## 1 Introduction  
A bearing is one of the core components of rotating mechanical system. It is a highly standardized precision mechanical device, which has the advantages of low friction, easy assembly and use, and high work efficiency [1]. However, as a connection between rotating parts, the bearing should also bear a certain load as a supporting part. Therefore, in the use of the bearing, it is inevitably subjected to a series of physical effects such as mechanical stress and mechanical wear, which will lead to deformation and corrosion of the bearing over time, leading to changes in the running state of the bearing. Moreover, due to the imperfect production technology and improper operation and installation, the bearing will also produce artificial damage, and the accumulation and deepening of this damage eventually leads to the failure of bearing [2]. Rolling bearings are mainly composed of inner race, outer race, ball elements and retainer, and the fault types of bearings are generally shown in the form of several parts defects described above, among which the most common types of rolling bearings are the failure of inner race, outer race and ball elements. A bearing is also the most easily worn out part of motor. According to statistics, more than 40% of motor faults are related to a bearing [3,4]. Therefore, fault diagnosis of rolling bearings is of great significance to ensure the reliability and safety of rotating mechanical system. At present, fault diagnosis methods based on different theories have been successfully applied to fault diagnosis of rolling bearings [5], such as vibration, acoustic noise [6,7], stator current, thermal-imaging, and multiple sensor fusion, etc. The fault diagnosis method based on vibration signal is one of the most commonly used fault diagnosis methods for rolling bearings in rotating machinery. Firstly, it is convenient to acquire vibration signal of a rolling bearing, and the cost of monitoring equipment based on vibrating sensors is low. Secondly, the vibration signal is not easily affected by external environment noise. A rolling bearing inevitably generates vibration along with rotation during operation. Vibration, as an external manifestation of a bearing's own dynamic characteristics, contains rich state information and can reflect bearing fault information. When there is a failure period of the rolling bearing, the vibration signal usually contains some periodic pulse signal. The signal is collected by the vibrating sensor on the bearing base for further analysis and processing, so that the rolling bearing state change information can be obtained and the bearing fault type can be identified. In recent years, scholars in the field of fault diagnosis of rolling bearings based on vibration signal continue to explore, and made a lot of research results. However, there is still the problem of low fault identification accuracy due to insufficient fault feature extraction. Especially, the research of fault severity analysis is one of the urgent problems in this field. According to the characteristics of vibration signal of rolling bearings, the fault diagnosis methods based on data-driven method, mathematical model and pattern recognition method are widely used [8,9]. Although the data-driven method is flexible in use, it is often used for fault detection and has low fault identification accuracy. The mathematical model-based method needs to model the running state of rolling bearings and accurately model different fault types to obtain better fault diagnosis results. Therefore, pattern recognition is one of the important fault diagnosis methods to analyze the vibration signal of a rolling bearing. It is mainly divided into two parts: effective feature extraction contained in vibration signal and classification of the fault features. For feature extraction of a rolling bearing vibration signal, the time-frequency analysis has become a principal method to extract the fault characteristics of rolling bearings because the vibration signal is often non-stationary.