Mechanical failure classification for spherical roller bearing ofhydraulic injection molding machine using DWT–SVM

Expert Systems with Applications 37 (2010) 6742–6747

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

Mechanical failure classification for spherical roller bearing of hydraulic injection molding machine using DWT–SVM Guang-ming Xian * Computer Engineering Department, South China Normal University, Guangdong, Foshan 528225, China

a r t i c l e

i n f o

Keywords: Discrete wavelet transform Support vector machine Mechanical failure classification Spherical roller bearing Hydraulic injection molding machine

a b s t r a c t This paper presents a combined discrete wavelet transform (DWT) and support vector machine (SVM) technique for mechanical failure classification of spherical roller bearing application in high performance hydraulic injection molding machine. The proposed technique consists of preprocessing the mechanical failure vibration signal samples using Db2 discrete wavelet transform at the fourth level of decomposition of vibration signal for mechanical failure classification. After feature extraction from vibration signal, support vector machine is used for decision of mechanical failure types of the spherical roller bearing. The classification results indicate the effectiveness of the combined DWT and SVM based technique for mechanical failure classification of hydraulic injection molding machine. Ó 2010 Published by Elsevier Ltd.

1. Introduction For a rotary machine, roller bearing is a widely used rotary components (Sugumaran, Sabareesh, & Ramachandran, 2008). Due to the requirement of increasing reliability and decreasing possible loss of production owing to mechanical failures (Abbasiona, Rafsanjani, Farshidianfar, & Irani, 2007), condition monitoring (Hao, Lu, & Chu, 2008) of roller bearing become increasingly important in manufacture. Extracting the mechanical failure features and identifying the condition from the roller bearing vibration signals are very important for the fault diagnosis of roller bearings in a hydraulic injection molding machine. Because of the mechanical failure vibration signals of roller bearings are non-stationary, how to acquire eigenvector for the mechanical failure classification is a sticking point (Cheng, Yu, & Yang, 2006). Some non-direct approach are used to research the roller bearing’s nature of vibration (Sugumaran et al., 2008). By means of applying some vibration analysis (Lou & Loparo, 2004; Ocak, Loparo, & Discenzo, 2007; Wong, Jack, & Nandi, 2006) processing methods of vibration signals, it is possible to acquire vital classification information from the vibration signals (Lei, He, Zi, & Chen, 2008) for diagnosing the problem of rotating machinery. Extracting feature and recognizing conditions take precedence over acquisition of information in procedure of roller bearing mechanical failure classification (Yang, Yu, & Cheng, 2007). Finding out good features is an important phase in distinguishing the different mechanical failure conditions and requires detailed domain knowledge (Sugumaran et al., 2008). Wavelet analysis (Purkait & Chakravorti, 2002) has been utilized for im* Tel.: +86 757 83386595; fax: +86 757 86687309. E-mail address: [email protected] 0957-4174/$ - see front matter Ó 2010 Published by Elsevier Ltd. doi:10.1016/j.eswa.2010.02.062

pulse mechanical failure classification. For example, using the frequency-selective feature of wavelet transform (WT) can effectively analyzed the inherent non-stationary pattern of transformer current waveforms during different mechanical failure conditions (Koley, Purkait, & Chakravorti, 2006). As far as roller bearing failure classification is concerned, the method of desired time-frequency analysis has superior computational efficiency and resolution both in the field of time and frequency. Optimizing signal decomposition levels by using wavelet analysis and support vector machine (SVM) is an effective technique for multi-failure classification (Abbasiona et al., 2007). Owing to having the performance of high accuracy and good generalization capabilities, support vector machine introduced by Vapnik (1995), Schölkopf, Burges, and Smola (1999) is utilized in a lot of situations in machine learning. The fundamental principle of SVM is to use the so-called support vector (SV) (Vapnik & Chervonenkis, 1964) approach to construct the optimal separating hyperplane for pattern recognition. The SV technique was generalized for nonlinear separating surfaces in (Boser, Guyon, & Vapnik, 1992), and it was further extended for constructing decision rules in the non separable case (Cortes & Vapnik, 1995). The classification performance of SVM classifiers based on statistical learning theory is better than artificial neural network (ANN) because it uses the principle of risk minimization. For the method of ANN, traditional empirical risk minimization (ERM) is applied on training data set to minimize the error. But for the approach of SVM, structural risk minimization (SRM) is utilized to minimize an upper bound on the expected risk (Saravana, Kumar Siddabattuni, & Ramachandran, 2008). In paper (Ribeiro, 2005), C-SVM and m-SVM classifiers are compared with radial basis function (RBF) neural networks by Bernardete Ribeiro in data sets corresponding to product faults in an industrial environment concerning a plastics

