Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network

Expert Systems with Applications 36 (2009) 8862–8875

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Faulted gear identification of a rotating machinery based on wavelet transform and artificial neural network Jian-Da Wu *, Jian-Ji Chan Graduate Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Rd., Changhua City, Changhua 500, Taiwan

a r t i c l e

i n f o

Keywords: Rotating machinery Fault diagnosis Continuous wavelet transform Artificial neural network Sound emission

a b s t r a c t In this paper, a condition monitoring and faults identification technique for rotating machineries using wavelet transform and artificial neural network is described. Most of the conventional techniques for condition monitoring and fault diagnosis in rotating machinery are based chiefly on analyzing the difference of vibration signal amplitude in the time domain or frequency spectrum. Unfortunately, in some applications, the vibration signal may not be available and the performance is limited. However, the sound emission signal serves as a promising alternative to the fault diagnosis system. In the present study, the sound emission of gear-set is used to evaluate the proposed fault diagnosis technique. In the experimental work, a continuous wavelet transform technique combined with a feature selection of energy spectrum is proposed for analyzing fault signals in a gear-set platform. The artificial neural network techniques both using probability neural network and conventional back-propagation network are compared in the system. The experimental results pointed out the sound emission can be used to monitor the condition of the gear-set platform and the proposed system achieved a fault recognition rate of 98% in the experimental gear-set platform. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Early fault diagnosis in rotating parts is used to prevent serious damage to mechanical systems. In general, the conditions of rotating machineries can be monitored by measuring the mechanical vibration signal. However, the sound emission signal from rotating machinery serves as a promising alternative to fault diagnosis. In the fault diagnosis field, extracting fault signatures plays an important role. The conventional fault diagnosis technique is used to view the amplitude difference only in the time or frequency domain. For example, the conventional fast Fourier transform (FFT) technique is used to follow the amplitude difference in the frequency domain for damage diagnosis. Meanwhile, time–frequency analysis can be used to see the representation of signals in both the time and frequency domains. The short time Fourier transform (STFT) has been applied to analyze the signals of the fault in both the time and frequency domains. However, STFT has a limit in time resolution because of using fixed time windows. Recently, wavelet analysis has become a useful approach in image processing (Heric & Zazula, 2007; Kim & Kang, 2007). In addition, it is also a popular and efficient tool in fault diagnosis of a mechanical system (Belotti, Crenna, Michelini, & Rossi, 2006). In 1997, Li and Ma proposed a

* 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.2008.11.020

new approach for bearing-localized defect detection based on wavelet transform (Li & Ma, 1997). In 2000, Sung et al. developed an approach to analyze the location defect based on discrete wavelet transform (Sung, Tai, & Chen, 2000). In 2002, Zheng et al. proposed a conception of time average wavelet spectrum (TAWS) based on continuous wavelet transform (CWT) (Zheng, Li, & Chen, 2002). Except wavelet analysis, there are several techniques proposed for fault diagnosis approach of the mechanical system. In 2001, Wang analyzed the condition of the gear tooth using the synchronous signal averaging technique and the resonance demodulation technique (Wang, 2001). Wang and Wong also described some signal processing approaches such as wavelet technique and autoregressive technology in gear fault diagnosis (Wang & Wong, 1999). In 2001, Baydar and Ball proposed a Wigner-Ville distribution method to distinguish the fault condition such as broken tooth, gear crack and tooth wear. Besides, the effects by using sound and vibration signals are compared (Baydar & Ball, 2001). In 2002, Chen and Wang developed an intelligent fault diagnosis system based on instantaneous scale-distribution (ISD). Throughout the ISD method, the features of gear fault diagnosis are depicted clearly (Chen & Wang, 2002). Meltzera and Dien provide an approach named the polar wavelet amplitude map (PWM) drawn from the wavelet map of a time-synchronous averaged signal (Meltzera & Dien, 2004). Finally, the residual PWM by deleting

J.-D. Wu, J.-J. Chan / Expert Systems with Applications 36 (2009) 8862–8875

u j+1

uj

8863

oj W LM

WNM

Fig. 4. Gear-set operated in run-up condition.

