3)

Node

(3,0)

Node

(3,1)

Node

(3,2)

Node

(3,3)

Node

(3,4)

Node

(3,5)

Node

(3,6)

Node

(3,7)

Fig. 6. The paving of wavelet packets at the maximum depth of 3.

Table 1The nine statistical feature parameters.

Kurtosis: 1N

PNi¼1x4

i Skewness: 1N

PNi¼1x3

i

Crest factor: maxðjxi jÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

PN

i¼1x2

i

q Clearance factor: maxðjxi jÞð1NPN

i¼1

ffiffiffiffiffijxi jp

Þ2

Shape factor:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

PN

i¼1x2

i

q1N

PN

i¼1jxi j

Impulse indicator: maxðjxi jÞ1N

PN

i¼1jxi j

Variance: 1N

PNi¼1x2

iSquare root amplitude value:

ð1NPN

i¼1

ffiffiffiffiffiffiffijxij

pÞ2

Absolute mean amplitude value: 1N

PNi¼1jxij

C. Shen et al. / Measurement 46 (2013) 1551–1564 1555

carry out sensitive fault feature selection. Sensitive faultfeatures usually exhibit a small degree of variance for sam-ples belonging to the same class and a relatively large de-gree for those belonging to different classes. One of themost effective methods for measuring the different sensi-tivities of these features is the DET, and the proceduresof this method are presented in [19–21]. After an evalua-tion via DET, all fault features are evaluated by k�j and

ranked according to their values. Larger value means high-er sensitivity. Hence, once a threshold k�r is provided, thenthe fault features with higher sensitivities than the thresh-old will be selected for the further processing.

3.3. Fault pattern recognition using a generic multi-classsolver

As previously noted, conventional multi-class problemsare usually solved using a variety of binary classifiers. Themax-win strategy, for example, usually suffers from theproblem of equal votes. In addition, identifying the classof a k class problem, given an input vector xi belonging toclass l, would require k(k � 1)/2 binary classifiers. How-ever, the results obtained by the binary classifiers of classi and j have less meaning, which would conversely affectthe votes for class l.

A new classification strategy called the generic multi-class solver and based on basic SVR theory is proposedhere. SVR has great potential for constructing the nonlinearrelationship between input vectors and output values. Thefault feature vectors of samples belonging to the same classshould have similar values and thus produce outputs witha small degree of variance in the SVR model. Define theclass labels as 1,2, . . . ,C for a C class problem, and constructdataset fxi; yig

Ni¼1, where xi is an input feature vector,

yi 2 f1;2; . . . ; Cg is the target value, and N is the totalnumber of training samples. For a sample of the ith class,whose target value is i during support vector regressiveclassifier construction, the output of the SVR model shouldproduce a smaller deviation from i than that of a different

1556 C. Shen et al. / Measurement 46 (2013) 1551–1564

class. According to the foregoing illustration, the testedsample belongs to class m if m satisfies the following pro-posed decision-making function:

arg minm¼1;2;:::;M

m�Xn

i¼1

ðai � a�i ÞKðxi;XÞ þ b

!����������; ð12Þ

where M denotes the condition number, X is the fault fea-ture vector for the testing sample.

4. Experimental validation of the proposed intelligentmachine fault diagnosis scheme

Rolling element bearings and gearbox are the mostcommon and important components used in rotatingmachinery. Faults occurring on the surface of these compo-nents could cause unexpected machine breakdown. There-fore, it is necessary to develop an effective intelligentbearing and gearbox fault diagnosis method. To verify theeffectiveness of the proposed method, bearing fault dataprovided by the Case Western Reserve University and thegearbox data collected in the laboratory are analysed.

4.1. Case 1: The proposed scheme validated by bearing faultdata

The data provided by Case Western Reserve University[34] was collected from a test rig as shown in Fig. 7. Thesebearing fault signals have been widely used to validate theeffectiveness of new algorithms for bearing fault diagnosis[35,36]. The experimental setup mainly included a 2hp mo-tor (left), a torque transducer and a dynamometer (right).

Fig. 7. The bearing test stand.

Table 2Description of the bearing data.