G.-m. Xian / Expert Systems with Applications 37 (2010) 6742–6747

injection molding machine. Experimental results obtained thus far illustrate improved generalization with the large margin classifier as well as better performance enhancing the strength and efficacy of the chosen model for the practical case study. Injection molding with hydraulic system is a kind of highly automatic machine. The productivity of injection molding is obviously decreased for the reason of the frequent mechanical failures. Traditionally, the expert system for mechanical failure classification depend on experiences of the expert (Wang et al., 2000). In this paper, a mechanical failure classification technique of roller bearings for high performance hydraulic and hybrid injection molding machines is proposed. Initially, the features of the vibration signal are extracted by the fourth level decomposition of the samples using Db2 wavelet. Subsequently, the extracted features are applied as inputs to a SVM for determining the mechanical failure types of spherical roller bearing. In the processing of non-stationary signals, the wavelet method is more advanced than Fourier transform (Saravanan, Kumar Siddabattuni, & Ramachandran, 2008). Hence, wavelet transform has got potential application in spherical roller bearing mechanical failure in which features are extracted from the wavelet transform coefficients of the vibration signals of the hydraulic injection molding machine. Wavelet transform is quite suitable for the mechanical failure classification of spherical roller bearing. The selected features were fed as input to SVM for mechanical failure classification. The vibration signal (He & Starzyk, 2006; Lei, He, Zi, & Chen, 2008; Parikh, Das, & Maheshwari, 2008) from a roller bearing of hybrid injection molding machine is captured for the following conditions: slight rub of outer race, serious flaking of outer race, roller rub faults, and compound faults in the outer and inner races. The sampling frequency was 15 kHz and sample length was 8248 for rotating speed at about 360 rpm.

Supposing ðfV n ; n 2 Zg; /ðtÞÞ is a orthogonal MRA, we can get the following two-scale equation.

High performance hydraulic injection molding machines (Pan, Liu, Cai, & Shen, 2005; Zheng & Alleyne, 2003) keep molders in the lead by means of supplying competitive manufacturing application solutions, such as multi-cavity molding, challenging material combinations and integrated process molding. The machine base support mold weight by way of roller bearings, which reduce stress to tie bars and ensure clamping unit accuracy. The characteristics of spherical roller bearings are inherently self-aligning and very robust. The bearings enable to carry heavy loads by using two rows of rollers. The spherically formed outer ring raceway enable to make self-alignment, for the reason of having the same center as the bearing. Having good self-aligning ability and the bearings is able to operate when the shaft deflection under load or the shaft deflection under load or the shaft misaligning in mounting. In this paper, spherical roller bearings of 213 K series are made for heavy-duty applications in hydraulic injection molding machines. Because of having a large diameter, spherical roller bearings have a maximum number of long rollers. Spherical roller bearings is used with narrow dimensional tolerances and an increased radial clearance (http://www.bearing-fastener.com/Spherical-Roller-Bearing-50.html).

X

/ðxÞ ¼

hm /ð2x  mÞ

m

Using the above scaling function /ðxÞ, we can construct function

uðxÞ as below.

uðxÞ ¼

X

g m uð2x  mÞ

m

n i o 0 If W i ¼ span 22 uð2i x  mÞ; m 2 Z , we can get W i ? W j0 ; i–i ; W i  V i ¼ V iþ1 . where uðxÞ is called wavelet function. In practical application by computer, continuous wavelet should be discrete. Considering the following function in continuous wavelet

  1 tb wa;b ¼ jaj2 u a where b 2 R; a 2 Rþ . Then the compatibility condition can be expressed as below.

