Fault Diagnosis of Rolling Bearings Based on EWT and KDEC
This study proposes a novel fault diagnosis method that is based on empirical wavelet transform (EWT) and kernel density estimation classifier (KDEC), which can well diagnose fault type of the rolling element bearings. With the proposed fault diagnosis method, the vibration signal of rolling element bearing was firstly decomposed into a series of F modes by EWT, and the root mean square, kurtosis, and skewness of the F modes were computed and combined into the feature vector. According to the
... According to the characteristics of kernel density estimation, a classifier based on kernel density estimation and mutual information was proposed. Then, the feature vectors were input into the KDEC for training and testing. The experimental results indicated that the proposed method can effectively identify three different operative conditions of rolling element bearings, and the accuracy rates was higher than support vector machine (SVM) classifier and back-propagation (BP) neural network classifier. Due to the working environment and mechanism of the rolling bearings, the vibration signal is non-stationary and nonlinear, and it is difficult to extract the fault feature [10, 11] . Conventional time-frequency analysis only applies to narrow-band signal and has significant limitations in the case of non-stationary signal and broadband signal [12, 13] . When compared with the traditional time-frequency analysis, wavelet transformation performs the non-stationary signal processing better, but wavelet basis function limits the wavelet decomposition [14, 15] . The widely used empirical mode decomposition (EMD) is a self-adaptive signal processing method that accurately obtains characteristic signal; however, it involves a series of problems, such as enveloping and mode mixing [16, 17] . In recent years, the Empirical Wavelet Transform (EWT) for processing of non-stationary signal has been proposed    . EWT uses the Fourier spectrum to achieve signal decomposition within the wavelet frame. The method has sufficient theoretical basis and the decomposition process resolves the mode mixing of EMD, extracts the natural mode of vibration of the signal, and obtains the component of natural mode of vibration [21, 22] . As a critical part of fault diagnosis, the classifier plays an important role in feature vector processing  . Bayesian classifier has been widely used in various fields due to its high ant jamming capability and high efficiency. However, the classifier ignores the dependency relationship among attributes, and it decreases the classification accuracy by assuming the independence of an attribute with respect to other attributes [24, 25] . In the field of nondestructive testing, the back propagation (BP) neural networks classifier is used in the acoustic emission test at the bottom of the tank. Riahi et al.  distinguished among the signals of different corrosion stages. Zhang Xiaoyuan et al.  classified different operating conditions of the bearing using an improved support vector machine (SVM) classifier and proposed a motor bearing fault detection method. However, the BP classifier has many drawbacks, such as a large number of parameter settings and slow convergence, which reduces its diagnosis accuracy. In the case of small samples, SVM classifier can achieve higher accuracy than BP classifier, but requires the pre-selection of basic kernel functions. This significantly restricts the SVM application    . Kernel density estimation classifier (KDEC) method is used for studying the distribution characteristics starting from the data; it is widely used in the engineering field due to its high efficiency, and it has no requirements for data distribution    . Hence, by the advantages of mutual information in measuring the similarities in random variables, based on kernel density estimation and mutual information a classifier is proposed. The feature vector of complex signal is processed and its density function is estimated. The density function is calculated using the feature vector, and the similarity is also computed by mutual information. Therefore, a classifier based on Kernel density estimation (KDE) and mutual information is proposed to identify different fault types. To address the shortcomings in these fault diagnosis methods, this study proposes a novel fault diagnosis method based on EWT and KDEC. Regarding this novel method, the vibration signal is analyzed by EWT first; then, the accurate mode components are obtained. In addition, the root mean square (RMS), kurtosis, and skewness of the F component are calculated and are combined into the feature vector. The KDE and mutual information are combined to achieve the kernel density estimation classification. Finally, the feature vector is input to the KEDC for training and testing to complete the fault diagnosis of rolling bearings. The rest of this paper is arranged as follows: Section 2 illustrates the EWT method and simulations. Section 3 presents the proposed classification using KDE and mutual information. Section 4 introduces the proposed fault diagnosis method of rolling bearing. In Section 5, the experimental results of the proposed fault-detection scheme are analyzed.