# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 1 Introduction
Second, an appropriate classification algorithm should be adopted to identify the fault types on the basis of accurately extracting the fault features of rolling bearings. The adopted classification algorithm should have good generalization, multi-classification performance, and a simple model structure [14; 15]. Obviously, the selection of an appropriate pattern recognition algorithm is another key point in determining the recognition rate of rolling bearing fault diagnoses. The vibration signal of the rolling bearing is composed of the vibration of the rolling bearing itself, the vibration caused by other moving parts of the electrical machinery, and the external disturbances. These vibration signals are superimposed on each other, resulting in extremely complex vibration signals acquired by the vibration sensors. To effectively extract the fault features from the non-linear and non-stationary vibration signals, many time-frequency analysis methods have been applied to rolling bearing fault diagnoses for vibration signal decomposition. The decomposed fault signal is helpful for further highlighting the fault characteristics of the vibration signal. The fast Fourier transform (FFT) is a classical time-frequency analysis method, but it is inherently unsuitable for non-stationary and transient signal analysis. The window shape and size of the short-time Fourier transform (STFT) is fixed for all frequencies, which causes the STFT to have obvious limitations regarding time-varying signals. In contrast to the FFT and STFT, the wavelet transform (WT) is a typical time-frequency analysis technique that can change both the time and frequency windows, thus enabling a multi-scale analysis of the vibration signal. However, the frequency resolution decreases with increasing frequency. Therefore, the WT cannot effectively split the high-frequencyband containing rich fault modulation information [16]. Empirical mode decomposition (EMD) is a self-adaptive time-frequency decomposition technique that can self-adaptively decompose a non-stationary non-linear signal into a series of intrinsic mode functions (IMFs) that include different frequency characteristics [1]. Nevertheless, EMD has an end effect and mode mixing problem that directly influences the stability of the decomposition results and the subsequent feature extraction effects [17]. To improve the above disadvantages, many derivative methods of EMD, such as EEMD and complete ensemble empirical mode decomposition (CEEMD) are presented. Local mean decomposition (LMD) can automatically decompose multi-component amplitude-modulated (AM) and frequency-modulated (FM) signals into a series of product functions (PFs), each of which is a mono-component AM-FM signal that contains the signal characteristics. However, as with the EMD, the LMD suffers from the problem of edge effects caused by the local extreme points [18]. The wavelet packet transform (WPT) has been introduced to overcome WT's application problems. The WPT is an extension of the WT that can select an arbitrary frequency resolution, which makes it relatively flexible [19]. Although some studies suggest that WT-based decomposition is not an adaptive method due to the need to preselect the wavelet kernel function, the WPT is still an effective time-frequency analysis method for the vibration signal characteristics of rotating machinery because of its complete theoretical basis and excellent decomposition results compared with those of EMD and LMD. To further extract the fault features of the decomposed vibration signal by the time-frequency analysis method, many entropy-based feature extraction methods have been investigated for rolling bearing fault diagnosis, such as approximate entropy (ApEn), fuzzy entropy (FE), permutation entropy (PE), and sample entropy (SampEn). [PERSON] et al. adopted EEMD to decompose the vibration signal into a set of IMF and calculated the PE values of the first several IMFs to reveal the intrinsic characteristics of a faulty vibration signal [11]. [PERSON] et al.