## 1 Introduction  
Fault diagnosis is a basic problem in reliability analysis [1]. Fault diagnosis is divided into fault detection and fault isolation [2]. Fault detection is to find out whether there is a fault in the system or equipment using various inspection and testing methods. Fault isolation requires locating the location of the fault. Therefore, fault diagnosis can determine the type and location of equipment failure so as to maintain the equipment and reduce the loss caused by the long downtime of equipment [3]. There are several steps for fault diagnosis in reliability engineering [4]. Firstly, we can determine whether the equipment has a fault or not. Then, we can analyze the reasons and determine the fault types. Finally, we can divide the fault categories and diagnose the specific fault location and causes of the equipment, so as to prepare for the recovery of the failed equipment [5; 6]. At present, the methods of fault diagnosis are also roughly divided into three categories: the fault diagnosis method based on the analytic model, the fault diagnosis method based on signal processing, and the fault diagnosis method based on artificial intelligence [7]. The research on bearing fault diagnosis methods based on an analytical model has lasted more than half a century [8]. In the last 10 years, due to the development of science and technology and the change of bearing application environment, the speed and temperature of bearings are much higher than in the past [9]. The rapid development of modern computers has led to the updating of relevant software, which provides conditions for the dynamic simulation of rolling bearings, and the advanced dynamic model of rolling bearing has replaced the simple static balance model [10]. Although the static model and dynamic model can be used to simulate the performance of rolling bearings, it mainly considers the static and moment balance equation. At present, fault diagnosis technology based on signal processing is widely used [11]. The signal characteristics of nonlinear and nonstationary signals are relatively poor, and empirical mode decomposition (EMD) decomposes the signal into finite signal characteristics according to the characteristics of the signal itself [12]. These intrinsic modal functions are local detail components of the original signal at different time scales and can approximate the original signal very well. So, the EMD method is suitable for nonstationary signals and linear nonstationary signals. The original acquisition signals of bearings are nonlinear and nonstationary signals, so EMD is widely used in bearing fault diagnosis [13]. With the progress of the times, in the era of big data, more and more importance has been attached to the fault diagnosis method based on artificial intelligence [14; 15; 16]. This method can overcome the drawback of excessive dependence on the model and can be used to diagnose potential faults, which significantly improves the accuracy of fault diagnosis [17; 18; 19]. Machine learning mainly obtains new experience and knowledge by autonomously learning the rules that exist in a large number of data and thus realizing the learned behavior of humans. Almost all fault diagnosis methods based on artificial intelligence are achieved through a machine learning algorithm [20; 21]. Based on the different learning forms, machine learning algorithms can be divided into supervised learning, unsupervised learning and reinforcement learning. Support vector machine (SVM) is a kind of supervised learning in machine learning [22]. The application and research of SVM arithmetic in engineering appear in the fault diagnosis of rolling bearings [23]. In recent years, with the development of machine learning in fault diagnosis, clustering, as another classification algorithm, has attracted more and more attention [24].