Cu ¼

Z

1

 Þj ^ ðl ju  <1 dl l

0

Usually, the parameter a and b can be defined as below.

a ¼ ai0 ;

b ¼ mai0 b0 ;

i2Z

Hence, the corresponding discrete wavelet ui;m ðtÞ is defined as i

   t  mai0 b0 i  ¼ a0 2 u ai 0 t  kb0 ai0

ui;m ðtÞ ¼ a0 2 u

And then we denote the discrete wavelet coefficient as

C i;m ¼ 2. Spherical roller bearing application in hydraulic and hybrid injection molding machines

6743

Z

1

1

f ðtÞui;m ðtÞdt <¼ hf ; ui;m i

The construction equation is

f ðtÞ ¼ C

1 X 1 X

C i;m ui;m ðtÞ

1 1

where C is a constant unrelated to the signal. Rather than using the detail and approximate information for future training and testing, we apply the energy at each decomposition level as a new input variable for SVM classification. We use the EDk and EAp to express the each decomposition level. EDk represents the energy of the detail at decomposition level k and EAp denotes the energy of the approximate at decomposition level p.

EDk ¼

M X

jDkl j;

k ¼ 1; . . . ; p

l¼1

EAp ¼

M X

jApj j2

l¼1

where i ¼ 1 . . . p is the wavelet decomposition level from level 1 to level p. M is an indication of the number of the coefficients of detail or approximate at each decomposition level. In this article, as far as a 4 level wavelet decomposition is concerned, a ð4 þ 1Þ dimensional eigenvectors are constructed for future mechanical failure diagnosis.

3. Discrete wavelet transform

4. SVM approach for classification

Wavelet transform (Burrus, Gopinath, & Guo, 1998; Daubechies, 1992) is widely applied in the field of engineering. Mallat firstly introduced multiresolution analysis (MRA) (Mallat, 1989).

Support vector machine (SVM) based on statical learning theory is proposed according to optimal hyperplane in the case of linear separable.

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G.-m. Xian / Expert Systems with Applications 37 (2010) 6742–6747

If the hyperplane (Lin, Chen, Truong, & Chang, 2005) separate all samples correctly, it must satisfy the following condition

yi ½ðx  xi Þ þ b  1 P 0;

i ¼ 1; . . . ; l

In order to find the optimal hyperplane, we need to minimize the following functionals.

1 1 uðxÞ ¼ kxk2 ¼ ðx  xÞ 2 2

l X 1 ai ½yi ðx  xi Þ þ b  1 ð x  xÞ  2 i¼1

l X

ai 

i¼1

l 1X ai aj yi yj ðxi  xj Þ 2 i;j¼1

yi ai ¼ 0; ai > 0;

ai yi xi

i¼1

It means that the weight coefficients of the optimal hyperplane is the linear combination of the training sample vector. According to the Kuhn–Tucker condition, the solution of optimal problem must satisfy

ai ½yi ðx  xi þ b  1 ¼ 0; i ¼ 1; . . . ; l After solving the above problem, we can get the optimal classification function as below.

" 



f ðxÞ ¼ sgn½ðx  xÞ þ b  ¼ sgn

l X

#

a

 i yi ðxi

 xÞ þ b



i¼1

The nonseparable problem can be solved by soft-margin SVM (Clarkson & Moreno et al., 1999; Ding, Chen, Liu, & Xu, 2002; Kecman, 2001; Vapnik, 1998). If we used the inner Kðx; x0 Þ substitute for the inner of the optimal hyperplane, the original feature space is mapped to new feature space. And the optimal function can be formulated as below:

Q ðaÞ ¼

l X

ai 

i¼1

l 1X umlj¼1 ai aj yi yj Kðxi  xj Þ 2 i¼1

subject to m X

where l; m and d are the parameters of kernel function. The classification performance of SVM are affected by three techniques, i.e., the selecting of the kernel, the choosing of the kernel parameters, and the choosing of the regularization parameter C (Beltrán, Duarte-Mermoud, Soto Vicencio, Salah, & Bustos, 2008).

i ¼ 1; . . . ; n

If ai is the optimal solution, then l X

r2 is the variance of the Gaussian function.

5.1. Classification performance comparison of mechanical failure using different methods

i¼1

x ¼

where parameter Sigmoid:

5. Experimental results and analysis

subject to l X

where parameter d is the degree of the polynomial. Radial basis function (RBF):

Kðx; xi Þ ¼ tanhðlxT xi þ mÞ

where ai > 0 is the Lagrange coefficient. The original problem can be transferred to the dual problem as below.