Dataset Health status Defect size (inches) Loading (HP)

I Inner race fault 0.007 1Ball fault 0.007 1Outer race fault 0.007 1Health – 1

II Inner race fault 0.014 0Ball fault 0.014 0Outer race fault 0.014 0Health – 0

The motor shaft was supported by bearings with the typeof 6205-2RS JEM SKF. The bearing inner race, outer raceand rolling element were artificially seeded a single pointfault by electro-discharge machining, respectively. For aninner race localised fault, a rolling element localised faultand an outer race localised fault, the accelerometers wereused to sample vibration signals at 12 k Hz and installedat 12 o’clock, 12 o’clock and 6 o’clock positions at the fanend, respectively. Two groups of signals which includehealth and three different fault conditions are listed in Ta-ble. 2. As shown in Table 2, 90 samples for each conditionare acquired. 30 samples are used for training and the rest60 samples are used for testing. The labels for inner race,ball, outer race faults and health are set as 1, 2, 3 and 4for a SVR based model, respectively.

Two sets of data are used for analysis here. The firstdataset was collected under 1hp loading, and the defectsize of each fault was 0.007 in. The second dataset was ob-tained from components with a defect size of 0.014 in., butno loading. The two bearing datasets are processed accord-ing to the flowchart of the proposed intelligent fault diag-nosis scheme illustrated in Fig. 5. As a widely used waveletbasis function for machine fault diagnosis, db9 wavelet isemployed for the WPT step in this study. After WPT, 126statistical features are extracted from the 14 nodes at threedecomposition levels. To alleviate the computational bur-den and avoid the negative impact of non-sensitive fea-tures, the DET is applied to measure the sensitivities ofthese features. Fig. 8 shows the sensitivities of the 126 ex-tracted features. Larger values imply higher sensitivities.

The three thresholds for the first dataset are set at0.2039, 0.2531 and 0.4499. Accordingly, 72, 54 and 30 sen-sitive features are selected. Figs. 9–11 present the trainingand testing results obtained by the constructed SVR-basedfault diagnosis models. It is clear that because fewer fea-tures are selected by the DET, more useless features are re-moved, and samples belonging to the same health statusconverge better than results with more features. At thesame time, the proposed intelligent fault diagnosis modelretains a high degree of accuracy.

Fig. 12 depicts the sensitivities of the 126 extracted fea-tures from the second dataset. For the 72, 54 and 30 sensi-tive features selected, 0.0905, 0.1162 and 0.2884,respectively, are set as the thresholds. Figs. 13–15 presentthe training and testing results obtained by the con-structed SVR-based fault diagnosis models. Again, becausefewer features are selected by the DET, more useless fea-tures are removed, and samples belonging to the same

Training samples Testing samples Identification label

30 60 130 60 230 60 330 60 4

30 60 130 60 230 60 330 60 4

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Feature Number

Feat

ure

sens

itivi

ty

Fig. 8. Sensitivities of different statistical features extracted from thepaving of wavelet packets for dataset one.

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

(a) +Actual sample label

Fig. 9. For dataset I, the diagnosed results of (a) the training sampl

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

(a)+Actual sample label

Fig. 10. For dataset I, the diagnosed results of (a) the training samp

C. Shen et al. / Measurement 46 (2013) 1551–1564 1557

health status converge better than the results with morefeatures, and the proposed intelligent fault diagnosis mod-el remains highly accurate.

If a threshold increases, the fewer sensitive features willbe selected. Computational burden will be accordingly re-duced. If the sufficient number of sensitive features is usedto train a classifier, different fault patterns will be well dis-tinguished. However, when the number of sensitive fea-tures decreases to an extent, these features used forreflecting different machine health status may weakenthe linearity in high dimensional feature space mappedby the kernel function. Hence, this study has been pursuingthe balance between the computational burden and thefeature representative ability in order to ensure the highaccuracy. The relationship between the recognition rateand the feature number which is determined by thethreshold is investigated here in dataset two. As shownin Fig. 16, with the increasing of thresholds, the numberof features decreases; the recognition rate increases first,

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue(b)

*Model output value

es and (b) the testing samples with the selected 72 features.

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

(b)*Model output value

les and (b) the testing samples with the selected 54 features.

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

+Actual sample label *Model output value

(b)(a)

Fig. 11. For dataset I, the diagnosed results of (a) the training samples and (b) the testing samples with the selected 30 features.

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Feature Number

Feat

ure

sens

itivi

ty

Fig. 12. Sensitivities of different statistical features extracted from thepaving of wavelet packets for dataset II.

