A study of fault diagnosis in a scooter using adaptive order tracking technique and neural network

A study of fault diagnosis in a scooter using adaptive order

tracking technique and neural network

Jian-Da Wu

, Yu-Hsuan Wang

, Peng-Hsin Chiang

, Mingsian R. Bai

a_{Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Rd., Changhua City, Changhua 500, Taiwan} b_{Department of Mechanical Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan}

Abstract

An expert system for scooter fault diagnosis using sound emission signals based on adaptive order tracking and neural networks is presented in this paper. The order tracking technique is one of the important approaches for fault diagnosis in rotating machinery. The different faults present different order figures and they can be used to determine the fault in mechanical systems. However, many break-downs are hard to classify correctly by human experience in fault diagnosis. In the present study, the order tracking problem is treated as a parametric identification and the artificial neural network technique for classifying faults. First, the adaptive order tracking extract the order features as input for neural network in the proposed system. The neural networks are used to develop the training module and testing module. The artificial neural network techniques using a back-propagation network and a radial basis function network are pro-posed to develop the artificial neural network for fault diagnosis system. The performance of two techniques are evaluated and compared through experimental investigation. The experimental results indicated that the proposed system is effective for fault diagnosis under various engine conditions.

Ó 2007 Elsevier Ltd. All rights reserved.

Keywords: Fault diagnosis; Adaptive order tracking; Neural network; Back-propagation; Radial basis function network

1. Introduction

Rotating machinery such as the internal combustion engine and transmission system of a scooter can be monitored by measuring the vibration and sound emission signals for early fault diagnosis. Some digital signal pro-cessing technique using vibration and sound emission sig-nals already exist, such as visual dot patterns of sound emission signals (Shibata, Takahashi, & Shirai, 2000), wavelet analysis techniques (Lin & Qu, 2000; Wang & McFadden, 1996), and adaptive order tracking techniques (Lee & White, 1997; Vold & Leuridan, 1993). An order tracking technique based on a recursive least-square filter-ing algorithm in rotatfilter-ing machinery fault diagnosis was proposed in past research (Bai, Jeng, & Chen, 2002). The

adaptive order tracking technique was used to extracting the order of features with vibration and sound emission signals for fault diagnosis. Order amplitudes figures were calculated with high resolution after the experiment and signal processing. In order to classify the mechanical sys-tem’s fault, the order figures of various conditions must be carefully inspected. Unfortunately, it is hard to classify correctly by visual inspection and human experience because the features of some operation conditions are eas-ily confused. In such condition, an expert system with intel-ligent classification is necessary to improve the recognition rate and fault diagnosis.

A number of expert system techniques have been pro-posed, such as fuzzy logic techniques (Huang, Yang, & Huang, 1997; Mechefske, 1998), and artificial neural network techniques (Subrahmanyam & Sujatha, 1997). In the present study, a technique of automatic fault diag-nosis based on an artificial neural network is proposed. 0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.eswa.2007.09.015

*

Corresponding author.

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

www.elsevier.com/locate/eswa Expert Systems with Applications 36 (2009) 49–56

Expert Systems with Applications

An artificial neural network uses the massive simple con-nected artificial neurons to imitate the ability of a biolog-ical neural network. It obtains the information from the external environment or other artificial neurons, and per-forms the extremely simple operation. The above neurons will be combined and became a kind of neural network. The neural network must penetrate the training module and repeat to study, until all outputs can conform cor-rectly to the optimal targets. The entire neural network has very high fault tolerance as it acts to solve the question in operation. If the input material combines a small amount of noise disturbance, the correctness of the neural network is still not affected in the process. It only gave a partial the material, then they may obtain the complete material. There is good performance of the associative memory and excellent fault tolerance. If there are more training samples and the difference is bigger, the abilities of the neural networks are stronger in the neural network. The neural networks may construct the non-linear model and accept the different types of variable as reference inputs. This technique has strong compatibility and good promotion.

Currently, many scholars have proposed variously kinds of neural network models which develop different algorithms to solve different demands. The common neural networks include back-propagation (BP) network (Li, Yu, Mu, & Sun, 2006; Randall & Robert, 2000), Hopfield net-work (Sun, 2002), radial basis function (RBF) netnet-work (Pulido, Ruisanchez, & Rius, 1999; Stubbings & Huter, 1999), and so on. In the present study, the BP neural net-work and RBF neural netnet-work are used for this intelligent fault diagnosis system. Both the BP and RBF neural net-work will train order curve figures of the scooter with nor-mal and fault conditions under various operations for fault diagnosis. The effectiveness of the proposed system using two neural networks in scooter fault diagnosis is investi-gated and compared. The following sections describe the principle and experimental work of high resolution adap-tive order tracking technique and neural networks in the scooter fault diagnosis system.