Max Q ðaÞ ¼

Kðx; xi Þ ¼ ðx  xi þ 1Þd

Kðx; xi Þ ¼ expðjx  xi j2 =2r2 Þ

Solution of the optimal problem is given by the saddles of Lagrange function as below.

Lðx; b; aÞ ¼

Usually, the kernel function Kðx; xi Þ (Cortes & Vapnik, 1995; Scholkopf, Smola, Williamson, & Bartlett, 2000; Vapnik, 1998) can be expressed as below. Polynomial:

ai yi ¼ 0 and 0 6 ai 6 C; i ¼ 0; . . . ; l:

To identify the mechanical failure of roller bearing, two classification methods were used, i.e., LVQNN, and SVM. Following data dimension reduction, a feature extraction procedure was performed using the techniques of PCA and wavelet analysis. Once the data dimension was reduced by using the feature extraction method, the total databases of 4000 cases of mechanical failure were divided in two sets: one for training-validation (containing 90% of the samples), and the other for test (containing 10% of the samples). Four different classes (C1–C4) of mechanical failure of roller bearing, named slight rub of outer race, serious? asking of outer race, roller rub faults, and compound faults in the outer and inner races, were considered in our research. Thirty-six hundred cases of each class were for training-validation and another four hundred cases were for test. The sample distribution of mechanical failure is shown in Table 1. The method of k-fold cross validation was used to measure the behavior and to obtain the optimal values of the parameters for each approach (Fukunaga & Hayes, 1989; Ripley, 1996). We used feature extraction methods in training-validation (cross validation with the aim to measure the behavior and to tune the optimal parameters for each classification of mechanical failure). Each identifier is assessed with the test set by using the whole training-validation set and the optimal parameters decided by cross validation. Because of the test set being never used in the training phase, it was completely unknown to the identifier and becoming a good performance measure of each technique (Beltrán et al., 2008). These high-frequency signals have been extracted by first level decomposition of the fault current by DWT using Db2 as mother wavelet. The RBF kernel function of the SVM has been used in

i¼1

The corresponding decision function is written as below

" # l X   f ðxÞ ¼ sgn ai ym Kðx  xi Þ þ b

Table 1 Training-validation and test set of samples for mechanical failure classification. Fault type

No. of trainingvalidation cases

No. of test cases

C1 C2 C3 C4

900 900 900 900

100 100 100 100

i¼1

here, Kðx  xi Þ is called kernel function. The regularization parameter C introduced representing the tradeoff between the incorrect classification rate and the capacity of the model can be determined by cross validation (Webb, 2002).

(slight rub of outer race) (serious flaking of outer race) (roller rub faults) (compound faults in the outer and inner races)

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G.-m. Xian / Expert Systems with Applications 37 (2010) 6742–6747

training-validation and test and the values of regularization parameter ðCÞ and the parameter ðrÞ have been selected as 3042 and 0.023, respectively. After the SVM is trained and validated with 3600 mechanical failure cases, its performance has been tested with the remaining 400 mechanical failure cases. For each of these mechanical failure cases, attributes of the spherical rolling bear have been provided at the input of SVM and the resultant output of the SVM has been compared with the corresponding correct mechanical failure type. Subsequently, the percentage of the correct classification of mechanical failure in validation identification algorithm has been expressed as

p1 ¼

number of correct classification indicated by SVM  100 3600

The percentage of the correct classification of mechanical failure in test identification algorithm has been computed as

p2 ¼

number of correct classification indicated by SVM  100 400

Table 2 gives the classification result for this mechanical failure classification problem based on the proposed method (SVM based on wavelet feature extraction), the method of SVM based on PCA feature extraction, the method of LVQNN based on wavelet feature extraction, and the method of LVQNN based on PCA feature extraction, respectively. As the results in Table 2, the best classification result of mechanical failure in the validation set (94.33%) and in the test set (95.25%) is obtained by using the proposed method of SVM based on wavelet feature extraction. These results clearly show the high percentage of correct classification reached for the validation set and test set, which clearly shows the good generalization capacity of SVM based on wavelet feature extraction for mechanical failure diagnosis of roller bearing.

