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An expert system for fault diagnosis in internal combustion engines using wavelet packet transform and neural network
Expert Systems with Applications 36 (2009) 4278–4286
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
An expert system for fault diagnosis in internal combustion engines using wavelet packet transform and neural network Jian-Da Wu *, Chiu-Hong Liu Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Road, Changhua City, Changhua 500, Taiwan, ROC
a r t i c l e
i n f o
Keywords: Wavelet packet transform Neural network Fault diagnosis Sound emission signal
a b s t r a c t In the present study, a fault diagnosis system is proposed for internal combustion engines using wavelet packet transform (WPT) and artificial neural network (ANN) techniques. In fault diagnosis for mechanical systems, WPT is a well-known signal processing technique for fault detection and identification. The signal processing algorithm of the present system is gained from previous work used for speech recognition. In the preprocessing of sound emission signals, WPT coefficients are used for evaluating their entropy and treated as the features to distinguish the fault conditions. Obviously, WPT can improve the continuous wavelet transform (CWT) used over a longer computing time and huge operand. It can also solve the frequency-band disagreement by discrete wavelet transform (DWT) only breaking up the approximation version. In the experimental work, the wavelets are used as mother wavelets to build and perform the proposed WPT technique. In the classification, to verify the effect of the proposed generalized regression neural network (GRNN) in fault diagnosis, a conventional back-propagation network (BPN) is compared with a GRNN network. The experimental results showed the proposed system achieved an average classification accuracy of over 95% for various engine working conditions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The condition monitoring and fault diagnosis in a mechanical system is important for avoiding serious damage. The internal combustion engine is classical rotating machinery that must be operated under various conditions for different performance needs. Sound emission and vibration signal of engine often give much dynamic information of mechanical system condition. The signal analysis has been set up as one of the useful methods for fault diagnosis. Many useful techniques for signal analysis have been proposed such as fast Fourier transform (FFT) (Corinthios, 1971), higher-order statistics (HOS) (Swami, Giannakis, & Zhou, 1997), and adaptive order-tracking (Bai, Huang, Hong, & Su, 2005; Wu, Huang, & Huang, 2004). Nonetheless, the fault diagnosis system of sound emission or vibration signals analysis is stressed in the time-frequency domain information. There are many other techniques that have been developed such as the short time Fourier transform (STFT) (Portnoff, 1980), Wigner–Ville distribution (WVD) (Andria, Savino, & Trotta, 1994; Staszewski, Worden, & Tomlinson, 1997) and wavelet transform (WT) (Chen, Sun, Zhang, & Wang, 2005; Lin & Qu, 2000; Prabhakar, Mohanty, & Sekhar, 2002; Serhat & Emine, 2003; Tse, Yang, & Tam, 2004; Wu & Chen, 2006; Zheng, Li, & Chen, 2002) . All the techniques were developed * Corresponding author. E-mail address: [email protected] (J.-D. Wu). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.03.008
successfully, but WT is the best of these tools because STFT only provides a constant time-frequency resolution and WVD produces interference terms on the time-frequency domain in a critical condition. The WT can be divided into continuous wavelet transform (CWT) and discrete wavelet transform (DWT). In 2000, Lin and Qu used vibration signals for the feature extraction and fault diagnosis based on the Morlet wavelet (Lin & Qu, 2000). In 2002, Zheng et al. published a gear fault diagnosis method based on continuous wavelet transform and proposed a new concept of time-averaged wavelet spectrum (TAWS) for reducing the huge operand (Zheng et al., 2002). In 2004, Tse et al. designed an innovative wavelet which called exact wavelet analysis to improve the robustness of vibration-based machine fault diagnosis (Tse et al., 2004). In 2006, Wu and Chen used a continuous wavelet transform algorithm for fault signal diagnosis in an internal combustion engine (Wu & Chen, 2006). All these studies are useful examples of the CWT approach. Unfortunately, CWT has a huge operand and requires a long time to use. Therefore, the DWT has been developed to improve the drawback of CWT by using the decomposition of the original complex signal to several resolutions. (Prabhakar et al., 2002; Serhat & Emine, 2003). In 2005, Chen et al. proposed a stress wave (SW) method based on wavelet analysis of low-speed rolling bearings (Chen et al., 2005). Unfortunately, the DWT is not a suitable method for analyzing the signal that contains a much higher frequency band. Alternatively, wavelet packet transform
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(WPT) provides the same frequency bandwidths in each resolution for recording the feature under each frequency bands. Meanwhile, the WPT working speed is faster than the traditional DWT. Applications of WPT are widespread such as speech recognition, electroencephalogram, fault detection and diagnosis. In 2000, Liu et al. proposed a unique technique using vibration signals for diesel engine diagnosis by WPT analysis (Liu, Du, & Yang, 2000). In 2002, Nikolaou and Antoniadis also used vibration signal for bearings with localized defects (Nikolaou & Antoniadis, 2002). In 2004, Meng et al. used WPT to analyze the signal when operating circuit breakers (Meng, Jia, & Rong, 2004). In 2005, Hu et al. proposed a novel and simple method to extract the feature from surface EMG signals based on WPT which the features are the relative wavelet packet energy (RWPE) evaluated by several selected frequency bands (Hu, Wang, & Ren, 2005). In 2006, Avic and Akpolat developed an expert system for speech recognition (Avic & Akpolat, 2006). In the study, wavelet packet adaptive network-based fuzzy inference system was proposed combining feature extraction and classification for real speech signals. In the present study, a fault diagnosis system using sound emission signals based on WPT and a neural network for internal combustion engine is proposed. The wavelet packet used the Daubechies, 1988 wavelet ‘‘db4”, ‘‘db8” and ‘‘db20” as mother wavelets to build and perform the proposed WPT technique for extracting the information of engine fault signals. Also, the signals are collocated and then use the ‘‘Shannon entropy” for features of fault signals. Finally, the neural network is used to recognize the engine running conditions and fault classification in five synthetic faults. The principle of the proposed WPT and neural network in the present study is described in the following sections.
