## 1 Introduction
However, the existing research mostly focuses on RUL prediction under single working condition, ignoring the consideration of environmental conditions and operating conditions to a certain extent. Therefore, it lacks generalization in practical engineering application, which affects the effectiveness of prediction. To sum up, it is difficult to accurately extract features containing bearing degradation information from non-stationary vibration signals in a time domain. In addition, the establishment of the degradation model usually requires clear prior knowledge and extensive empirical data. The degradation model is not updated in real time according to the actual degradation state of the bearing, which has a large error with the actual degradation trend of the bearing and affects the RUL prediction accuracy. To solve the above problems, this paper proposes a RUL prediction method dealing with rolling bearings under variable rotational speed, based on angular domain transformation and time-varying degradation model parameters. Firstly, the angle domain transform is used to process the original time domain signal and extract the real-time degradation features of bearings. Secondly, a finite element method (FEM)-based time-varying parameter degradation model consistent with the bearing performance degradation state is established. The unscented particle filter algorithm (UPF) is used to estimate the bearing degradation state for predicting its RUL. This method not only alleviates the limitations of RUL prediction methods based on data-driven and physical models, but also predicts the future degradation trend of bearings more accurately. There are three main contributions of this paper. (i) Aiming at the difficulty in extracting features of non-stationary signals under variable operating conditions, this paper proposes an angular domain unscented particle filter (UPF) RUL prediction method. The angle domain transform is used to process the signals, which can accurately extract the features containing important information, and combined with the UPF algorithm to update and estimate the bearing state, thereby improving the accuracy of the remaining useful life prediction of the bearing. (ii) In the process of establishing the bearing degradation model based on the Paris-Erdogan theorem, the parameters of the model are not selected according to empirical formulas, but by establishing a finite element model consistent with the bearing degradation model to update model parameters in real time, to make it more in line with the real degradation trend of the bearing. (iii) The effectiveness of the proposed method is verified by two bearing experiments. Compared with the state-of-the-art methods, the developed method obtained a superior performance. The rest of this paper is arranged as follows. Section 2 introduces the basic theory of angular domain transformation, the unscented particle filter, and the time-varyingparameter degradation model. Effectiveness of the proposed method is verified by a benchmark dataset experiment and an accelerated life prognosis experiment as presented in Section 3, respectively. Conclusions are obtained in Section 4.