5.2. Kernel function and parameters selection of SVM for mechanical failure classification As the results in Table 3, a 4  4 confusion matrix C is constructed to show the mechanical failure classification performance for the proposed method based on DWT–SVM. The diagonal elements represent the correctly classified mechanical failure. The off-diagonal elements represent the mis-classification of mechanical failure samples. The DWT–SVM method proposed can effectively identify different kinds of mechanical failure. From the results shown in Table 3, the best classification of mechanical failure results in the validation set (94.33%) and in the test set (95.25%) are obtained for RBF kernel function. The mechanical failure classification results of RBF kernel is clearly better than that of polynomial kernel and sigmoid kernel in validation set and test set. RBF kernel is the most accurate one for mechanical failure diagnosis in our experiment. In order to select the optimal values of the parameters C and r of the RBF kernel for mechanical failure classification, a series of experiments had been carried out by varying the values of these two parameters. The variation range of parameter C and r is as follows: (1) C, from 1 to 15,000; and (2) r, from 0.001 to 0.1. The classification results in validation and in test obtained for different combinations of C and r are shown in Table 4. Table 4 illustrated that the maximum correct classification result of mechanical failure in validation (94.33%) and test (95.25%) is obtained for C ¼ 3042 and r ¼ 0:023.

5.3. Noise analysis for the proposed DWT–SVM technique For testing performance of the proposed DWT–SVM method in different noise environments, different noises with the signal-tonoise ratio (SNR) (He & Starzyk, 2006) values ranging from 5 to

Table 2 Classification result of mechanical failure in validation and test using different methods. Method

Average % of correct classification in validation Average % of correct classification in test

Wavelet + SVM

PCA + SVM

Wavelet + LVQNN

PCA + LVQNN

94.33 95.25

87.78 83.50

86.47 80.50

83.68 78.75

Table 3 Classification results of mechanical failure for SVM method of different kernel function in validation set and test set. Kernel function

SVM Validation set

Polynomial

Test set

C1 C2 C3 C4 Average % of correct classification

C1 822 35 39 11 91.56

C2 29 831 32 26

C3 15 0 814 34

C4 34 34 15 829

C1 C2 C3 C4 Average % of correct classification

C1 873 32 0 17 94.33

C2 12 838 21 10

C3 0 30 846 34

C4 15 0 33 839

C1 C2 C3 C4 Average % of correct classification

C1 814 15 18 33 90.08

C2 17 808 23 39

C3 36 45 838 45

C4 33 32 21 783

RBF

Sigmoid

C1 C2 C3 C4 Average % of correct classification

C1 90 1 4 0 89.75

C2 2 91 4 6

C3 3 4 89 5

C4 5 5 3 89

C1 C2 C3 C4 Average % of correct classification

C1 97 1 1 2 95.25

C2 2 96 4 0

C3 0 2 93 3

C4 1 1 2 95

C1 C2 C3 C4 Average % of correct classification

C1 94 2 5 2 92.75

C2 3 93 2 0

C3 2 3 91 5

C4 1 2 2 93

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G.-m. Xian / Expert Systems with Applications 37 (2010) 6742–6747

Table 4 SVM classification results of mechanical failure using different values of C and

r.

C

r

% Correct classification in validation

% Correct classification in test

1 10 115 501 1023 3042 516 8893 9835 12,890

0.001 0.005 0.008 0.014 0.015 0.023 0.058 0.072 0.084 0.100

88.22 89.75 92.36 92.78 93.83 94.33 93.56 92.86 90.11 89.14

90.25 91.50 92.75 93.25 94.50 95.25 94.75 93.25 91.25 89.50

achieve satisfied classification accuracy (over 90%) for mechanical failure in validation and test.