tion within the original signals. Therefore, the signal with great quantity of middle and high frequency signals can offer superior time-frequency analysis. The WPT suits signal processing, especially nonstationary signals because the same frequency bandwidths can provide good resolution regardless of high and low frequencies. The principle of WPT can be described as follows (Li, Song, & Li, 2004; Ortiz & Syrmos, 2006; Yen & Lin, 2000). The WPT is a generalization of the wavelet transform and the wavelet packet function is also a time-frequency function, it can be defined as j
W nj;k ðtÞ ¼ 22 W n ð2j t kÞ;
ð1Þ
where the integers j and k are the index scale and translation operations. The index n is an operation modulation parameter or oscillation parameter. The first two wavelet packet functions are the scaling and mother wavelet functions: W 00;0 ðtÞ ¼ /ðtÞ;
ð2Þ
W 10;0 ðtÞ
ð3Þ
¼ wðtÞ:
When n ¼ 2; 3; . . . the function can be defined by the following recursive relationships: pffiffiffi X W 2n 2 hðkÞW n1;k ð2t kÞ; ð4Þ 0;0 ðtÞ ¼ k
pffiffiffi X 2 gðkÞW n1;k ð2t kÞ;
2nþ1 ðtÞ ¼ W 0;0
where hðkÞ and gðkÞ are the quadrature mirror filter (QMF) associated with the predefined scaling function and mother wavelet function. The wavelet packet coefficients, wnj;k are computed by the inner product hf ðtÞ; W nj;k i where defined as Z wnj;k ¼ hf ðtÞ; W nj;k i ¼ f ðtÞW nj;k ðtÞdt: ð6Þ
2. Principle of wavelet packet transform and feature extraction 2.1. Wavelet packet transform
The framework of WPT algorithm broken up to three resolution levels is shown in Fig. 1. In the figure, S03 presents the symbol for a subspace that stands for the third resolution and the 0th subspace. In the present study, the sound emission signals will be broken up to four resolutions ðj ¼ 4Þ. As a result, four resolutions will produce sixteen subspaces and the frequency intervals of each subspace can be computed by (Hu et al., 2005):
The structure of wavelet packet transform (WPT) is similar to discrete wavelet transform (DWT). Both have the framework of multi-resolution analysis (MRA). The main difference in the two techniques is the WPT can simultaneously break up detail and approximation versions, but DWT only breaks up as an approximation version. Therefore, the WPT have the same frequency bandwidths in each resolution and DWT does not have this property. The mode of decomposition does not increase or lose the informa-
i ðn 1Þ2j1 fs ; n2j1 fs ;
n ¼ 1; 2; 3 . . . ; 16;
G:
H:
h (k )
g (k )
↓2
Low pass filter and decimation
↓2
High pass filter and decimation
S00 G
H
S11
S10 H
G
S20 H
S30
H
S 21 G
S31
H
S32
G
S 23
S 22 G
S33
ð5Þ
k
H
S34
G
S35
H
S36
G
S37
Fig. 1. Tree structures of wavelet packet transform, S03 represents the third resolution and the 0th subspace (Yen & Lin, 2000).
ð7Þ
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where fs is sampling frequency. For example, in this work fs ¼ 5000 Hz, S00 is the original signal with the frequency interval ð0; 21 fs ¼ ð0; 2500, S03 with the frequency interval (0, 312.5], S73 with the frequencies interval (2187, 2500]. The wavelet packet transform is used regarding the data preprocessing for fault diagnosis.
input
Radial Basis Layer Q× R
IW1,i
Q×Q
LW 2,i
P R ×1
dist
En ¼
16 X
n2 wn2 j;k logðwj;k Þ;
n¼1
where wnj;k is the coefficients of the subspace after wavelet packet decomposition and n ¼ 0; 1; 2; . . . ; 15 (Avic & Akpolat, 2006). The low frequencies in Shannon entropy of E0 will not used because it probably contains massive noise. Therefore, a feature vector T that is composed of En can be expressed as T ¼ ½E1 ; E2 ; . . . E14 ; E15 :
ð9Þ
To classify the different faults of engine by neural network, the feature vector T will be adopted in fault classification.
3. Principle of neural network classifier for fault recognition In the present system, a recognition method for engine fault condition using neural networks is examined to evaluate the effectiveness of the proposed system. In the artificial neural network (ANN) so far, back-propagation neural network (BPNN) is the most basic type and the most representative of the neural network. The framework of BPNN can be divided into three layers: input layer, hidden layer and output layer. The basis principle of BPNN is using the gradient steepest descent method to use the error between output and target of network to adjust the weight repeatedly. The error is used to adjust the weight till the error is smaller than a threshold or when expecting times with recurring learning. Finally, use the data which completes training of the network classifica-
1
1
*
ð8Þ
a2 = y
Q×1
2.2. Feature extraction of fault conditions using Shannon entropy In the present study, the feature of ‘‘Shannon entropy” will be used in various fault conditions after data preprocessing of wavelet packet transform. Entropy is a common idea used in many fields, especially in signal processing (Zhang, Walter, Miao, & Lee, 1995). Wavelet packet decomposition is applied to the engine fault signal using the ‘‘db4”, ‘‘db8” and ‘‘db20” wavelet packet filters w with the ‘‘Shannon entropy” and is defined as
Specail Linear Layer
n
a
Q×1
Q×1
Q×1
2
Nprod
a
Q×1
b1
1
Q×1
R
Q
Q
Fig. 2. Structure of GRNN (Yibin & Ying, 2005).
tion. Then, input the test model in order. The network may export the test result. BPNN has high learning precision, fast recall and wide application. Although it has these merits, BPNN also has many flaws such as: existence of local minimum, improper learning rate and a network unable to achieve convergence. To improve these drawbacks, some ANNs have been developed. In 1988, Specht proposed a new neural network called PNN (Specht, 1988). PNN only suits the classified problem but is unable to solve the continual variable problem. To solve the flaw of PNN, the GRNN was proposed by Specht (1991). The GRNN speed is very quick because it does not need an iterative training for converging to a wanted solution. Fig. 2 shows the structure of GRNN which contains three layers: input layer, hidden layer (radial basis layer) and output layer (special linear layer). GRNN adopts direct mapping from the input cell to the hidden layer, but between the hidden layer and the output layer the mapping adopts the linearly weighted sum of hidden layers as the mapping mode (Yibin & Ying, 2005). GRNN is not similar to regression analysis of the traditional method that needs to suppose exact function. It only needs the method of probability density function (PDF) to be presented. The principle of GRNN was described in previous work by Specht (1991), f ðx; yÞ stands for the known joint continuous PDF of a vector random variable x and a scalar random variable y. The conditional mean of y given X (also called regressing y on X) is given by Z 1 Z 1 yf ðX; yÞdy= f ðX; yÞdy: ð10Þ E½yjX ¼ 1
Fig. 3. Experimental structure of engine fault diagnosis system.