Hidden

Input

Output

Fig. 1. Structure of BP neural network.

J1 I1

I2 I3

K1

J2

P1

J3 K2

J4

P2

J5 Input layer

Hidden layer

Summation layer Output layer

Fig. 2. Structure of PNN neural network.

the all the harmonic parts of meshing frequency is used because its fault presence is clearer than the overall PWM.

Servomotor

After extracting fault features, a proper artificial neural network is indispensable for aiding of the fault classification (Kashya & Shenoy, 2003; Rafieea, Arvania, Harifib, & Sadeghi, 2007). An intelligent fault diagnosis system is performed throughout combing the approach to fault diagnosis with an artificial neural network. For examples, Chen and Wang combined instantaneous scale-distribution (ISD) and multilayer perceptron (MLP) network to carry out an intelligent fault diagnosis system. In addition, MLP was introduced for classifying gear faults. And then to quantify the misclassification of gear faults, the misclassification rate is defined (Chen & Wang, 2002). In 1996, Murnion analyzed the experimental data by using the analysis of the discrete wavelet transform and the applications of neural networks (Murnion, 1996). In 2007, Rafiee et al. developed a new approach to extract the gear and bearing fault based on wavelet packet coefficients combined with a multilayer probabilistic neural network (Gaganis, Pasiouras, & Doumpos, 2007). In the present study, an experimental investigation of faulted gear identification in gear-set platform using a sound emission signal is proposed. A continuous wavelet transform technique combined with a feature selection of energy spectrum is used for analyzing fault signals in a gear-set platform. The artificial neural network techniques both using the probability neural network and conventional back-propagation network are compared in recognition of experimental data. The principles of proposed time average wavelet transform and neural network in the experimental system are described in the following sections.

Gear A:33T Gear C:21T Gear E:19T

Tachometer

Gear B:17T

Gear D:29T Gear F:31T PC

Microphone Fig. 3. Experimental set up and measurement of gear-set fault diagnosis.

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Fig. 5. Sound emission signal in time domain of different gear faults at 1500 rpm, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 6. Sound emission signal in time domain of gear-set in run-up operation, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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2. Feature extraction of rotating machinery sound emission signal

Wðxk Þ ¼

2.1. Continuous wavelet transform In general, the vibration and sound emission signals from rotating machinery can be used in condition monitoring and fault diagnosis. They were analyzed in time or frequency domain signal processing technique. The wavelet transform uses a series of oscillating functions with different frequencies as window function to deal with transient signals by modulating its resolution in different time-interval. The wavelet technique has particular advantages for characterizing signals at different localization levels in time as well as frequency domains. The principle of CWT of the signal f(t) is described as follows:

W f ðx; y; wÞ ¼< wx;y ðtÞ; f ðtÞ >¼ x1=2

Z

f ðtÞw

  ty dt x

  ðm  nÞdt fm w xk m¼0

N 1 X

1

Z1 1

ð2Þ

ð3Þ

wðtÞdt ¼ 0

ð4Þ

Eq. (3) means the energy is finite in finite time, meanwhile, Eq. (4) means the shape of wðtÞ is symmetric. If the function wðtÞ matches these two conditions, it is defined as the mother wavelet. In the present study, the scale factor is chosen as

k ¼ 0; 1; . . . ; K  1

ð8Þ

By using the formula, the values of the fault feature vectors are regarded as the inputs of the neuron network.

The back-propagation neural network was proposed by McClelland & Rumelhart (1986). The structure of the back-propagation is shown in Fig. 1. In the present study, the structure of BP includes three layers, input layer, hidden layer, and output layer. In addition, the variable ‘‘M” means the total neuron number is M in the input layer, the variable ‘‘N” means the total neuron number is N in the hidden layer, and the variable ‘‘L” means the total neuron number is L in the output layer. Between the input and the hidden layer, there are weighted values wNM. And there are weighted values wLN between the hidden and the output layer. The operation of BP is divided into three main parts. (1) Feed-forward stage:

ð9Þ

1 Oj ðnÞ ¼ uðv j ðnÞÞ ¼ 1 þ expðv j ðnÞÞ

ð10Þ

where uj (n) means the input, uj+1 (n) means the output of hidden layer, and Oj (n) is the output. In addition, the sign u represents the activation function.

