1. Introduction
Since bearing is a crucial component in the machine, its failure will hugely affect to the disruption of the machine. Therefore, condition monitoring for rolling bearings has become more and more important to detect early damage and increase safe of the operating systems. In the literature, two approaches can be applied to detect the bearing defects: (1) acoustic signal analysis, where the acoustic signal is acquired to obtain bearing characteristic information, and (2) vibration signal analysis, where the vibration signal is acquired. Among them, using vibration signal usually provides better defect detecting accuracy becuase it contains rich information of the bearing characteristics and less measurement noise [
1].
Bearing defects can be detected by either analyzing the fault frequency spectrum [
2] or pattern recognition [
3]. However, the analysis in [
4] shown that the pattern recognition can give higher accuracy compared to the spectrum approach. In the approach of traditional pattern recognition, the system will include three major components: feature extraction, feature selection and feature classification. The goal of the feature extraction task is to get as much information about the condition of the system as good. For this purpose, we employ the NLM-EMD method, which has been developed in our previous work [
5] and proved its effectiveness, to extract a rich bearing feature set.
Feature extraction usually results in a large feature set. Unfortunately, the large feature set does not neccessarily provide higher classification accuracy as it possibly contains irrelevant and redundant features. Thus, it is signiticant to eliminate the irrelevant and redundant features before it is fed back to a classifier. To obtain an optimal feature subset, a minimum-redundancy maximum-relevance (mRMR) feature selection method has been developed [
6]. The mRMR tries to search an outstanding combination of candidate features for minimum redundancy and maximum relevance. Due to the merits of the mRMR, it is employed in this paper to select the effective features.
Once the salient features are selected, they are fed into a classifier to identify the system condition. Due to its high performance classification and less requirement on sample data input, the support vector machine (SVM) proposed by Cortes and Vapnik [
7] has been successfully applied to signal processing [
8], regression analysis [
9], pattern recognition [
10], and bearing fault diagnosis [
11]. However, the original SVM classifier provides high computational burden due to the method used to solve the quadratic programming problem in the SVM [
12]. In order to reduce this, many methods have been developed, for example the SVM light decomposition algorithm [
13], sequential minimal optimization (SMO) algorithm [
14], neighbor algorithm [
15], and least squares SVM (LSSVM) [
16]. Among them, the LSSVM is commonly applied in real applications due to its simplicity in implementation and efficiency in classification and computation [
17].
In the SVM classifier, a kernel function is used to transform the data from the lower dimension space to a high dimension space. Hence, the prior selection of the kernel will decide the way of classification of the SVM [
18]. Several kind of kernels have been developed for SVM, for example, polynomial, dot product, and radial basis function (RBF) kernels. Among them, RBF kernel has shown to be more effective because it has good capacity to approximate nonlinear functions. Recently, wavelet kernel has been developed as an effective method for nonlinear approximation and mapping [
4,
19]. In [
20], Zhang et al. has employed the wavelet kernel for the SVM classifier, and a wavelet SVM (WSVM) classifier has been proposed as a result. Since the wavelet transform provides better approximation capacity than the RBF, the WSVM classifier provides higher accuracy than the SVM with RBF kernel. Since then, the WSVM have been employed in many real applications, such as in the medical field [
21], and machine fault diagnosis [
22]. Due to the merits of the LSSVM classifier and the approximation capability of the wavelet kernel, a new least squares wavelet support vector machine (LSWSVM) is proposed first time in this paper to improve both computational efficiency and classification accuracy. However, the generalization performance of the LSWSVM is affected by its parameters. Thus, it is necessary to optimize the parameters to obtain a better performance. In the literature, Particle swarm optimization (PSO) [
23] has been developed as an effective optimization technique to optimize parameters of a process. Compared with other optimization methods, PSO have many advantages, such as simple implementation, few parameters, parallel computation ability, and quickly converge [
24]. The PSO had proved its optimization capacity when applying for many practical applications, such as for optimizing the parameters of SVMs [
25] and other optimization problems [
26,
27]. Therefore, the PSO is used in this paper to effectively select the parameters of the LSWSVM, leading to a new PSO-LSWSVM classifier, which addresses all difficulties in the use of the SVM classifier.
In summary, the novelties and main contributions of this paper can be listed as follows:
A new methodology for bearing fault diagnosis is developed by combining between feature extration based on a NLM-EMD method, a feature selection based on a mRMR and a new PSO-LSWSVM classifier.
To improve the generalization performance of the SVM, a novel PSO-LSWSVM classifier, which combines between a least squares procedure, a new wavelet kernel function and the PSO, is proposed.
7. Conclusions
Two major contributions have been presented in this paper:
A new pattern recognition approach for bearing fault diagnosis is developed by combining between feature extration based on a NLM-EMD method, a feature selection based on a mRMR and a new PSO-LSWSVM classifier.
A novel PSO-LSWSVM classifier, which combines between a least squares procedure, a new wavelet kernel function and the PSO, is proposed.
In the presented method, the combined NLM-EMD is first employed to acquire more effective IMF components of vibration signals. Then, for the de-noised signal and each IMF component, the energy and time-domain feature parameters are extracted to obtain characteristic parameters. Next, the mRMR feature selection technique is adopted to eliminate the irrelevant and redundant features and select the best combined feature subset. Finally, the selected feature subset is fed into the proposed PSO-LSWSVM classifier to identify the bearing conditions, wherein a novel combination of a PSO, a least squares procedure, and a new wavelet kernel is proposed to address the difficulties in the use of the traditional SVM classifier. By experimenting with a real bearing vibration signal, we verified that the proposed wavelet kernel function has a better generalization performance than the previous kernels, i.e., RBF kernel, and the proposed PSO-LSWSVM classifier can overcome all difficulties in the use of the traditional SVM classifer. In addition, the uses of the NLM-EMD for the feature extraction and mRMR for the feature selection are effective. Therefore the proposed fault diagnosis methodology based on the NLM-EMD, mMRM feature selection and PSO-LSWSVM classifier improves the bearing recognition accuracy significantly, up to 95.53%.