1
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Signal
Feature extraction
Wavelet Packet Decomposition
E1
E2
E16
E3
Classification
BPN and GRNN
without fault, air leakage, cam-shaft sensor fault, ECT sensor fault, one-cylinder miss-fire, two-cylinder miss-fire
If the density f ðx; yÞ is unknown, it must usually be estimated from a sample of observation of x and y. The probability estimator ^f ðX; YÞ is based on the sample values X i and Y i of the random variables x and y, where n is the number of sample observations and p is the dimension of the vector variable x: " # n 1 1 X ðX X i ÞT ðX X i Þ ^f ðX; YÞ ¼ exp 2r2 ð2pÞðpþ1Þ=2 rðpþ1Þ n i¼1 " # ðY Y i Þ2 exp ; ð11Þ 2r2 where the r is the smoothing parameter (sigma weight) and defining the scalar function D2i as D2i ¼ ðX X i ÞT ðX X i Þ:
ð12Þ
Combining Eqs. (10)–(12) an estimation of conditional mean shown ^ by Specht, named YðXÞ, can be written as !, ! n n X X D2i D2i i ^ ð13Þ Y exp 2 exp 2 : YðXÞ ¼ 2r 2r i¼1 i¼1
Fig. 4. Structure of the engine diagnosis system for fault classification.
A1
B1
0.5
1 0.5
Shannon entropy
0
2
4
6
8
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14
0
2
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A2
8
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1 0.5
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8 B3
0.5
1 0.5
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2
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10
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14
0
2
4
6
8
Number of subspaces Fig. 5. Entropy diagrams of using mother wavelets ‘‘db4”, ‘‘db8” and ‘‘db20” to construct WPT without fault, A1–A3 represents in idle condition; B1–B3 represents in run-up condition.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
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10
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14
0
2
4
cam-shaft sensor fault 0.4
0.4
0.2
0.2
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2
one cylinder miss-firing 0.4
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wo cylinders miss-firing
0.4
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ECT sensor faul
14
0
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8
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14
Number of subspaces Fig. 6. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in idle condition.
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When the smoothing parameter r is enlarged, the estimated density is forced to be smooth and in the limit becomes a multivariate Gaussian with covariance r2 I. On the other hand, a smaller value of r allows the estimated density to assume non-Gaussian shapes, but with the hazard that wild points may have too great an effect on the estimate (Specht, 1991). 4. Experimental investigation and classification of sound emission signals 4.1. Experimental work and signal processing To estimate the proposed fault diagnosis system, experiments are carried out to measure the sound emission signals for various engine running conditions. The sound emission signals were recorded by a data acquisition system. Subsequently, we analyzed the sound emission signals using the WPT algorithm and then extracted the feature vector by ‘‘Shannon entropy”. The experimental setup of engine fault diagnosis system is shown in Fig. 3. The equipment for the experiment included an internal combustion
engine (Mitsubishi V type, four-stroke, six cylinders, 3.0-L gasoline direct-injection (GDI)), an optical encoder (PW-PH02), a microphone (PCB 130D20), a dynamic signal analyzer (SR785) and a data acquisition system (Hardware: NI-6024E; Software: Lab-view). The microphone is used to measure the sound emission signal from the experimental platform. To know the revolution of the engine, an optical encoder is set up to close the crankshaft. Both of the signals can be recorded by a data record system and can be seen with a dynamic signal analyzer. The sampling rate of the data acquisition system is set at 5 kHz. In the experimental work, six conditions are designed to estimate the proposed fault diagnosis system. They include an engine without any fault, air leakage of the intake manifold, camshaft sensor fault, electronic control thermal (ECT) sensor fault, one cylinder misfiring, and two cylinders misfiring. The engine is run in the idle condition (750 rpm), 2000 rpm and run-up (from idle condition accelerate to 3500 rpm) conditions. In particular, the run-up test highlighted WPT is able to provide good resolution when the signal suddenly changes. Fig. 4 shows the structure of the engine diagnosis system for fault classification.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
8
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12
14
0
2
4
cam-shaft sensor fault 0.4
0.4
0.2
0.2
0
2
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0
2
one cylinder miss-firing 0.4
0.2
0.2
2
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10 1 12
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two cylinders miss-firing
0.4
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 7. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in idle condition.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
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10
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14
0
2
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cam-shaft sensor fault 0.4
0.4
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2
one cylinder miss-firing 0.4
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2
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8
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14
two cylinders miss-firing
0.4
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 8. Entropy diagrams of using mother wavelet db20 to construct WPT with various faults in idle condition.
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4.2. Faults classification The Daubechies, 1988 wavelets ‘‘db4”, ‘‘db8” and ‘‘db20” are the mother wavelets to build and perform the proposed WPT technique. Fig. 5 shows the results of idle (A1–A3) and run-up (B1– B3) conditions after being computed and represented by the ‘‘Shannon entropy”. The horizontal axis stands for the number of subspaces and vertical axis stands for the size of the ‘‘Shannon entropy”. The variation of each subspace can be seen. Further, the differences can be obviously seen between ‘‘db4”, ‘‘db8” and ‘‘db20”. This showed the use of these three kinds of mother wavelets to analyze and produce the different results. In this investigation, the lower frequencies ‘‘Shannon entropy” (E0 that computed by S04 ) are not used because it probably contains massive noise. Figs. 6–8 show the entropy diagrams of using three different mother wavelets to build WPT with various faults in the idle condition. The variations of entropy in different conditions are easy to discriminate from the figures. Figs. 9–11 show the entropy diagrams of using three different mother wavelets to build WPT with various
faults in an engine run at 2000 rpm. Figs. 12–14 show the entropy diagrams of using three different mother wavelets to build WPT with various faults in an engine operated in a run-up condition. To understand the effectiveness of the proposed system, signals are used to classify by the BPN and GRNN after feature selection of ‘‘Shannon entropy”. The features of ‘‘Shannon entropy” in each fault condition are summarized for the input of the neural networks. The number of experimental data in each operation condition is 150. The 30 data sets are used to training and the 120 data sets are used to test the recognition rate of the proposed network. The recognition rate is defined as the rate of total number of tests and correct classification. Tables 1–3 summarized the recognition rate of three different engine operation conditions using both the BPN and GRNN algorithms. All the recognition rates are over 95%. In the tables, although both of the BPN and GRNN achieved effectiveness in the recognition, however, GRNN spent less time than BPN in classification. The experimental results show the proposed WPT fault diagnosis system is useful for classifying the faults in various engine working conditions.
without fault
air leakage of the intake manifold
1.5 1
1
0.5
0.5
0
Shannon entropy
1.5
2
4
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8
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14
0
2
4
cam-shaft sensor fault 1.5 1
1 0.5 2
4
6
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0
2
one cylinder miss-firing
10
12
14
4
6
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14
two cylinders miss-firing
1.5
1.5
1
1
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0.5
0
8
1.5
0.5 0
6
ECT sensor fault
2
4
6
8
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14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 9. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in 2000 rpm condition.
without fault
air leakage of the intake manifold
1.5 1
1
0.5
0.5
0
Shannon entropy
1.5
1 2 3 4 5 6 7 8 9 1011 12 13 14 15
0
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4
cam-shaft sensor fault 1.5
1
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4
6
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one cylinder miss-firing
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two cylinders miss-firing
1.5
0
8
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1
0
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ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 10. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in 2000 rpm condition.