6. Conclusion This paper presents a combined wavelet-support vector machine technique for mechanical failure diagnosis application hydraulic injection molding machines. Discrete wavelet transform based multiresolution analysis is utilized for feature extraction at the fourth level of decomposition. After feature extraction from mechanical failure vibration signal, support vector machine is used for decision of mechanical failure types of the spherical roller bearing. Then RBF kernel based SVM is used for mechanical failure types classification. The combined WT and SVM based technique is tested for mechanical failures and provides accurate results for mechanical failure classification. Experimental results obtained for the SVM classifier, using an RBF kernel, for different values of C and r, using wavelet decomposition level 4. By using this technique, the best classification result of mechanical failure in validation was 94.33%, whereas in test, this rate was 95.25%, highlighting the good generalization property of the SVM. Acknowledgement The authors acknowledge the support of the South China Normal University and South China University of Technology. The work was support by the project of research of support vector machine in classification and regression, under project number Guangdong financial education (2008) 342. References

Fig. 1. Classification result of mechanical failure under different SNR condition.

40 dB are discussed in this article. Beng a term for the power ratio between a signal and the background noise in engineering, signalto-noise ratio can be written as:

SNR ¼

 2 Psignal Asignal ¼ Pnoise Anoise

ð1Þ

where P is average power and A is RMS amplitude. We must gauge both signal and noise power at the same or equivalent points in a system. SNRs are usually expressed in terms of the logarithmic decibel scale for the reason of many signals having a very extensive dynamic range. In decibels, the SNR is defined as 10 times the logarithm of the power ratio. As the following equation shown, the SNR can be acquired by computing 20 times the base-10 logarithm of the amplitude ratio, when the signal and the noise is measured across the same impedance

SNRðdBÞ ¼ 10log10

    Psignal Asignal 2 ¼ 20log10 Pnoise Anoise

ð2Þ

For each class of mechanical failure (C1–C4), 3600 cases were for training–validating and another 400 cases were for testing. We use the Db2 wavelet for analysis with four level of decomposition, respectively. Fig. 1 indicates the experiments results carried outing at various values of SNR. From Fig. 1, it can be observed that even in very low SNR (5DB) condition, the proposed DWT–SVM method can still

Abbasiona, S., Rafsanjani, A., Farshidianfar, A., & Irani, N. (2007). Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine. Mechanical Systems and Signal Processing, 21, 2933–2945. Beltrán, N. H., Duarte-Mermoud, M. A., Soto Vicencio, V. A., Salah, S. A., & Bustos, M. A. (2008). Chilean wine classification using volatile organic compounds data obtained with a fast GC Analyzer. IEEE Transactions on Instrumentation and Measurement, 57, 2421–2436. Boser, B., Guyon, I., & Vapnik, V. (1992). A training algorithm for optimal margin classifiers. In Proceedings fifth annual ACMWorkshop on computational learning theory (pp. 144–152). Burrus, C. S., Gopinath, R. A., & Guo, H. (1998). Introduction to wavelets and wavelet transforms: A primer. Englewood Cliffs, NJ: Prentice-Hall. Cheng, J., Yu, D., & Yang, Y. (2006). A fault diagnosis approach for roller bearings based on EMD method and AR model. Mechanical Systems and Signal Processing, 20, 350–362. Clarkson, P., & Moreno, P. J. (1999). On the use of support vector machines for phonetic classification. In Proceedings of the IEEE international conference acoustics, speech, signal processes (Vol. 2, pp. 585–588). Cortes, C., & Vapnik, V. (1995). Support vector networks. Machinery Learning, 20, 273–297. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia, PA: Society for Industrial and Applied Mathematics. Ding, P., Chen, Z., Liu, Y., & Xu, B. (2002). Asymmetrical support vector machines and applications in speech processing. In Proceedings of the IEEE international conference acoustics, speech, signal processes (Vol. 1, pp. I-73–I-76). Fukunaga, K., & Hayes, R. (1989). Estimation of classifier performance. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(10), 1087–1101. Hao, R., Lu, W., & Chu, F. (2008). Morphology filters for analyzing roller bearing fault using acoustic emission signal processing. Journal of Tsinghua University, 48(5), 812–815. He, H., & Starzyk, J. A. (2006). A self-organizing learning array system for power quality classification based on wavelet transform. IEEE Transactions on Power Delivery, 21(1). Kecman, V. (2001). Learning and soft computing. Cambridge, MA: MIT Press. Koley, C., Purkait, P., & Chakravorti, S. (2006). Wavelet-aided SVM tool for impulse fault identification in transformers. IEEE Transactions on Power Delivery, 21(3). Lei, Y., He, Z., Zi, Y., & Chen, X. (2008). New clustering algorithm-based fault diagnosis using compensation distance evaluation technique. Mechanical Systems and Signal Processing, 22, 419–435. Lei, Y., He, Z., Zi, Y., & Chen, X. (2008). New clustering algorithm-based fault diagnosis using compensation distance evaluation technique. Mechanical Systems and Signal Processing, 22, 419–435.