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

+Actual sample label

(a)

Fig. 13. For dataset II, the diagnosed results of (a) the training samp

1558 C. Shen et al. / Measurement 46 (2013) 1551–1564

and then keep high when the number of features variesfrom 48 to 30. However, the recognition rate decreases asthe number of features is less than 30. Hence, the numberof selected features is suitable for the cases in this paper.Moreover, the selected features whose sensitivity valueshave been presented in Figs. 8 and 12 are kurtosis, vari-ance, square root amplitude value and the absolute meanamplitude value. From the mathematical formulas of thesesensitive features, it is seen that kurtosis evaluateswhether the data are peaked or flat relative to a normaldistribution, variance measures the dispersion of a wave-form around its mean. The square root amplitude valueand absolute mean amplitude value are related to signalabsolute amplitudes and thus sensitive to the signal en-ergy. For different fault categories, the signal varies prom-inently in the signal amplitude distribution, impactinterval and energy, which have remarkable effect on thesefeatures.

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

*Model output value

(b)

les and (b) the testing samples with the selected 72 features.

0 20 40 60 80 100 1200

0.5

1

1.5

2

2.5

3

3.5

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4.5

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Labe

l val

ue

0 50 100 150 2000

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3

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4.5

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Labe

l val

ue

(b)(a)+Actual sample label *Model output value

Fig. 14. For dataset II, the diagnosed results of (a) the training samples and (b) the testing samples with the selected 54 features.

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Labe

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ue

(b)

+Actual sample label *Model output value

(a)

Fig. 15. For dataset II, the diagnosed results of (a) the training samples and (b) the testing samples with the selected 30 features.

20 25 30 35 40 45 50 55 60 65 700.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Number of selected features

Rec

ogni

tion

rate

Fig. 16. Depiction of the recognition rate with the change of the numberof selected features.

C. Shen et al. / Measurement 46 (2013) 1551–1564 1559

Table 3 summarises the results of the proposed method.It is clear that with an increase in the threshold, fewer sen-sitive features are selected, and the identified rate in-creases for each health status. The proposed intelligentfault diagnosis scheme achieves satisfactory performance.

To further validate the superior performance of the pro-posed scheme, the max-win strategy for multi-classifica-tion with the conventional binary SVM classifier isemployed here for comparison. Table 4 presents the diag-nosis results obtained by the conventional binary SVMclassifier. With the same features, multi-classificationbased on ‘one-against-one’ binary SVM classifiers achievesa lower degree of accuracy than the proposed method.

4.2. Case 2: The proposed scheme validated by gear fault data

To further validate the presented scheme, gearbox datacollected from an automobile transmission gearbox is

Table 3Bearing health status identification results obtained by the generic support vector regressive classifier.

Dataset Feature selection Inner race fault Ball fault Outer race fault Health

Thresholdvalue

Featurenumber

Identified rate Identified rate Identified rate Identified rate

Training(%)

Testing(%)

Training(%)

Testing(%)

Training(%)

Testing(%)

Training(%)

Testing(%)

I 0.2039 72 100 100 100 100 100 95 100 98.330.2531 54 100 100 100 100 100 100 100 1000.4499 30 100 100 100 100 100 100 100 100

II 0.0905 72 100 100 100 93.3 100 100 100 96.670.1162 54 100 100 100 96.67 100 100 100 1000.2884 30 100 100 100 98.3 100 100 100 100

Table 4Bearing health status identification results obtained by ‘one-against-one’ SVM classifiers.

Dataset Feature selection Inner race fault Ball fault Outer race fault Health

Thresholdvalue

Featurenumber

Identified rate Identified rate Identified rate Identified rate

Training(%)

Testing(%)

Training(%)

Testing(%)

Training(%)

Testing(%)

Training(%)

Testing(%)

I 0.2039 72 96.67 93.33 56.67 61.67 90 86.67 100 1000.2531 54 100 93.33 93.33 91.67 86.67 83.33 100 1000.4499 30 100 100 100 91.67 100 100 100 100

II 0.0905 72 100 93.33 36.67 46.67 100 93.33 100 1000.1162 54 100 98.33 70 65 100 100 100 1000.2884 30 100 95 93.33 81.66 100 96.67 100 100

Fig. 17. Description of gearbox vibration signal collection platform.

Table 5Specification of the third speed gears.