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without fault
air leakage of the intake manifold
1.5
1.5
1
1
0.5
0.5
Shannon entropy
0
2
4
6
8
10
12
0
14
2
4
cam-shaft sensor fault
6
8
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14
ECT sensor fault
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1.5
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2
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14
Number of subspaces Fig. 11. Entropy diagrams of using mother wavelet db20 to construct WPT with various faults in 2000 rpm condition.
without fault 300
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200
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100
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Shannon entropy
air leakage of the intake manifold
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ECT sensor fault
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10
12
14
Number of subspaces Fig. 12. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in run-up condition.
without fault 300
200
200
100
100
0
Shannon entropy
air leakage of the intake manifold
300
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 300
300
200
200
100
100
0
2
4
6
8
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14
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2
one cylinder miss-firing 300
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100 2
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6
8
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two cylinders miss-firing
300
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 13. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in run-up condition.
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without fault 300
200
200
100
100
0
Shannon entropy
air leakage of the intake manifold
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4
6
8
10
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14
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4
cam-shaft sensor fault 300
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two cylinders miss-firing
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ECT sensor fault
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Number of subspaces Fig. 14. Entropy diagrams using mother wavelet db20 to construct WPT with various faults in run-up condition.
Table 1 Fault recognition rates using different mother wavelets to construct WPT in idle with various engine fault conditions.
Table 3 Fault recognition rates using different mother wavelets to construct WPT in run-up with various engine fault conditions
Engine condition: idle db4
Engine condition: run-up
db8
db20
db4
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
97.5 92.5 98.33 100 96.67 97.5 97.08
100 95 99.17 100 99.17 100 98.89
100 98.33 95.83 100 99.17 99.17 98.75
100 95 99.17 100 99.17 100 98.89
98.33 96.67 100 100 95 100 98.33
100 94.17 100 100 100 100 99.03
Recognition time (s)
13.42
4.86
11.31
5.05
12.17
6.39
Table 2 Fault recognition rates using different mother wavelets to construct WPT in 2000 rpm with various engine fault conditions Engine condition: 2000 rpm db4
db8
db20
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
100 100 97.5 100 99.17 97.5 99.03
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
Recognition time (s)
11.13
4.86
11.27
4.94
10.39
4.95
5. Conclusions In the present study, a fault diagnosis technique is used to prevent early faults in a mechanical system. The proposed system is based on WPT analysis combined with neural network for detecting and classifying the internal combustion engine in various working conditions. The proposed WPT technique has several advantages over CWT and DWT, and provided great features which effectively distinguish the features each of fault condition for the internal combustion engine. In the classification, the experimental results showed the GRNN was effective in fault diagnosis for internal combustion engine with various fault conditions.
db8
db20
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
97.5 100 100 100 90 95 97.08
95 95 100 100 85 90 94.17
95 100 100 97.5 92.5 97.5 97.08
95 95 100 100 87.5 92.5 95
95 100 100 100 90 97.5 97.08
97.5 95 100 100 90 92.5 95.83
Recognition time (s)
6.72
1.80
8.22
1.69
7.71
1.67
Acknowledgement The work was supported by the National Science Council in Taiwan, Republic of China, under Project Number NSC-96-2622-E018-001-CC3. References Andria, G., Savino, M., & Trotta, A. (1994). Application of Wigner Ville distribution to measurements on transient signals. IEEE Transactions on Instrumentation and Measurement, 43, 187–193. Avic, E., & Akpolat, Z. H. (2006). Speech recognition using a wavelet packet adaptive network based fuzzy inference system. Expert Systems with Applications, 31, 495–503. Bai, M., Huang, J., Hong, M., & Su, F. (2005). Fault diagnosis of rotating machinery using an intelligent order tracking system. Journal of Sound and Vibration, 280, 699–718. Chen, C., Sun, C., Zhang, Y., & Wang, N. (2005). Fault diagnosis for large-scale wind turbine rolling bearing using stress wave and wavelet analysis. ICEMS 2005 Proceedings of the Eighth International Conference on Electrical Machines and Systems, 3, 2239–2244. Corinthios, M. J. (1971). A fast Fourier transform for high-speed signal processing. IEEE Transactions on Computers, C20, 843–846. Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Communication on Pure and Applied Mathematics, 41, 909–996. Hu, X., Wang, Z., & Ren, X. (2005). Classification of surface EMG signal using relative wavelet packet energy. Computer Methods and Programs in Biomedicine, 79, 189–195. Li, C., Song, Z., & Li, P. (2004). Bearing fault detection via wavelet packet transform and rough set theory. Proceedings of Fifth World Congress on Intelligent Control and Automation, 2, 1663–1666. Lin, J., & Qu, L. (2000). Feature extraction based on Morlet wavelet and its application for mechanical diagnosis. Journal of Sound and Vibration, 234(1), 135–148.
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Liu, S., Du, R., & Yang, S. (2000). Fault diagnosis for diesel engines by wavelet packet analysis of vibration signal measured on cylinder head. Journal of Vibration Engineering, 13, 577–584. Meng, Y., Jia, S., & Rong, M. (2004). Application of frequency band energy decomposition using wavelet packet in condition monitoring of circuit breakers. Journal of Xi’ An Jiaotong University, 38, 1013–1017. Nikolaou, N. G., & Antoniadis, I. A. (2002). Rolling element bearing fault diagnosis using wavelet packets. NDT&E International, 35, 197–205. Ortiz, E., & Syrmos, V. (2006). Support vector machines and wavelet packet analysis for fault detection and identification. IJCNN 06. International Joint Conference on Neural Networks, 3449–3456. Portnoff, M. (1980). Time-frequency representation of digital signals and systems based on short-time Fourier analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP, 28, 55–69. Prabhakar, S., Mohanty, A. R., & Sekhar, A. S. (2002). Application of discrete wavelet transform for detection of ball bearing race faults. Tribology International, 35, 793–800. Serhat, S., & Emine, A. (2003). Feature extraction related to bearing damage in electric motors by wavelet analysis. Journal of the Franklin Institute, 340, 125–134. Specht, D. F. (1988). Probabilistic neural networks for classification mapping or associative memory. IEEE International Conference on Neural Networks, 1, 525–532. Specht, D. F. (1991). A general regression neural network. IEEE Transactions on Neural Networks, 2, 568–576.