2. Fault diagnosis system with neural networks

The principle of adaptive order tracking technique has been previously proposed and described (Wu, Huang, & Huang, 2004; Wu, Wang, & Bai, 2007). The analysis of the order tracking with the sound emission signal and engine speed can be calculated as the amplitude of the fre-quency-modulation. The order amplitudes figures can be calculated with high resolution after signal processing. In order to classify the fault of scooter platform, the sound emission signal is transferred conveniently to fine feature as input for this diagnosis system. The neural network is a smart system that learns the knowledge in the fault diag-nostic system. The principles of BP and RBF neural net-works used in the present study are described in following section.

2.1. Principle of BP neural network

The BP network structure is composed of one input layer, one output layer and several hidden layers. The num-ber of hidden layers is selected according to the degree of complication for the system. The structure of BP neural network is shown in Fig. 1. Neurons in the hidden layer are nuclei to influence the training result. Determining the number of the neurons is the most important factor in hidden layer. The BP neural network has feed-forward stage and back-propagation stages. The parameters of feed-forward stage are defined as

mg¼ f ðwgÞ; ð1Þ wg¼ X3 f¼1 Ufglf; ð2Þ nh¼ f ðwhÞ; ð3Þ wh¼ X5 g¼1 Vghmg; ð4Þ fðxÞ ¼ 1 1þ ex; ð5Þ

where mgand nhare the neuron output of the hidden layer

and the output layer, respectively. lf is the input vector,

wgand wh are the input of the gth neuron in the hidden

layer and the hth neuron in the output layer, respectively. Ufg and Vgh are the weight values between the input layer

and the hidden layer, the hidden layer and the output layer, respectively. f(x) is activation function. After the feed-for-ward stage, the BP network can not arrive at the optimum target, which is to minimize error in this structure. So the weight values are adjusted to decrease the expected error by the back-propagation stage. The BP neural network is designed to minimize error function in the weight space. The minimum error used to train the network is as follows: E¼ 1 2P Xh 1 Xp q¼1 ðnqh tqhÞ 2 ; ð6Þ

where nqhis the corresponding actual output and p is the

training sample number; tqh is the hth component of the

Input signals Input layer Hidden layer Output layer Output signals lf l₁ m_g n1 nh Ufg Vgh … … r … …

qth expected value. The weight values in back-propagation stage is defined as

Ufgðt þ 1Þ ¼ UfgðtÞ þ gdglf þ a½UfgðtÞ  Ufgðt  1Þ; ð7Þ

Vghðt þ 1Þ ¼ VghðtÞ þ gdhmgþ a½VghðtÞ  Vghðt  1Þ: ð8Þ

Here, g is the learning rate; a is the momentum coefficient; and dgand dhare learning signals as follows:

dg¼

Xh 1

Vghf0ðwgÞ; ð9Þ

dh¼ ðnh thÞf0ðwhÞ: ð10Þ

The network adjusts the weight value until the training re-sult arrives at the convergence conditions. When the condi-tion is convergent, the network finishes the procedure for the training module in the BP neural network.

2.2. Principle of RBF neural network

The RBF neural network is a feed-forward network with two layers and a structure is shown in Fig. 2. First, the input signals (xi) are sent to a hidden layer that is

com-posed of RBF neural units. The second layer is the output layer, and the transfer functions of the neurons are linear units. The transfer function of hidden layer is generally a non-linear Gaussian function which is shown in Fig. 3, and this equation is defined as

aj¼ aðvjÞ ¼ exp  v2 j 2r2 j ! ; ð11Þ

where rj is a width of the jth neuron, vj is presented by

Euclidean norm of the distance between the input vector and the neuron center calculated as follows:

vjðxÞ ¼ x  cj    ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xr i¼1 ðxi cj;iÞ 2 s ; i¼ 1; 2; . . . ; r; ð12Þ where cjis a center of the jth RBF unit.

The width of an RBF unit is selected as the root mean-square distance to the nearest jth RBF unit. For the jth unit, the width rjis defined as

rj¼ 1 e Xe h¼1 cj ch   2 !1=2 ; ð13Þ

where cjis a center of the jth RBF unit, c1, c2, . . . , ceare the

nearest unit centers to the unit j. And the output value is defined as

y_k ¼X

s

j¼1

djkaj; ð14Þ

where ykis the kth subsection of the y in the output layer,

djkis the weight from the jth hidden layer neuron to the kth

output layer neuron, and ajis the output of the jth node in

the hidden layer.