Gear Number ofteeth

Rotatingfrequency (Hz)

Meshingfrequency (Hz)

Driving gear 25 20 500Driven gear 27 18.5 500

Table 6The gearbox health status and their running periods.

Running cycle Health status Meshing times (thousand)

1 Running-in 0–7002 Normal wear 700–28003 Slight wear 2800–56004 Medium wear 5600–63005 Broken tooth 6300–7000

1560 C. Shen et al. / Measurement 46 (2013) 1551–1564

taken for another case study. The tested gearbox has onebackward speed and five forward speeds as shown inFig. 17. The vibration signals were collected by an acceler-ometer installed at the outer case of the gearbox during theautomobile was using the third pair of gears for forwardmotion. During the test, only the third speed gears wereused for wear process testing and their parameters are

listed in Table 5. The input rotating speed was set to1600 rpm and the sampling frequency was equal to3000 Hz. The gears experienced 5 running cycles duringthe running as shown in Table 6. At the beginning of thefifth cycle, a tooth broken fault occurred at the drivinggear.

Table 7Description of the gearbox datasets.

Dataset Healthstatus

Trainingsamples

Testingsamples

Identificationlabel

I Slightwear

30 30 1

Mediumwear

30 30 2

Brokentooth

30 30 3

Normalwear

30 30 4

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0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Feature Number

Feat

ure

sens

itivi

ty

Fig. 18. Sensitivities of different statistical features extracted from thepaving of wavelet packets for gearbox data.

C. Shen et al. / Measurement 46 (2013) 1551–1564 1561

As shown in Table 7, 60 samples are acquired for eachhealth status, half of which are used for training and halffor testing. In the construction of a SVR-based model, slightwear, medium wear, broken tooth and normal wear are la-belled as 1, 2, 3 and 4, respectively.

Similarly, the 126 features extracted from the paving ofthe wavelet packets are evaluated by the DET. The values

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0.5

1

1.5

2

2.5

3

3.5

4

4.5

Sample Number

Labe

l val

ue

(a)+Actual sample label

Fig. 19. For the gearbox dataset, the diagnosed results of (a) the training

that measure the sensitivity of these features are shownin Fig. 18.

Three thresholds are chosen: 0.5657, 0.6045 and0.6915. As a result, 72, 54 and 30 sensitive features areused in the subsequent procedures. Figs. 19–21 presentthe training and testing results obtained by the con-structed SVR-based models.

The results of the proposed scheme are summarised inTable 8, from which it can be seen that fewer featuresare selected with an increase in the threshold, and theidentified rate increases for each gearbox health status.

The max-win strategy for multi-classification with theconventional binary SVM classifier is employed to analysethe same data for comparison purposes. When the samefeatures are used as the SVM input, the identification rateof the classifiers based on the ‘one-against-one’ schemeas shown in Table 9 is lower than that of the proposedscheme.

5. Discussion on the effect of wavelet basis function onthe performance of the proposed scheme

In signal processing-based fault diagnosis, wavelet basisfunction selection is a particularly important step in pro-ducing better visual inspection ability for potential peri-odic transient identification [37]. To investigate theeffects of different wavelet basis functions on the perfor-mance of the proposed intelligent fault diagnosis scheme,representative wavelets are analysed, including the Haar(haar), Daubechies (db), Symlet (sym), Coiflet (coif), Bior-thogonal (bior), Reverse biorthogonal (rbio) and DiscreteMeyer (dmey) wavelets. In addition, 30 features are se-lected by the DET. The fault diagnosis results for the wholedataset including all health conditions are presented inTable 10.

These results indicate that employing the proposedscheme with different wavelet basis functions results indifferent fault recognition rates, and all demonstrate satis-factory performance because the features are extractedfrom the entire paving of the wavelet packets. They thus

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Labe

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samples and (b) the testing samples with the selected 72 features.

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Labe

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ue

(b)+Actual sample label *Model output value

(a)

Fig. 20. For the gearbox dataset, the diagnosed results of (a) the training samples and (b) the testing samples with the selected 54 features.

0 20 40 60 80 100 1200

0.5

1

1.5

2

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3

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Labe

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ue

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Labe

l val

ue+Actual sample label *Model output value

(b)(a)

Fig. 21. For the gearbox dataset, the diagnosed results of (a) the training samples and (b) the testing samples with the selected 30 features.

