Scooter Engine Wigner

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Expert Systems with Applications 36 (2009) 2187–2199

Expert Systemswith Applications

Application of Wigner–Ville distribution and probabilityneural network for scooter engine fault diagnosis

Jian-Da Wu *, Peng-Hsin Chiang

Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Road, Changhua City, Changhua 500, Taiwan, ROC

Abstract

An expert system for internal combustion engine fault diagnosis using Wigner–Ville distribution for feature extraction and probabilityneural network for fault classification is described in this paper. Most of the conventional techniques for fault signal analysis in amechanical system are based chiefly on the difference of signal amplitude in the time and frequency domains. Unfortunately, in someconditions the performance is limited, such as when analysis signals are non-stationary. In the present study, the Wigner–Villedistribution is proposed for sound emission signal features classification, because it provides high resolution of instantaneous energydensity both in time and frequency domains. Meanwhile, the instantaneous power spectrum is presented to obtain high-energy densitywhen the engine fault condition occurs. These features of signals are classified using the probability neural network. To examine the effi-ciency of the probability neural network, both back-propagation and radial basis function neural networks are used in comparison withfault classification. The experimental results showed all three networks can achieve high recognition rate with feature extraction usingWigner–Ville distribution method. It also suggested the probability neural network can complete training in an extremely short time.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Fault diagnosis system; Feature extraction; Wigner–Ville distribution; Neural network; Probability neural network

1. Introduction

Road vehicles have gradually become indispensabletransportation in people’s daily life. The safety and stabilityof road vehicles has received much attention in recent years.One of the most important road vehicle parts is the vehicleengine, which produces and controls the power for a vehicle.Therefore, monitoring vehicle engine condition is impor-tant. The advanced faults diagnosis system can prevent seri-ous damage, so the fault diagnosis system has developed alarge amount lately. Formerly, the vehicle faults diagnosisdepended on the experience of the technician but the con-ventional method is not a precise approach because of per-sonal subjectivity. It obviously shows the conventionalmethod is a time-consuming and personnel wastingapproach. An efficient and precise faults diagnosis systemis set up by automatic and complete computer system.

0957-4174/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2007.12.012

* Corresponding author.E-mail address: [email protected] (J.-D. Wu).

The feature extraction from the sound emission signal isone of the important procedures for engine fault diagnosis.In the past, Fourier analysis could present the signal charac-ters in frequency domain but could not show variation of sig-nal characteristic in the time domain. Although short timeFourier transform overcomes the above-mentioned problemthat can process signals with a time–frequency window (Bay-dar & Ball, 2001). Unfortunately, short time Fourier trans-form cannot describe the instantaneous energy densityspectrum of signals. The Wigner–Ville distribution is anacceptable algorithm that can improve the problem andhas been widely applied in energy-based features extractionin the time–frequency domain (He, 1998; Loutridis, 2006;Staszewski, Worden, & Tomlinson, 1997). In the presentstudy, Wigner–Ville distribution is used for the sound emis-sion feature extraction in an internal combustion enginefault diagnosis system. The energy density is clearlypresented in both the time and frequency domain with Wig-ner–Ville distribution and the vital features will be extractedfrom the instantaneous energy density spectrum.

mailto:[email protected]

Training procedure

Weight value Network structure

Recall procedure

Recognition result

Training procedure

Weight value Network structure

Recall procedure

Recognition result

Fig. 2. Operation procedure of probability neural network.

Σ

Σ

Σ

C

Input Layer Hidden Layer Output Layer

ResultsInputdata

ΣΣ

ΣΣ

ΣΣ

C

Input Layer Hidden Layer Output Layer

ResultsInputdata

Fig. 1. Architecture of probability neural network.