ð5Þ

where x0 ¼ 2dt; dj ¼ 0:05; K ¼ 140, and dt is the sampling interval (Zheng et al., 2002). Besides, it is important to pick up proper wavelet for analyzing the signal. The proposed strategy for choosing wavelet function is to find the wavelet which is similar to the faulty signal. Thus, a Morlet wavelet is used in this research according to the Vass and Cristalli study (Vass & Cristalli, 2005) and its formula is described as follows: b2 t 2 b wðtÞ ¼ pffiffiffiffiffiffiffi  eiwt  e 2 2p

0; WðX kþ1 Þ > WðX k Þ 1; WðX kþ1 Þ 6 WðX k Þ;

v j ¼ wLN ðnÞ  ujþ1 ðnÞ

1

k ¼ 0; 1; 2; . . . ; K

 TðKÞ ¼

3.1. Principle of back-propagation

jwðtÞj2 dt < 1 jtj

xk ¼ x0 2kdj ;

where N is the sampling number. According to the formula, the characters and tendencies are similar in the same fault condition. The feature vector is defined as follows:

3. Faulted gear identification using neural networks

where m, n = 0, 1, 2, . . ., N1, dt means the sampling point number and w means complex conjugate of the mother wavelet. The wavelet function has to satisfy the following two conditions

Z

ð7Þ

ð1Þ

where x is the scale parameter, y is the time parameter and the horizontal bar marks the complex conjugate of the mother wavelet. It also can be rewritten as a discrete sequence fm. The formula is described as

W n ðxk Þ ¼

N1 1 X jW ðxk Þj2 N k

Original signal acquirement

Wavelet analysis

TAWS

ð6Þ

where i is the imaginary unit and the extraction of impulses with variable decay is provided by an adaptive parameter b controlling the time–frequency resolution of the Morlet wavelet. In addition, the function of a Morlet wavelet is a sinusoidal signal decreasing exponentially on both sides.

FEDT

Digitize fault feature

2.2. Frequency–energy distribution tendency method

BP The continuous wavelet power spectrum is described as jWðxk Þj2 . The TAWS is defined as

PNN

Fig. 7. Flow chart of signal processing in fault diagnosis system.

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Fig. 8. Wavelet representation of sound emission in different gear faulted at 1500 rpm, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 8 (continued)

(1) Back-propagation stage:

dj ðnÞ ¼ ej ðnÞ  u ðv j ðnÞÞ ¼ ðdj ðnÞ  Oj ðnÞÞOj ðnÞð1  Oj ðnÞÞ 0

ð11Þ

where dj ðnÞ is the local gradient function, ej (n) is the error function, Oj (n) represents the actual output and dj (n) means the desired output. (1) Adjust weighted value:

wNM ðn þ 1Þ ¼ wNM ðnÞ þ DwNM ðnÞ ¼ wNM ðnÞ þ gdj ðnÞ  yi ðnÞ

(3) Summation layer: It contains two summation variables (K1 and K2). The function of these two neurons is to sum up all the results gained from the hidden layer. After that, the activation of each neuron is activated and gets the probabilistic density function value in each class. (4) Output layer: The structure of this layer constructs is composed of the compete transfer function (CTF) and its main object is to distinguish which one is the largest. Then make the largest one is to be as ‘1’ and the others are ‘0’.

ð12Þ

where g represents the learning rate and the available value is situated between 0.1 to 1. dj ðnÞ represents the calculation result of step 2. By repeating the above three steps, the value of the error function will be zero or a fixed value. But in some conditions, the backpropagation neural network consisted of three layers that cannot satisfy the demand of the experiment, therefore the hidden layer will be add more than one layer.