Training the RBF network involves determining the number of RBF units, the width of RBF units and the out-put layer weight values. The criterion is to minimize the sum of squared errors (SSE) defined as

SSE¼1 2 XS i¼1 X k ti_k yi kðX i_Þ  2 ; ð15Þ where ti

k are the expected values of the network output

in-put vector Xi, and S is the number of training samples. The number of hidden RBF units is an important factor to determine the predictive properties of the network. The number of hidden units is calculated automatically until the expected SSE value in this research is found. The neural network uses various numbers of RBF units to evaluate the best predictive property. The hidden layer determines the number of RBF units and the width of RBF unit. After procedure of the hidden layer, the network has one weight value connected to the output layer. The output layer weight value is trained by linear squares regression. 3. Experimental investigation and Implementation of neural networks

3.1. Experimental arrangement of scooter platform

An experimental investigation is used to verify the pro-posed adaptive order tracking with neural networks for the fault diagnosis in scooter platform. Using the adaptive order tracking approach analyzes sound emission signal djk Input signals Hidden layer Output layer Input signal (x2) Input signal (x1) Input signal (xi) … j a k y y1 … r Input signal (x2) Input signal (x1) Input signal (xi) … k y y1 ……

Fig. 2. Structure of RBF neural network.

for extracting its order features, and neural networks utilize order features to classify fault clusters under various oper-ating conditions. The experimental arrangement and proce-dure of the scooter fault diagnosis system are shownFig. 4. In this experimental arrangement, a scooter platform with an electronic fuel injection system engine is used. A con-denser microphone (PCB 130D20) is utilized to measure the sound emission of the scooter. A fiber optical sensor (PW-PH02) is employed to extract the crankshaft speed and angular displacement of the engine as reference inputs of the order tracking procedures in the diagnostic system. In this research, five engine operation conditions of the scooter are designed in the experimental procedure. These conditions include no fault in the platform, pulley dam-aged, belt damdam-aged, air leakage of the intake manifold and clutch damaged. In the experimental work, the engine is operated in idling condition (1700 rpm), 2000 rpm, 2500 rpm, 3000 rpm, 3500 rpm and run-up test condition. The shaft speed of the engine in the run-up test condition is shown inFig. 5.

3.2. Evaluation of neural networks in fault diagnosis system After the measurement of the experimental work, the adaptive order tacking technique is used to establish the different order figures from the dynamic sound emission signals. The frequency normalized is defined as the sound emission features with various engine crankshaft speeds. The order amplitude figures under the idle condition

with-out any fault in the scooter platform are shown inFig. 6, which presents the first ten order amplitude figures. Then each order figure is converted into an averaged value. The averaged value of each order is defined as

Ku¼

RAs

Nt

; ð16Þ

where Asis a point of every order amplitude, and Ntis the

number of points in the order figures. The order figure is then converted into the order curve figure of average value, as shown inFig. 7. The order curve figure is convenient to be a feature as input for neural networks in this diagnostic system.

After the procedure of extraction, the neural networks approach is used in the proposed scooter fault diagnosis. In the present study, both BP network and RBF network are evaluated for the proposed system, worked in both training module and testing module. The process of the proposed neural network is shown in Fig. 8. The neural networks use the knowledge base to train data and then utilize the testing engine to verify the experimental results. In the scooter experiment, 10 data sets are used to train various faults in neural network, and 40 testing data sets are used to verify the results of training under various engine operating conditions. The training module is the most important procedure in the neural network. The two networks have different training techniques and differ-ent structures for the training module, but they have the same testing module to verify the training results in the testing module.

The principle of BP neural network training has been introduced and the process of the training block diagram is shown inFig. 9. First, the BP network decides the train-ing structure, is composed of one input layer, one hidden layer and one output layer. Training of the BP network establishes some initial conditions, including the number of neurons, the convergence condition and the expectation output. In particular, determining the number of the neu-rons is the crucial factor for the hidden layer. If too many neurons are used, it is difficult for the network to converge and training time is increased. When using too few neu-rons, it leads to poor efficiency. Determining the number of neurons in the hidden layer according to human experi-ence is necessary. After deciding the initial conditions, the

NI DAQ 6024E

Data record system

Fiber optical sensor

Microphone CVT system engine Feature extraction Order tracking Fault Diagnosis Neural network

Fig. 4. Experimental arrangement and procedure of the scooter fault diagnosis system. 0 1 2 3 4 5 6 0 1000 2000 3000 4000 5000 Time (sec) Shaft speed (rpm)

feed-forward stage and back-propagation stage are used to adjust the weight values continuously until the result of training module arrives at the convergence condition and the expect output. If the result of training module can not converge, the initial conditions will be emended. When the condition is convergent, they finish the procedure of training module in the BP neural network.

Similar to the BP neural network, the RBF neural net-work is also used for the training structure, which involves in a hidden layer and an output layer. The training struc-ture of the RBF network is simpler than BP network. Fig. 6. Order figures displayed for engine at idle condition.

Fig. 7. Order curve figure displayed for engine speed at idle condition.

Tachometer signals

Order tracking Testing module of

neural network Decision

Features Well-known Knowledge Training module of neural network Microphone signals

Fig. 8. Experimental procedure and neural network of the scooter fault diagnosis system.