Staszewski, W. J., Worden, K., & Tomlinson, G. R. (1997). Time-frequency analysis gearbox fault detection using the Wigner Ville distribution and pattern recognition. Mechanical Systems and Signal Processing, 11(5), 673–692. Swami, A., Giannakis, G. B., & Zhou, G. (1997). Bibliography on higher order statistics. Signal Processing, 60, 65–126. Tse, P. W., Yang, W. X., & Tam, H. Y. (2004). Machine fault diagnosis through an effective exact wavelet analysis. Journal of Sound and Vibration, 277, 1005–1024. Wu, J. D., & Chen, J. C. (2006). Continuous wavelet transform technique for fault signal diagnosis of internal combustion engines. NDT & E International, 39, 304–311. Wu, J. D., Huang, C. W., & Huang, R. (2004). An application of a recursive Kalman filtering algorithm in rotating machinery fault diagnosis. NDT & E International, 37, 411–419. Yen, G. G., & Lin, K. C. (2000). Wavelet packet feature extraction for vibration monitoring. IEEE Transactions on Industrial Electronics, 47, 650–667. Yibin, S., & Ying, R. (2005). A predictive model of nonlinear system based on generalized regression neural network. ICNN&B 05 International Conference on Neural Networks and Brain, 3, 2009–2012. Zhang, J., Walter, G. G., Miao, Y., & Lee, W. N. W. (1995). Wavelet neural networks for function learning. IEEE Transactions on Signal Processing, 43, 1485–1497. Zheng, H., Li, Z., & Chen, X. (2002). Gear fault diagnosis based on continuous wavelet transforms. Mechanical Systems and Signal Processing, 16(2–3), 447–457.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
An expert system for fault diagnosis in internal combustion engines using wavelet packet transform and neural network Jian-Da Wu *, Chiu-Hong Liu Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Road, Changhua City, Changhua 500, Taiwan, ROC
a r t i c l e
i n f o
Keywords: Wavelet packet transform Neural network Fault diagnosis Sound emission signal
a b s t r a c t In the present study, a fault diagnosis system is proposed for internal combustion engines using wavelet packet transform (WPT) and artificial neural network (ANN) techniques. In fault diagnosis for mechanical systems, WPT is a well-known signal processing technique for fault detection and identification. The signal processing algorithm of the present system is gained from previous work used for speech recognition. In the preprocessing of sound emission signals, WPT coefficients are used for evaluating their entropy and treated as the features to distinguish the fault conditions. Obviously, WPT can improve the continuous wavelet transform (CWT) used over a longer computing time and huge operand. It can also solve the frequency-band disagreement by discrete wavelet transform (DWT) only breaking up the approximation version. In the experimental work, the wavelets are used as mother wavelets to build and perform the proposed WPT technique. In the classification, to verify the effect of the proposed generalized regression neural network (GRNN) in fault diagnosis, a conventional back-propagation network (BPN) is compared with a GRNN network. The experimental results showed the proposed system achieved an average classification accuracy of over 95% for various engine working conditions. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The condition monitoring and fault diagnosis in a mechanical system is important for avoiding serious damage. The internal combustion engine is classical rotating machinery that must be operated under various conditions for different performance needs. Sound emission and vibration signal of engine often give much dynamic information of mechanical system condition. The signal analysis has been set up as one of the useful methods for fault diagnosis. Many useful techniques for signal analysis have been proposed such as fast Fourier transform (FFT) (Corinthios, 1971), higher-order statistics (HOS) (Swami, Giannakis, & Zhou, 1997), and adaptive order-tracking (Bai, Huang, Hong, & Su, 2005; Wu, Huang, & Huang, 2004). Nonetheless, the fault diagnosis system of sound emission or vibration signals analysis is stressed in the time-frequency domain information. There are many other techniques that have been developed such as the short time Fourier transform (STFT) (Portnoff, 1980), Wigner–Ville distribution (WVD) (Andria, Savino, & Trotta, 1994; Staszewski, Worden, & Tomlinson, 1997) and wavelet transform (WT) (Chen, Sun, Zhang, & Wang, 2005; Lin & Qu, 2000; Prabhakar, Mohanty, & Sekhar, 2002; Serhat & Emine, 2003; Tse, Yang, & Tam, 2004; Wu & Chen, 2006; Zheng, Li, & Chen, 2002) . All the techniques were developed * Corresponding author. E-mail address: [email protected] (J.-D. Wu). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.03.008
successfully, but WT is the best of these tools because STFT only provides a constant time-frequency resolution and WVD produces interference terms on the time-frequency domain in a critical condition. The WT can be divided into continuous wavelet transform (CWT) and discrete wavelet transform (DWT). In 2000, Lin and Qu used vibration signals for the feature extraction and fault diagnosis based on the Morlet wavelet (Lin & Qu, 2000). In 2002, Zheng et al. published a gear fault diagnosis method based on continuous wavelet transform and proposed a new concept of time-averaged wavelet spectrum (TAWS) for reducing the huge operand (Zheng et al., 2002). In 2004, Tse et al. designed an innovative wavelet which called exact wavelet analysis to improve the robustness of vibration-based machine fault diagnosis (Tse et al., 2004). In 2006, Wu and Chen used a continuous wavelet transform algorithm for fault signal diagnosis in an internal combustion engine (Wu & Chen, 2006). All these studies are useful examples of the CWT approach. Unfortunately, CWT has a huge operand and requires a long time to use. Therefore, the DWT has been developed to improve the drawback of CWT by using the decomposition of the original complex signal to several resolutions. (Prabhakar et al., 2002; Serhat & Emine, 2003). In 2005, Chen et al. proposed a stress wave (SW) method based on wavelet analysis of low-speed rolling bearings (Chen et al., 2005). Unfortunately, the DWT is not a suitable method for analyzing the signal that contains a much higher frequency band. Alternatively, wavelet packet transform
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(WPT) provides the same frequency bandwidths in each resolution for recording the feature under each frequency bands. Meanwhile, the WPT working speed is faster than the traditional DWT. Applications of WPT are widespread such as speech recognition, electroencephalogram, fault detection and diagnosis. In 2000, Liu et al. proposed a unique technique using vibration signals for diesel engine diagnosis by WPT analysis (Liu, Du, & Yang, 2000). In 2002, Nikolaou and Antoniadis also used vibration signal for bearings with localized defects (Nikolaou & Antoniadis, 2002). In 2004, Meng et al. used WPT to analyze the signal when operating circuit breakers (Meng, Jia, & Rong, 2004). In 2005, Hu et al. proposed a novel and simple method to extract the feature from surface EMG signals based on WPT which the features are the relative wavelet packet energy (RWPE) evaluated by several selected frequency bands (Hu, Wang, & Ren, 2005). In 2006, Avic and Akpolat developed an expert system for speech recognition (Avic & Akpolat, 2006). In the study, wavelet packet adaptive network-based fuzzy inference system was proposed combining feature extraction and classification for real speech signals. In the present study, a fault diagnosis system using sound emission signals based on WPT and a neural network for internal combustion engine is proposed. The wavelet packet used the Daubechies, 1988 wavelet ‘‘db4”, ‘‘db8” and ‘‘db20” as mother wavelets to build and perform the proposed WPT technique for extracting the information of engine fault signals. Also, the signals are collocated and then use the ‘‘Shannon entropy” for features of fault signals. Finally, the neural network is used to recognize the engine running conditions and fault classification in five synthetic faults. The principle of the proposed WPT and neural network in the present study is described in the following sections.