3.2. Principle of probability neural network The probabilistic neuron network was proposed by Specht (1998). It has become popular in recent years because the training time is short. The structure of PNN is shown in Fig. 2. It includes four layers, the input layer, hidden layer, summation layer and output layer. All of them have their own assignments and are described clearly as follows:

(1) Input layer: It contains three input variables (I1–I3). The number of the variable is decided as the case changes. (2) Pattern (hidden) layer: It contains five input variables (J1–J5). Each neuron in the pattern layer calculates a distance by using the presented input vector and the input vector comes from the training data.

Throughout the four steps, classifying each fault condition will be figured out clearly.

4. Experimental investigation of faults identification 4.1. Experimental set up of gear-set platform The complete experimental arrangement of the proposed platform is shown in Fig. 3. The main parts of the gear-set contain a speed control unit, six gears and a server motor. The measuring instruments includes an optical fiber sensor as a tachometer, a condenser microphone (PCB 130D20), a spectrum analyzer (SR-785) and a data record system (NI PCI-6024E) on a personal computer. The sampling frequency is chosen to be 10 kHz. The microphone is located beside the gear-set platform for measuring the sound emission signal. The tooth number of gear A is 33, gear B is 17, gear C is 21, gear D is 29, gear E is 19 and gear F is 21. In addition, the speed control unit is used to control the rotational speed of the gear-set. In the experiment, the gear-set is driven by a servomotor. The gear-set is operated in 300, 600, 900, 1200 and 1500 rpm. The experiment also operated a run-up condition of speed from 300 rpm up to 900 rpm in seven seconds as shown in Fig. 4. Seven gear-conditions are tested in the experimental investigation, including no fault in the gear-set and different gear faults broken on the tooth.

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Fig. 9. Wavelet representation of sound emission in different gear faulted at run-up condition, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 9 (continued)

4.2. Experimental results and data analyzing In the fixed shaft speed, the gear-set is operated at 300, 600, 900, 1200 and 1500 rpm. Fig. 5 shows the sound emission signal in the time domain in the normal condition and different gear fault conditions. Normally, the amplitude of fault conditions is higher than without fault condition. Although it is easy to distinguish the fault and no fault conditions, however, it is not easy to identify the fault gear. In addition, the sound emission in the run-up condition of gear shaft speed from 300 rpm up to 900 rpm is shown in Fig. 6. Obviously, it is not easy to distinguish the fault gear. In the present study, the wavelet and frequency–energy distribution tendency method are proposed for the feature extraction in sound emission. Fig. 7 described the flowchart of signal processing in fault diagnosis. The sound emission signals are recorded and processed by a continuous wavelet transform technique combined with a feature selection of energy spectrum for analyzing fault signals in a gear-set platform. The neural network techniques both using BP and PNN are compared in the system. Fig. 8 shows the wavelet representation of sound emission in different gear faults at 1500 rpm. Meanwhile, Fig. 9 shows the wavelet representation of sound emission in different gear faults at run-up condition. The reason for using the wavelet transform technology is because of its resolution. By using the wavelet transform technology, a non-stationary signal can be analyzed using different resolutions at different times. In the figures, the relationship of time, frequency and energy are noted. However, it is not easy to know the differences between the seven conditions by human experience. Therefore, the TAWS method is proposed to analyze the sound emission signal. By using the TAWS, the relationship between time, frequency and power spectrum is shown in a twodimensional chart. By the transform of TAWS, the features of seven conditions with the shaft speed fixed at 1500 rpm are shown in Fig. 10, run-up condition is shown in Fig. 11. The illustration shows the energy distribution of the sound signal in different fault conditions. Further, the

patterns by using TAWS are digitized into the serial composed of 0 and 1. After spectrum trend feature method processing, the feature vectors are shown in Figs. 12 and 13. They are diagnostic trouble codes for the BP and PNN neural network. For quantifying the results of fault classification, the recognition rate is defined as follows:

