## 1 Introduction  
Rotating machinery is widely used in aerospace, automobile manufacturing, wind power generation and other important engineering fields. Rolling bearing is a key component in rotating machinery. Because this mechanical equipment often operates under complex working conditions, bearings are prone to pitting, breaking, gluing and other failures, which will lead to the paralysis of the mechanical equipment and cause significant economic losses [1]. Statistical analysis results provided by multiple studies have shown that more than 40% of the equipment faults are related to bearings [2]. Thus, how to improve the fault diagnosis of bearings under variable working conditions is related to the stable operation of the whole equipment and production line. The traditional fault diagnosis method determines the equipment health state by establishing the corresponding dynamic model. For instance, [PERSON] et al. [3] not only considered the bearing internal stiffness, damping, clearance and other nonlinear characteristics, but also took the bearing external load, eccentricity and other characteristics as factors affecting the normal operation of the bearing ball. The dynamics model of the ball bearing motion process with two degrees of freedom was established to reveal the dimensionless relationship and the influence on the system response. In the study by [PERSON] et al. [4], the traditional loaded tooth contact analysis (LTCA) method was extended to calculate the mesh stiffness and contact stress of spalled gear pairs, and established a novel dynamic model for spalled gear pairs to describe the dynamic response of the gear pair under different spall modes. Such methods heavily rely on the researcher expertise, and specific devices are needed to establish specific dynamic models, greatly limiting their applicability [5]. In addition, some scholars analyze the characteristic frequency of faults. For instance, [PERSON] et al. [6] used Fourier transform and recurrence analysis to analyze the vibration signal during engine operation, and could accurately determine the location of the failed cylinder. In order to solve the problem that composite bearing faults are difficult to diagnose, [PERSON] et al. [7] first established a functional model of bearing vibration signals, and then a single fault frequency feature set was separated through decoupling, so as to complete the diagnosis of composite faults. [PERSON] et al. [8] used discrete wavelet to analyze the electric signal of the motor in time domain, remove the interference components, and successfully extract the more obvious fault characteristic frequency. This kind of research is mainly based on the purpose of removing noise interference to extract the characteristic fault frequency of bearings, but this method requires a large number of marker signal samples, and also requires manual selection of features. In addition, the above research focused on the validity of a single working condition verification method, and there is a lack of exploration and research on fault diagnosis under variable working conditions. In recent years, machine learning has accelerated the development of intelligent fault diagnosis through technologies such as ensemble learning [9], support vector machine (SVM) [10], and artificial neural networks [11]. However, such fault diagnosis methods require additional processing of data characteristics and cannot provide fast diagnostic services [12; 13]. As another branch of machine learning, deep neural network has been successfully applied in the field of fault diagnosis due to its advantages of feature self-extraction [14]. As a representative of the current deep neural network, convolutional neural network (CNN) has the characteristics of parameter sharing and translation invariance, which can extract more robust features. [PERSON] et al. [15] established a multi-scale convolutional neural network model by integrating feature extraction and pattern recognition for fault diagnosis. Further, [PERSON] et al.