Decide network structure

Initialization

Feed forward stage

Back-propagation (Calculate weight value) Check converge condition

Arrive expected output

Yes

No

The feed-forward stage is used to calculate the result of output in the training RBF network. The hidden RBF unit is a key factor to decide the predictive properties of the net-work. The hidden layer is composed of the number of RBF units and the width of RBF units. The number of hidden units is calculated automatically, and the RBF units are increased one by one until the expected output is found. The width of each neuron can be determined for the suit-able form. From the result of various numbers and width ones estimate the best predictive property in neural net-work. After the procedure for the hidden layer, the output layer weight value is trained by linear squares regression

approach. This structure combines the result of the hidden layer and output layer to finish the training module in the RBF neural network. After the procedure for the training module, the testing engine is used to verity the training results in the neural networks. The results and discussion will be presented in following section

4. Results and discussion

The results of the proposed fault diagnosis system applied in a motor scooter platform under various operat-ing condition with both BP and RBF neural networks is

Order 0 1 2 3 4 5 6 7 8 9 10 Order 0 1 2 3 4 5 6 7 8 9 10 Order 0 1 2 3 4 5 6 7 8 9 10 Order 0 1 2 3 4 5 6 7 8 9 10 Order 0 1 2 3 4 5 6 7 8 9 10 Order 0 1 2 3 4 5 6 7 8 9 10 Magnitude (dB) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Without fault Pulley damged Belt damged Air leakage Clucth damaged Magnitude (dB) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Magnitude (dB) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Magnitude (dB) 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Magnitude (dB) 0.00 0.02 0.04 0.06 0.08 Magnitude (dB) 0.00 0.02 0.04 0.06 0.08 0.10 0.12

a

b

c

d

e

f

presented in this section. Firstly, the order amplitude figures have been established, and the order figures are transferred to order curve features as input in the neural network of fault diagnosis system. However, the different faults occur with different properties of the order curve fig-ure in the mechanical system. The order curve figfig-ures of order tracking in various conditions are summarized in Fig. 10. By observing the figures for normal conditions, pulley damaged, belt damaged, intake air leakage and clutch damaged conditions under various engine operating conditions are indicated by the different lines.

The results of fault classification under various engine operating conditions using the BP and RBF neural net-works are summarized in Tables 1 and 2. The results of BP and RBF neural network have an acceptable recogni-tion rate for fault classificarecogni-tion in various fault condirecogni-tions. In particular, the results of RBF neural network are more efficient than the BP neural network for classifying fault clusters in this system, and the best recognition rate of RBF neural reaches 100% under several engine operating conditions. Meanwhile, the initial condition of RBF neural network only defines expected output, and the number of hidden units is calculated automatically and trained to expected target more conveniently. However, the initial conditions of the BP neural network include the number of neurons, the convergence conditions and the expected output. In particular, determining the number of neurons by a trial and error approach will take too much time and present difficulty for the optimal training target. The BP neural network has feed-forward stage and back-prop-agation stage, while the RBF only has a feed-forward

stage. The RBF neural network has a simple structure for the training module, and there are fewer calculations than the BP neural network. So the RBF neural network needs less associative memory, although the learning speed and the convergence rate are very rapid. The characteristic comparison between BP and RBF neural networks in this fault diagnosis system are summarized inTable 3. Accord-ing to the summation of the above advantages and experi-mental results, the RBF neural network is more efficient than the BP neural network for fault diagnosis although the BP neural network can find the optimal final parame-ters for training module and presents an acceptable recog-nition rate.

5. Conclusions

The present study describes a fault diagnosis system using acoustic emission signals with an adaptive order tracking technique and neural networks for a scooter plat-form. The adaptive order tracking extracts the order fea-tures as input for a neural network in the proposed fault diagnosis system. The neural networks have property of self-learning to cluster together for the same order features. This intelligent system establishes the training module and testing module. The experimental results indicate that the proposed system has great probability for accuracy in fault diagnosis under various operation conditions.

Acknowledgement

The study was supported by the National Science Coun-cil of Taiwan, the Republic of China, under Project Num-ber NSC-95-2622-E-018-001-CC3.

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Table 3

Characteristic comparison between BP and RBF neural networks in fault diagnosis system

Characteristics Neural network

BP RBF

Structure Complex Simple

Initial conditions Some One

Training type Feed-forward stage, back-propagation stage

Feed-forward stage

Calculation quantity Large less

Determining number of neurons

Trial and error Automatic

Convergence speed (Training time)

Tardy (long) Rapid (short)

Recognition rate Acceptable Excellent

Table 2

Results of fault diagnosis system using RBF neural network at various fault conditions

Engine operation

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Results of fault diagnosis system using BP neural network at various fault conditions

Engine operation

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