tion within the original signals. Therefore, the signal with great quantity of middle and high frequency signals can offer superior time-frequency analysis. The WPT suits signal processing, especially nonstationary signals because the same frequency bandwidths can provide good resolution regardless of high and low frequencies. The principle of WPT can be described as follows (Li, Song, & Li, 2004; Ortiz & Syrmos, 2006; Yen & Lin, 2000). The WPT is a generalization of the wavelet transform and the wavelet packet function is also a time-frequency function, it can be defined as j
W nj;k ðtÞ ¼ 22 W n ð2j t kÞ;
ð1Þ
where the integers j and k are the index scale and translation operations. The index n is an operation modulation parameter or oscillation parameter. The first two wavelet packet functions are the scaling and mother wavelet functions: W 00;0 ðtÞ ¼ /ðtÞ;
ð2Þ
W 10;0 ðtÞ
ð3Þ
¼ wðtÞ:
When n ¼ 2; 3; . . . the function can be defined by the following recursive relationships: pffiffiffi X W 2n 2 hðkÞW n1;k ð2t kÞ; ð4Þ 0;0 ðtÞ ¼ k
pffiffiffi X 2 gðkÞW n1;k ð2t kÞ;
2nþ1 ðtÞ ¼ W 0;0
where hðkÞ and gðkÞ are the quadrature mirror filter (QMF) associated with the predefined scaling function and mother wavelet function. The wavelet packet coefficients, wnj;k are computed by the inner product hf ðtÞ; W nj;k i where defined as Z wnj;k ¼ hf ðtÞ; W nj;k i ¼ f ðtÞW nj;k ðtÞdt: ð6Þ
2. Principle of wavelet packet transform and feature extraction 2.1. Wavelet packet transform
The framework of WPT algorithm broken up to three resolution levels is shown in Fig. 1. In the figure, S03 presents the symbol for a subspace that stands for the third resolution and the 0th subspace. In the present study, the sound emission signals will be broken up to four resolutions ðj ¼ 4Þ. As a result, four resolutions will produce sixteen subspaces and the frequency intervals of each subspace can be computed by (Hu et al., 2005):
The structure of wavelet packet transform (WPT) is similar to discrete wavelet transform (DWT). Both have the framework of multi-resolution analysis (MRA). The main difference in the two techniques is the WPT can simultaneously break up detail and approximation versions, but DWT only breaks up as an approximation version. Therefore, the WPT have the same frequency bandwidths in each resolution and DWT does not have this property. The mode of decomposition does not increase or lose the informa-
i ðn 1Þ2j1 fs ; n2j1 fs ;
n ¼ 1; 2; 3 . . . ; 16;
G:
H:
h (k )
g (k )
↓2
Low pass filter and decimation
↓2
High pass filter and decimation
S00 G
H
S11
S10 H
G
S20 H
S30
H
S 21 G
S31
H
S32
G
S 23
S 22 G
S33
ð5Þ
k
H
S34
G
S35
H
S36
G
S37
Fig. 1. Tree structures of wavelet packet transform, S03 represents the third resolution and the 0th subspace (Yen & Lin, 2000).
ð7Þ
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where fs is sampling frequency. For example, in this work fs ¼ 5000 Hz, S00 is the original signal with the frequency interval ð0; 21 fs ¼ ð0; 2500, S03 with the frequency interval (0, 312.5], S73 with the frequencies interval (2187, 2500]. The wavelet packet transform is used regarding the data preprocessing for fault diagnosis.
input
Radial Basis Layer Q× R
IW1,i
Q×Q
LW 2,i
P R ×1
dist
En ¼
16 X
n2 wn2 j;k logðwj;k Þ;
n¼1
where wnj;k is the coefficients of the subspace after wavelet packet decomposition and n ¼ 0; 1; 2; . . . ; 15 (Avic & Akpolat, 2006). The low frequencies in Shannon entropy of E0 will not used because it probably contains massive noise. Therefore, a feature vector T that is composed of En can be expressed as T ¼ ½E1 ; E2 ; . . . E14 ; E15 :
ð9Þ
To classify the different faults of engine by neural network, the feature vector T will be adopted in fault classification.
3. Principle of neural network classifier for fault recognition In the present system, a recognition method for engine fault condition using neural networks is examined to evaluate the effectiveness of the proposed system. In the artificial neural network (ANN) so far, back-propagation neural network (BPNN) is the most basic type and the most representative of the neural network. The framework of BPNN can be divided into three layers: input layer, hidden layer and output layer. The basis principle of BPNN is using the gradient steepest descent method to use the error between output and target of network to adjust the weight repeatedly. The error is used to adjust the weight till the error is smaller than a threshold or when expecting times with recurring learning. Finally, use the data which completes training of the network classifica-
1
1
*
ð8Þ
a2 = y
Q×1
2.2. Feature extraction of fault conditions using Shannon entropy In the present study, the feature of ‘‘Shannon entropy” will be used in various fault conditions after data preprocessing of wavelet packet transform. Entropy is a common idea used in many fields, especially in signal processing (Zhang, Walter, Miao, & Lee, 1995). Wavelet packet decomposition is applied to the engine fault signal using the ‘‘db4”, ‘‘db8” and ‘‘db20” wavelet packet filters w with the ‘‘Shannon entropy” and is defined as
Specail Linear Layer
n
a
Q×1
Q×1
Q×1
2
Nprod
a
Q×1
b1
1
Q×1
R
Q
Q
Fig. 2. Structure of GRNN (Yibin & Ying, 2005).
tion. Then, input the test model in order. The network may export the test result. BPNN has high learning precision, fast recall and wide application. Although it has these merits, BPNN also has many flaws such as: existence of local minimum, improper learning rate and a network unable to achieve convergence. To improve these drawbacks, some ANNs have been developed. In 1988, Specht proposed a new neural network called PNN (Specht, 1988). PNN only suits the classified problem but is unable to solve the continual variable problem. To solve the flaw of PNN, the GRNN was proposed by Specht (1991). The GRNN speed is very quick because it does not need an iterative training for converging to a wanted solution. Fig. 2 shows the structure of GRNN which contains three layers: input layer, hidden layer (radial basis layer) and output layer (special linear layer). GRNN adopts direct mapping from the input cell to the hidden layer, but between the hidden layer and the output layer the mapping adopts the linearly weighted sum of hidden layers as the mapping mode (Yibin & Ying, 2005). GRNN is not similar to regression analysis of the traditional method that needs to suppose exact function. It only needs the method of probability density function (PDF) to be presented. The principle of GRNN was described in previous work by Specht (1991), f ðx; yÞ stands for the known joint continuous PDF of a vector random variable x and a scalar random variable y. The conditional mean of y given X (also called regressing y on X) is given by Z 1 Z 1 yf ðX; yÞdy= f ðX; yÞdy: ð10Þ E½yjX ¼ 1
Fig. 3. Experimental structure of engine fault diagnosis system.