2188 J.-D. Wu, P.-H. Chiang / Expert Systems with Applications 36 (2009) 2187–2199

Research interest in mechanical fault diagnosis usingsound emission analysis has developed in the last few dec-ades. In the procedure of data analysis, several algorithmswere applied in the fault diagnosis expert system such asthe genetic algorithm (Wen & Chang, 1998), fuzzy logic(Ebrahim, 2001) and artificial neural networks (Kong &Chen, 2004; Olmez & Dokur, 2003; Yang, Han, & An,2004). In this study, artificial neural network is taken asthe classifier for the present faults diagnosis system. Inthe fault classification, three neural networks are used;they are the back-propagation neural network, radialbasis function neural network and probability neural net-work. Among these networks, back-propagation networkis the most popular multi-layer perception in an expertsystem but there are several defects like network struc-ture, local minimum and long training time which limitthe network performance (Parvoti & Anandarajan,2002). Although many improved structures for theback-propagation network have been developed, theireffects were restricted. Meanwhile, radial basis functionnetwork offers a more efficient training approach thatcan automatically organize its architecture in the trainingprocedure and its training procedure does not requireiteration calculation (Lai, Peter, Zhang, & Shi, 2004; Loo-ney, 2002). Even though radial basis function does notneed iteration calculation, the network requires muchmemory in the training procedure. However, the proba-bility network only needs one training epoch to completeits training procedure. It means the probability networkcan accomplish convergence in an extremely short timeand the network does not have the problem of back-prop-agation network structure (Cang & Yu, 2005; Hajmeer &Basheer, 2002; Karthikeyan, Gopal, & Vimala, 2005; Rut-kowski, 2004).

2. Principle of Wigner–Ville distribution for sound emission

signal

In this section, the features of sound emission signal arepresent by using Wigner–Ville distribution. They are usedas the inputs of neural networks for training and fault clas-sification. The Wigner–Ville distribution provides a highresolution of instantaneous energy density both in timeand frequency domains. For a signal x(t), the definitionof WVD is shown as

W zðt; f Þ ¼Z 1

�1xðt þ s=2Þx�ðt � s=2Þe�2pftds ð1Þ

where x*(t) means the complex conjugate of x(t). If x(t) is areal signal, the analytic signal is defined as follows:

~xðtÞ ¼ xðtÞ þ jxhtðtÞ ð2Þ

where xht(t) is the Hilbert transform of x(t), which is shownas

Signal extraction(NI DAQ 6024E)

Micro phone

Fiber optical sensorEngine revolution signal

Sound emission signal

Features extraction(WVD)

Fault diagnosis system(Neural networks)

Training

Testing

Signal extraction(NI DAQ 6024E)

Micro phone

Fiber optical sensorEngine revolution signal

Sound emission signal

Features extraction(WVD)

Fault diagnosis system(Neural networks)

Training

Testing

Fig. 3. Experimental setup of fault diagnosis system.

Fig. 4. Engine sound emission signal of idle without fault condition. (a) Time domain and (b) Wigner–Ville distribution.

J.-D. Wu, P.-H. Chiang / Expert Systems with Applications 36 (2009) 2187–2199 2189

Fig. 5. Engine sound emission signal of idle with belt damaged condition. (a) Time domain and (b) Wigner–Ville distribution.


xhtðtÞ ¼1

p

Z þ1

�1xðsÞ 1

t � sds ð3Þ

The Wigner–Ville distribution results of signal are usedas the input of this fault diagnosis system. Obviously, thecalculation quality of the system using Wigner–Ville distri-bution is huge in a practical sound emission application.Therefore, a reprocessing approach is proposed to decreasethe computation quantity of diagnosis system; it can bedescribed as

rðf Þ ¼Pt2�t1

n¼1 W zðt; f Þt2 � t1

ð4Þ

where r(f) stands for the point of time average in Wigner–Ville distribution. After reprocessing of Wigner–Ville dis-tribution, the domain of Wigner–Ville distribution data is

lower than a two-dimension data. The values of reprocess-ing approach will be used as the input to the neural net-work for training and testing of various neural networks;the principle of proposed neural network will be describedin the following section.

