# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 1 Introduction  
Rolling bearings, one of the important parts of rotating machinery, reduce the friction loss between mechanical components. Moreover, rolling bearings are a highly standardized precision mechanical device with the advantages of low friction, convenient assembly and use, and high working efficiency. As the connection between rotating parts, rolling bearings also serve as supporting parts and bear certain loads. Therefore, it is inevitable that these components suffer from a series of physical effects, such as mechanical stress and mechanical wear, which over time cause deformation and corrosion of the bearings, resulting in the degradation of their working performance. Rolling bearings are one of the most vulnerable parts of mechanical equipment because of their poor impact capacity [1]. Many failure modes of mechanical equipment, especially rotating machinery, are closely related to rolling bearingfailure. It is of great practical significance to carry out research on the condition monitoring and fault diagnosis technology of rolling bearings to effectively improve the reliability of mechanical equipment operations [2]. Many rolling bearing fault-diagnosis-related methods have been proposed in succession. [PERSON] et al. developed a scheme based on wavelet packet decomposition and hidden Markov modelling (HMM) for tracking the severity of bearing faults [3]. In this scheme, the wavelet packet decomposed vibration signals into a series of sub-signals and the energies of the sub-signals were extracted as features. The probabilities of HMM trained by features were used to track the condition of rolling bearings. [PERSON] et al. proposed a methodology termed indicated repeatable runout with wavelet decomposition that represents a novel approach for the determination of specific sources of vibration [4]. [PERSON] et al. presented a signal compression method based on ensemble empirical mode decomposition (EEMD) [5]. On the basis of ensuring the accuracy of the fault diagnosis, the burden of wireless transmission was reduced. Given their importance, the condition monitoring and fault diagnosis of rotating machinery are always a research focus and have attracted the attention of numerous scholars for years [6]. The model-based fault diagnosis technology is formed with the idea of analytic redundancy. The advantage of this method is that it can delve into the essence of a dynamic system and detect and diagnose faults in real time. The difficulty of its implementation lies in the need for an accurate system model. Model-based fault detection methods use residuals to indicate changes between the process and the model. One general assumption is that the residuals are changed significantly so that a detection is possible. The model-based method is often used for fault detection, but the analysis of the fault type and fault severity is insufficient [7; 8]. The vibration-based signal processing technique is one of the principal tools for diagnosing the malfunctions of rolling bearings [9]. Generally, rolling bearing fault diagnoses based on vibration analysis methods consist of two main parts: The feature extraction of vibration signals and the pattern recognition of faults [10]. First, the performance of the feature extraction method is the key point of rolling bearing fault diagnosis. Current feature extraction methods of vibration signals can be classified into three categories: Time domain feature extraction, frequency domain feature extraction, and time-frequency feature extraction. The vibration signals of faulty rolling bearing exhibit non-stationarity and non-linearity, leading to complex feature extraction processes and low separability of feature extraction results. In recent years, time-frequencyanalysis has become the main feature extraction method of rolling bearing fault diagnosis, predominating over the other feature extraction methods [11; 12; 13].