1
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Signal
Feature extraction
Wavelet Packet Decomposition
E1
E2
E16
E3
Classification
BPN and GRNN
without fault, air leakage, cam-shaft sensor fault, ECT sensor fault, one-cylinder miss-fire, two-cylinder miss-fire
If the density f ðx; yÞ is unknown, it must usually be estimated from a sample of observation of x and y. The probability estimator ^f ðX; YÞ is based on the sample values X i and Y i of the random variables x and y, where n is the number of sample observations and p is the dimension of the vector variable x: " # n 1 1 X ðX X i ÞT ðX X i Þ ^f ðX; YÞ ¼ exp 2r2 ð2pÞðpþ1Þ=2 rðpþ1Þ n i¼1 " # ðY Y i Þ2 exp ; ð11Þ 2r2 where the r is the smoothing parameter (sigma weight) and defining the scalar function D2i as D2i ¼ ðX X i ÞT ðX X i Þ:
ð12Þ
Combining Eqs. (10)–(12) an estimation of conditional mean shown ^ by Specht, named YðXÞ, can be written as !, ! n n X X D2i D2i i ^ ð13Þ Y exp 2 exp 2 : YðXÞ ¼ 2r 2r i¼1 i¼1
Fig. 4. Structure of the engine diagnosis system for fault classification.
A1
B1
0.5
1 0.5
Shannon entropy
0
2
4
6
8
10
12
14
0
2
4
6
A2
8
10
12
14
10
12
14
10
12
14
B2
0.5
1 0.5
0
2
4
6
8 A3
10
12
14
0
2
4
6
8 B3
0.5
1 0.5
0
2
4
6
8
10
12
14
0
2
4
6
8
Number of subspaces Fig. 5. Entropy diagrams of using mother wavelets ‘‘db4”, ‘‘db8” and ‘‘db20” to construct WPT without fault, A1–A3 represents in idle condition; B1–B3 represents in run-up condition.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 0.4
0.4
0.2
0.2
0
2
4
6
8
10
12
14
0
2
one cylinder miss-firing 0.4
0.2
0.2
2
4
6
8
10
12
8
10
12
14
4
6
8
10
12
14
wo cylinders miss-firing
0.4
0
6
ECT sensor faul
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 6. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in idle condition.
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When the smoothing parameter r is enlarged, the estimated density is forced to be smooth and in the limit becomes a multivariate Gaussian with covariance r2 I. On the other hand, a smaller value of r allows the estimated density to assume non-Gaussian shapes, but with the hazard that wild points may have too great an effect on the estimate (Specht, 1991). 4. Experimental investigation and classification of sound emission signals 4.1. Experimental work and signal processing To estimate the proposed fault diagnosis system, experiments are carried out to measure the sound emission signals for various engine running conditions. The sound emission signals were recorded by a data acquisition system. Subsequently, we analyzed the sound emission signals using the WPT algorithm and then extracted the feature vector by ‘‘Shannon entropy”. The experimental setup of engine fault diagnosis system is shown in Fig. 3. The equipment for the experiment included an internal combustion
engine (Mitsubishi V type, four-stroke, six cylinders, 3.0-L gasoline direct-injection (GDI)), an optical encoder (PW-PH02), a microphone (PCB 130D20), a dynamic signal analyzer (SR785) and a data acquisition system (Hardware: NI-6024E; Software: Lab-view). The microphone is used to measure the sound emission signal from the experimental platform. To know the revolution of the engine, an optical encoder is set up to close the crankshaft. Both of the signals can be recorded by a data record system and can be seen with a dynamic signal analyzer. The sampling rate of the data acquisition system is set at 5 kHz. In the experimental work, six conditions are designed to estimate the proposed fault diagnosis system. They include an engine without any fault, air leakage of the intake manifold, camshaft sensor fault, electronic control thermal (ECT) sensor fault, one cylinder misfiring, and two cylinders misfiring. The engine is run in the idle condition (750 rpm), 2000 rpm and run-up (from idle condition accelerate to 3500 rpm) conditions. In particular, the run-up test highlighted WPT is able to provide good resolution when the signal suddenly changes. Fig. 4 shows the structure of the engine diagnosis system for fault classification.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 0.4
0.4
0.2
0.2
0
2
4
6
8
10
12
14
0
2
one cylinder miss-firing 0.4
0.2
0.2
2
4
6
8
10
12
8
10
12
14
4
6
8
10 1 12
14
two cylinders miss-firing
0.4
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 7. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in idle condition.
without fault 0.4
0.2
0.2
0
Shannon entropy
air leakage of the intake manifold
0.4
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 0.4
0.4
0.2
0.2
0
2
4
6
8
10
12
14
0
2
one cylinder miss-firing 0.4
0.2
0.2
2
4
6
8
10
12
8
10
12
14
4
6
8
10
12
14
two cylinders miss-firing
0.4
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 8. Entropy diagrams of using mother wavelet db20 to construct WPT with various faults in idle condition.