3. Fault diagnosis using probability neural network

3.1. Principle of probability neural network

The probability neural network (PNN) is a feed-forwardneural network with three layers. The architecture of PNNis shown in Fig. 1. The structure of PNN includes one inputlayer, one hidden layer and one output layer; the outputlayer contains summation and comparative units. Thereare several neurons in each layer and these layers are

Fig. 6. Engine sound emission signal of idle with intake air leakage condition. (a) Time domain and (b) Wigner–Ville distribution.


connected by weights. The performance of PNN embracestwo procedures: training and recall procedure. In the train-ing procedure, PNN utilizes the information of input datato organize network structure and sets weight values. ThePNN uses training input data to set up the weights (WIH)between input and hidden layer. When there are m clusterof p training data (Aj) with data length k in the PNN, thedefinition of WIH is presented as follows:

Aj ¼ ½a1; a2; a3; . . . ; ak�t ¼ W IH ¼ ½wij�i�j; i ¼ 1; 2; . . . ; p

aj ¼ wij

ð5Þ

where wij is the jth weight value of weight WIH. The PNNwill define the weight among the hidden layer and outputlayer (WHO) after it establishes WIH. WHO is shown as

wjc ¼1 if the jth sample 2 condition c

0 others

�ð6Þ

if the jth sample and the neuron belong to the same condi-tion c, the weight value is defined as 1 and others are 0.

In the recall procedure, the testing data is put into net-work for classification. At first, the weight WIH calculatesthe Euclidean norm (D) of testing and training data. TheEuclidean norm equation is described as

Dj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXðwij � xiÞ2

qð7Þ

where xi stands for the testing vector. Then, the Euclideannorm will be sent to the hidden layer for calculating theprobability density of each condition. The PNN adoptsthe Gaussian function as activation function in hiddenlayer, which is given as

Fig. 7. Engine sound emission signal of idle with clutch damaged condition. (a) Time domain and (b) Wigner–Ville distribution.


uj ¼ exp � Dj

2r2

� �¼ exp �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPðwij � xiÞ2

q2r2

0@

1A ð8Þ

where r is the spread parameter of the Gaussian function,this parameter controls the sensitivity of the Gaussianfunction. After computing all probabilities of each condi-tion, the weight WHO sends these probabilities to the out-put layer and estimates the classification result. Theoutput layer contains summation units and comparativeunits. Summation units assemble all probability densitiesand transmit them to comparative units for estimatingthe probability of each condition. Comparative units use‘winner takes all’ criterion to compare the probability den-

sity of each condition in the output layer, the criterion isshown as

V c ¼Xr

c¼1

ujwjc ð9Þ

P c ¼V cPrc¼1wjc

¼ 1Prc¼1wjc

Xr

c¼1

ujwjc ð10Þ

R ¼Max ðP cÞ; c ¼ 1; 2; 3; . . . ;m ð11Þ

where Vc is the input vector of comparative units, Pc

denotes the probability of each condition and R standsfor the result of comparative units output. Among compar-ative units, only one unit has the output value 1 with the

Fig. 8. Engine sound emission signal of idle with pulley broken condition. (a) Time domain and (b) Wigner–Ville distribution.


maximum probability density, other units are 0. Then, thenetwork will recognize the fault condition according to theresult of recall procedure. The operating procedure of PNNis described in Fig. 2.

3.2. Remarks of proposed neural network

Back-propagation (BP) neural network is one of thepopular multi-layer perceptions and generally be appliedin an expert system. Unfortunately, BP network requiresiteration calculation in a training procedure that is time-consuming and has local minimum trouble. Further, thearchitecture of BP network is another problem. Thestructure affects the training efficiency of network but itis difficult to obtain the ideal structure of BP network.

That demands repeated trial-and-error to get the suitablearchitecture and it is hard for a beginner. The radialbasis function (RBF) network provides a more efficienttraining approach, which avoids much computation qual-ity and local minimum trouble. Besides, RBF networkcan automatically establish the ideal network structurein a training procedure. Although the training approachof RBF network does not need a back-propagation pro-cedure, the network still requires a feed-forward proce-dure that consumes certain time. Moreover, the RBFnetwork demands lots of memory to store all parametersin a training procedure. However, PNN does not needany iteration calculation; it only needs one training epochto complete training that PNN can be converged with ashort time in the training procedure. The PNN can

Fig. 9. Reprocess features of Wigner–Ville distribution in idle with various fault conditions. (a) Without fault condition, (b) belt damaged condition, (c)intake air leakage condition, (d) clutch damaged condition and (e) pulley broken condition.


obtain the ideal network structure from the informationof training data that PNN does not need use muchmemory for storing the training parameters. The experi-mental comparison will be presented in the followingsection.