Table 8Gearbox health status identification results obtained by the generic support vector regressive classifier.

Feature selection Slight wear Medium wear Broken tooth Normal wear

Threshold value Feature number Identified rate Identified rate Identified rate Identified rate

Training (%) Testing (%) Training (%) Testing (%) Training (%) Testing (%) Training (%) Testing (%)

0.5657 72 100 90 100 100 100 100 100 1000.6045 54 100 100 100 100 100 100 100 1000.6915 30 100 100 100 100 100 100 100 100

Table 9Gearbox health status identification results obtained by ‘one-against-one’ SVM classifier.

Feature selection Slight wear Medium wear Broken tooth Normal wear

Threshold value Feature number Identified rate Identified rate Identified rate Identified rate

Training Testing Training Testing Training Testing Training Testing

0.5657 72 100 100 100 76.67 100 60 100 600.6045 54 100 100 100 96.67 100 46.67 100 900.6915 30 100 100 100 96.67 100 96.67 100 100

1562 C. Shen et al. / Measurement 46 (2013) 1551–1564

Table 10The rotating machine fault diagnosis results based on different wavelet selection for the proposed scheme.

Wavelet Bearing Gearbox

Dataset one Dataset two Dataset

Training Testing Training Testing Training Testing

haar 100 100 99.17 99.17 97.50 94.17db2 100 100 100 99.17 100 100db5 100 100 100 99.17 100 99.17db7 100 100 100 98.75 100 99.17db9 100 100 100 99.58 100 100db10 100 100 100 98.75 100 100db20 100 100 100 97.92 100 99.17db30 100 100 100 99.58 100 98.33db43 100 100 100 99.17 100 96.67db44 100 100 100 98.75 100 96.67sym1 100 100 99.58 99.17 97.50 94.17sym3 100 100 100 99.58 100 99.17sym6 100 100 100 99.58 100 100coif1 100 100 100 100 100 99.17coif3 100 100 100 99.58 100 100coif5 100 100 100 97.92 100 100bior1.1 100 100 99.58 99.17 97.50 94.17bior2.2 100 100 100 100 100 100bior4.4 100 100 100 98.75 100 100rbio1.1 100 100 99.58 99.17 97.50 94.17rbio2.2 100 100 100 99.17 100 98.33rbio3.9 100 100 100 98.33 100 98.33dmey 100 100 100 98.75 100 98.33

C. Shen et al. / Measurement 46 (2013) 1551–1564 1563

display great representative ability for different types ofrotating machine health status, and overcome the short-comings of those extracted from the wavelet packet nodesat a fixed decomposition level. Consequently, the proposedscheme is highly accurate in rotating machine faultdiagnosis.

6. Conclusions

In this paper, a new intelligent machine fault diagnosisscheme is proposed. The proposed scheme involves statis-tical parameters extracted from WPT paving, a DET for thedimensionality reduction of the feature space and a newmachine health status decision mechanism based on SVR.

First, to obtain more fault-related information from theoriginal vibration signals, the wavelet packet coefficients atdifferent decomposition depths (the paving of the waveletpackets) are determined. Then, statistical parameters areextracted from the wavelet packet paving. Second, theDET is employed to evaluate the sensitivity of the features.The fault pattern of the machine health status can thus beexpressed by a few features that represent the main char-acteristics of different types of machine health status. Fi-nally, to avoid the disadvantages of multi-classifiersconstructed using multiple binary classifiers, a singlehealth status identification mechanism is constructed onthe basis of SVR and the proposed decision function.

The results of investigation of both bearing and gearboxdatasets demonstrate the superior performance of the pro-posed intelligent machine fault diagnosis scheme relativeto the method based on binary multiple SVMs. Moreover,the results of analysis of the effects of different wavelet ba-sis functions on the performance of the proposed scheme

show it to achieve a high degree of accuracy in rotatingmachine fault diagnosis.

Acknowledgements

The work described in this paper was partly supportedby a Natural Science Foundation of China (Grant No.51075379) and a grant from the Research Grants Councilof the Hong Kong Special Administrative Region, China(Project No. CityU 122011). The authors would like tothank Professor K.A. Loparo of Case Western Reserve Uni-versity for his kind permission to use their bearing data.The authors also would like to appreciate two anonymousreviewers for their constructive comments andsuggestions.

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