G.-m. Xian / Expert Systems with Applications 37 (2010) 6742–6747 Lin, C.-C., Chen, S.-H., Truong, T.-K., & Chang, Y. (2005). Audio Classification and categorization based on wavelets and support vector machine. IEEE Transactions on Speech and Audio Progressing, 13(5). Lou, X. S., & Loparo, K. A. (2004). Bearing fault diagnosis based on wavelet transform and fuzzy inference. Mechanical Systems and Signal Processing, 18, 1077–1095. Mallat, S. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. Ocak, H., Loparo, K. A., & Discenzo, F. M. (2007). Online tracking of bearing wear using wavelet packet decomposition and probabilistic modeling – A method for bearing prognostics. Journal of Sound and Vibration. doi:10.1016/ j.jsv.2007.01.001. Pan, C., Liu, H., Cai, W., & Shen, Z. (2005). The research for close-loop control system of hydraulic injection molding machine. Control and Automation(5), 16–17. Parikh, U. B., Das, B., & Maheshwari, R. P. (2008). Combined wavelet-SVM technique for fault zone detection in a series compensated transmission line. IEEE Transactions on Power Delivery, 23, 1789–1794. Purkait, P., & Chakravorti, S. (2002). Pattern classification of impulse faults in transformers by wavelet analysis. IEEE Transactions on Electrical Insulation, 9(4), 555–561. Ribeiro, B. (2005). Support vector machines for quality monitoring in a plastic injection molding process. IEEE Transactions on Systems, Man and Cybernetics – Part C: Application and Reviews, 35(3). Ripley, B. D. (1996). Pattern recognition and neural networks. Cambridge, UK: Cambridge University Press. Saravana, N., Kumar Siddabattuni, V. N. S., & Ramachandran, K. I. (2008). A comparative study on classification of features by SVM and PSVM extracted using Morlet wavelet for fault diagnosis of spur bevel gear box. Expert Systems with Applications, 35, 1351–1366.

6747

Saravanan, N., Kumar Siddabattuni, V. N. S., & Ramachandran, K. I. (2008). A comparative study on classification of features by SVM and PSVM extracted using Morlet wavelet for fault diagnosis of spur bevel gear box. Expert Systems with Applications, 35, 1351–1366. Schölkopf, B., Burges, C., & Smola, A. (1999). Advances in kernel methods – Support vector learning. Cambridge, MA: MIT Press. Scholkopf, B., Smola, A., Williamson, R. C., & Bartlett, P. L. (2000). New support vector algorithms. Neural Computation, 12, 1207–1245. Sugumaran, V., Sabareesh, G. R., & Ramachandran, K. I. (2008). Fault diagnostics of roller bearing using kernel based neighborhood score multi-class support vector machine. Expert Systems with Applications, 34(4), 3090–3098. Vapnik, V. N. (1995). The nature of statistical learning theory. New York: SpringerVerlag. Vapnik, V. N. (1998). Statistical learning theory. New York: Wiley. Vapnik, V., & Chervonenkis, A. (1964). A note on one class of perceptrons. Automatic Remote Control, 25. Wang, W., Song Z., Han B., & Li, P. (2000). A fault diagnosis expert system for hydraulic system of injection moulding. In Proceedings of the world congress on intelligent control and automation (WCICA) (Vol. 1, pp. 229–232). Webb, A. (2002). Statistical pattern recognition. Hoboken, NJ: Wiley. Wong, M. L. D., Jack, L. B., & Nandi, A. K. (2006). Modified self-organising map for automated novelty detection applied to vibration signal monitoring. Mechanical Systems and Signal Processing, 20, 593–610. Yang, Y., Yu, D., & Cheng, J. (2007). A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM. Measurement, 40, 943–950. Zheng, D., & Alleyne, A. (2003). Modeling and control of an electro-hydraulic injection molding machine with smoothed fill-to-pack transition. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 125(1), 154–163.