4. Experimental investigation of fault diagnosis system

In the experimental investigation, the scooter soundemission signals were analyzed to verify the proposed faultdiagnosis system as shown in Fig. 3. A scooter with an elec-

Fig. 10. Reprocess features of Wigner–Ville distribution in 2000 rpm with various fault conditions. (a) Without fault condition, (b) belt damagedcondition, (c) intake air leakage condition, (d) clutch damaged condition and (e) pulley broken condition.


tronic fuel injection system, single-cylinder, four-stroke,0.125-l internal combustion engine is used in this experi-ment. The sound emission signals are extracted by the con-denser microphone (PCB 130D20) and NI board (DAQ6024E) with 10 kHz sampling frequency. This experimentcomprises five engine conditions and five engine rotating

speeds, the five engine conditions are without fault inengine platform, belt damage, intake air leakage, clutchdamaged and pulley broken. The engine rotating speedsare: idle, 2000, 2500, 3000 and 3500 rpm. Each conditionof the time domain signal and Wigner–Ville distributionin the idle condition are indicated in Figs. 4–8.



In the signal processing, all experiment data aredivided into two parts because of the PNN adoptingsupervised learning. The experiment data are separatedinto the training and testing part. There are 48 data ineach condition, the number of training data is 8 andthe testing data is 40. After sound emission extraction,the vital features are extracted by Wigner–Ville distribu-

tion and normalized using Eq. (4). The whole databaseset is 48 � 6 of one engine rotating speed condition; asmentioned before, 8 � 6 data set are taken as trainingdatabase and others for testing data; all network trainingvectors are shown in Figs. 9–13. Obviously, differentfaults in the mechanical system occur with differentenergy in figures. Unfortunately, the conventional inspec-



tion is not a precise approach for damage diagnosis. Inthe present study, the energy amplitude figures of scootersound emission are used for the data bank in the pro-posed intelligent fault diagnosis system. All recognitionrates and training time using different network structures

are summarized in Table 1. Although, the result showsthe average recognition rates of three networks are over98%, however, the PNN can complete training in far lessthan 0.1 s. This means the proposed approach is workingand efficient.



5. Conclusions

In the present study, a prototype of an expert system forfault diagnosis in scooters platform using Wigner–Ville dis-tribution in sound emission signal features classificationand faults diagnosis using artificial neural network is pre-

sented. The approach improves the conventional methodwhich is performed according to the experience of techni-cians. The conventional method is not only time-consumingbut also a personnel wasting approach. The proposedapproach is an automatic and on-line fault diagnosis systemthat can improve the cost of fault diagnosis system and

Table 1Fault recognition rates using different neural network in various engine faults and operation conditions

BP RBF PNN

Idle 2000 2500 3000 3500 Idle 2000 2500 3000 3500 Idle 2000 2500 3000 3500

Without fault (%) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100Belt damaged (%) 97.5 97.5 100 100 100 92.5 100 97.5 100 97.5 92.5 100 97.5 100 97.5Intake air leakage (%) 100 100 95 97.5 100 100 100 100 100 100 100 100 100 100 100Clutch damaged (%) 97.5 100 100 100 100 100 100 100 100 100 100 100 100 100 100Pulley broken (%) 87.5 95 100 100 95 97.5 100 100 100 100 97.5 100 100 100 100

Averaged recognition rate (%) 98.50 99.40 98.88Training time (s) 8.109 0.61 0.094


reduce mistaken recognition. The experimental results showthe proposed fault diagnosis system with three differentneural networks can be effectively used in scooter diagnosisof various faults. However, PNN can accomplish thetraining procedure in an extremely short time and achievesatisfactory fault recognition rate in the experimentalplatform.

Acknowledgements

The work was supported by the National Science Coun-cil in Taiwan, Republic of China, under the project numberNSC- 96-2622-E-018-001-CC3.

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