Recognition rate 

Samples of the correct fault classification Total testing samples  100% ð13Þ

Finally, the recognition rates by BP and PNN are summarized in Tables 1 and 2. The comparison of the averaging recognition rates is shown in Fig. 14. It showed the classification accuracy achieved was about 98% by using the BP neural network. In comparison, a PNN neural network classifier has achieved an overall classification rate of 99% in averaged performance. When the fault is in gear A, the fault recognition rate is decreased. The comparison signed the fault technique using PNN is more effective than the BP algorithm in the proposed fault detection. Throughout the proposed fault diagnosis system, the recognition rates of fault conditions using PNN or BP are all over 98% in the experimental investigation. The performance of the recognition rate in PNN is better than BP except the recognition rate of gear B, but the variation is tiny. On the other hand, the learning constant and the number of hidden layers need to be set up by the user in the BP neural network. Both of them have an obvious influence on the fault classification. It is important to decide the proper learning constant and the number of hidden layers. Nevertheless, the weight value and the neuron number of hidden layer are fixed according to the training data throughout PNN. Therefore, the procedure of operating the PNN is easier than the BP neural network. Besides, because the weight value is setup therefore the training time of PNN is shorter than the training time of BP.

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Fig. 10. TAWS plot of the sound emission at 1500 rpm, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 11. TAWS plot of the sound emission at run-up condition, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 12. Feature vectors of the sound emission at 1500 rpm, (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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Fig. 13. Feature vectors of the sound emission at run-up condition: (a) normal; (b) gear A faulted; (c) gear B faulted; (d) gear C faulted; (e) gear D faulted; (f) gear E faulted; (g) gear F faulted.

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J.-D. Wu, J.-J. Chan / Expert Systems with Applications 36 (2009) 8862–8875 Table 1 Recognition rate of faulted gear identification using BP neural network. Gear-set conditions

300 rpm (%)

600 rpm (%)

900 rpm (%)

1200 rpm (%)

1500 rpm (%)

Run-up (%)

Average (%)

Without fault Gear A faulted Gear B faulted Gear C faulted Gear D faulted Gear E faulted Gear F faulted

100 96 96 99 99 100 98

100 92 91 100 96 100 100

98 100 95 100 100 98 98

100 100 97 100 94 100 100

99 100 98 100 99 99 100

98.4 100 100 100 100 98.4 100

99.23 98 96.17 99.83 98 99.23 99.33

Table 2 Recognition rate of faulted gear identification using PNN neural network. Gear-set conditions

300 rpm (%)

600 rpm (%)

900 rpm (%)

1200 rpm (%)

1500 rpm (%)

Run-up (%)

Average (%)

Without fault Gear A faulted Gear B faulted Gear C faulted Gear D faulted Gear E faulted Gear F faulted

100 100 98 100 99 100 100

100 100 97 100 96 100 99

97 100 91 100 100 97 100

100 100 91 100 98 100 100

100 100 99 100 95 100 99

100 100 100 100 100 100 100

99.5 100 96 100 98 99.5 99.67

No fault

Gear A Gear B Gear C Gear D Gear E Gear F

Fig. 14. The comparison of the averaging recognition rates of BP and PNN.

5. Conclusions In this paper, a gear-set fault diagnosis system based on the continuous wavelet transform technique for feature extraction and classification using artificial neural network was proposed. In the experimental work, the approach of extract fault features is to combine wavelet technique with TAWS method. The artificial neural network techniques both using BP and PNN were carried out and compared in the proposed system. The experimental results showed the sound emission can be used to monitor the condition of the gear-set platform and the proposed system achieved a fault recognition rate over 98% in the experimental work. Future research should be focus on the parallel development of a fault diagnosis detection instrument for technicians to preserve factories and for remote monitoring. Acknowledgement The study was supported by the National Science Council of Taiwan, Republic of China, under project number NSC 95-2622-E-018001-CC3. References Baydar, N., & Ball, A. (2001). A comparative study of acoustic and vibration signals in detection of gear failures using Wigner-Ville distribution. Mechanical System and Signal Processing, 15, 1091–1107.

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