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4.2. Faults classification The Daubechies, 1988 wavelets ‘‘db4”, ‘‘db8” and ‘‘db20” are the mother wavelets to build and perform the proposed WPT technique. Fig. 5 shows the results of idle (A1–A3) and run-up (B1– B3) conditions after being computed and represented by the ‘‘Shannon entropy”. The horizontal axis stands for the number of subspaces and vertical axis stands for the size of the ‘‘Shannon entropy”. The variation of each subspace can be seen. Further, the differences can be obviously seen between ‘‘db4”, ‘‘db8” and ‘‘db20”. This showed the use of these three kinds of mother wavelets to analyze and produce the different results. In this investigation, the lower frequencies ‘‘Shannon entropy” (E0 that computed by S04 ) are not used because it probably contains massive noise. Figs. 6–8 show the entropy diagrams of using three different mother wavelets to build WPT with various faults in the idle condition. The variations of entropy in different conditions are easy to discriminate from the figures. Figs. 9–11 show the entropy diagrams of using three different mother wavelets to build WPT with various
faults in an engine run at 2000 rpm. Figs. 12–14 show the entropy diagrams of using three different mother wavelets to build WPT with various faults in an engine operated in a run-up condition. To understand the effectiveness of the proposed system, signals are used to classify by the BPN and GRNN after feature selection of ‘‘Shannon entropy”. The features of ‘‘Shannon entropy” in each fault condition are summarized for the input of the neural networks. The number of experimental data in each operation condition is 150. The 30 data sets are used to training and the 120 data sets are used to test the recognition rate of the proposed network. The recognition rate is defined as the rate of total number of tests and correct classification. Tables 1–3 summarized the recognition rate of three different engine operation conditions using both the BPN and GRNN algorithms. All the recognition rates are over 95%. In the tables, although both of the BPN and GRNN achieved effectiveness in the recognition, however, GRNN spent less time than BPN in classification. The experimental results show the proposed WPT fault diagnosis system is useful for classifying the faults in various engine working conditions.
without fault
air leakage of the intake manifold
1.5 1
1
0.5
0.5
0
Shannon entropy
1.5
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 1.5 1
1 0.5 2
4
6
8
10
12
14
0
2
one cylinder miss-firing
10
12
14
4
6
8
10
12
14
two cylinders miss-firing
1.5
1.5
1
1
0.5
0.5
0
8
1.5
0.5 0
6
ECT sensor fault
2
4
6
8
10
12
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 9. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in 2000 rpm condition.
without fault
air leakage of the intake manifold
1.5 1
1
0.5
0.5
0
Shannon entropy
1.5
1 2 3 4 5 6 7 8 9 1011 12 13 14 15
0
2
4
cam-shaft sensor fault 1.5
1
0.5
0.5 2
4
6
8
10
12
14
0
2
one cylinder miss-firing
10
12
14
1.5
1
1
0.5
0.5 2
4
6
8
10
12
4
6
8
10
12
14
two cylinders miss-firing
1.5
0
8
1.5
1
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 10. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in 2000 rpm condition.
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without fault
air leakage of the intake manifold
1.5
1.5
1
1
0.5
0.5
Shannon entropy
0
2
4
6
8
10
12
0
14
2
4
cam-shaft sensor fault
6
8
10
12
14
12
14
ECT sensor fault
1.5
1.5
1
1
0.5
0.5
0
2
4
6
8
10
12
0
14
2
one cylinder miss-firing
4
6
8
10
two cylinders miss-firing
1.5
1.5
1
1
0.5
0.5
0
2
4
6
8
10
12
0
14
2
4
6
8
10
12
14
Number of subspaces Fig. 11. Entropy diagrams of using mother wavelet db20 to construct WPT with various faults in 2000 rpm condition.
without fault 300
200
200
100
100
0
Shannon entropy
air leakage of the intake manifold
300
0
2
4
6
8
10
12
0
14
0
2
4
cam-shaft sensor fault 300
300
200
200
100
100
0
0
2
4
6
8
10
12
0
14
0
2
one cylinder miss-firing 300
200
200
100
100 0
2
4
6
8
10
8
10
12
14
12
4
6
8
10
12
14
two cylinders miss-firing
300
0
6
ECT sensor fault
14
16
0
0
2
4
6
8
10
12
14
Number of subspaces Fig. 12. Entropy diagrams of using mother wavelet db4 to construct WPT with various faults in run-up condition.
without fault 300
200
200
100
100
0
Shannon entropy
air leakage of the intake manifold
300
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 300
300
200
200
100
100
0
2
4
6
8
10
12
14
0
2
one cylinder miss-firing 300
200
200
100
100 2
4
6
8
10
12
8
10
12
14
4
6
8
10
12
14
two cylinders miss-firing
300
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 13. Entropy diagrams of using mother wavelet db8 to construct WPT with various faults in run-up condition.
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without fault 300
200
200
100
100
0
Shannon entropy
air leakage of the intake manifold
300
2
4
6
8
10
12
14
0
2
4
cam-shaft sensor fault 300
300
200
200
100
100
0
2
4
6
8
10
12
14
0
2
one cylinder miss-firing 300
200
200
100
100 2
4
6
8
10
8
10
12
14
12
4
6
8
10
12
14
two cylinders miss-firing
300
0
6
ECT sensor fault
14
0
2
4
6
8
10
12
14
Number of subspaces Fig. 14. Entropy diagrams using mother wavelet db20 to construct WPT with various faults in run-up condition.
Table 1 Fault recognition rates using different mother wavelets to construct WPT in idle with various engine fault conditions.
Table 3 Fault recognition rates using different mother wavelets to construct WPT in run-up with various engine fault conditions
Engine condition: idle db4
Engine condition: run-up
db8
db20
db4
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
97.5 92.5 98.33 100 96.67 97.5 97.08
100 95 99.17 100 99.17 100 98.89
100 98.33 95.83 100 99.17 99.17 98.75
100 95 99.17 100 99.17 100 98.89
98.33 96.67 100 100 95 100 98.33
100 94.17 100 100 100 100 99.03
Recognition time (s)
13.42
4.86
11.31
5.05
12.17
6.39
Table 2 Fault recognition rates using different mother wavelets to construct WPT in 2000 rpm with various engine fault conditions Engine condition: 2000 rpm db4
db8
db20
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
100 100 97.5 100 99.17 97.5 99.03
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
100 100 100 100 100 100 100
Recognition time (s)
11.13
4.86
11.27
4.94
10.39
4.95
5. Conclusions In the present study, a fault diagnosis technique is used to prevent early faults in a mechanical system. The proposed system is based on WPT analysis combined with neural network for detecting and classifying the internal combustion engine in various working conditions. The proposed WPT technique has several advantages over CWT and DWT, and provided great features which effectively distinguish the features each of fault condition for the internal combustion engine. In the classification, the experimental results showed the GRNN was effective in fault diagnosis for internal combustion engine with various fault conditions.
db8
db20
BPN
GRNN
BPN
GRNN
BPN
GRNN
Without fault Air leakage of intake manifold Cam–Shaft sensor fault ECT sensor fault One cylinder miss-firing Two cylinders miss-firing Average recognition rate
97.5 100 100 100 90 95 97.08
95 95 100 100 85 90 94.17
95 100 100 97.5 92.5 97.5 97.08
95 95 100 100 87.5 92.5 95
95 100 100 100 90 97.5 97.08
97.5 95 100 100 90 92.5 95.83
Recognition time (s)
6.72
1.80
8.22
1.69
7.71
1.67
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