## 1 Introduction  
As one of the important parts of rotating machinery, rolling bearings need to consume a lot of manpower and material resources for maintenance in the case of failure [1, 2, 3]. Generally, the working conditions of the bearing are complex, and the working environment is harsh. The performance and health of the bearing will inevitably degrade during the production process [4, 5, 6]. If real-time monitoring of rolling bearing operating status and remaining useful life (RUL) prediction can be performed, early fault warning changes post-maintenance into condition-based maintenance. This can effectively reduce maintenance costs and avoid major safety accidents [7, 8, 9]. RUL prediction methods include physical model-based and data-driven ones [10, 11]. The data-driven method combines historical data and condition monitoring data with machine learning technology, such as artificial neural networks [12], support vector machines (SVMs) [13], and Gaussian process regression [14]. It establishes a prediction model to predict RUL. The advantage of data-driven methods is that they can directly understand the potential degradation trend of bearings from the available sensor data. As such, users do not need to know the exact failure mechanism of bearings. [PERSON] et al. [15] used the Hilbert-Huang transform to extract fault features. The obtained characteristic frequency was used to construct prediction index that was fed into SVMs for RUL prediction. [PERSON] et al. [16] used an overall empirical mode decomposition strategy to calculate time domain features, and constructed a support vector regression model to predict the health status of rolling bearings. [PERSON] et al. [17] developed a prediction method based on an artificial neural network for bearing RUL prediction. However, the above data-driven method mainly establishes the relationship between the degradation state and the system through a large amount of historical data. The prediction accuracy depends not only on the quantity of historical data, but also on the quality of historical data. In the process of RUL prediction, it is assumed that the decline process of the system follows certain rules without any mutation. Therefore, it is not suitable for RUL prediction of rolling bearings under varying working conditions and other uncertain factors. On the other hand, the model-based method depends on a physical model to describe the overall decline trend of the bearing through the failure mechanism, and then uses statistical estimation techniques, such as the Kalman filter (KF) [18], particle filter (PF) [18], and the unscented particle filter (UPF) [19] to update and estimate the bearing state and predict the bearing RUL. [PERSON] et al. [20] used the maximum likelihood algorithm to initialize the parameters of the Paris-Erdogan model, where the PF model was employed to recursively predict the bearing state. [PERSON] et al. [21] used the multipored autoregressive model to establish the bearing degradation model, and combined this with enhanced PF for bearing RUL prediction. [PERSON] et al. [22] constructed a nonlinear state space model, and used the unscented Kalman filter (UKF) algorithm to update and estimate the state, which realized the bearing performance evaluation and RUL prediction. The main advantage of the model-based method is that the prediction results are more intuitive, and the full combination of expert knowledge and real-time information from the machine can effectively carry out the bearing RUL prediction. However, the above methods mainly aim for the RUL prognostics of bearings under constant conditions, and they are not involved in varying working scenarios, such as variable rotational speed. The Kalman filter (KF) [18] is an optimal recursive data Processing algorithm, which can optimally estimate the future state of dynamic system. However, KF is more effective for a linear system, and is not suitable for dealing with serious nonlinear signals.