## 1 Introduction  
Rolling bearings are a core component of rotating machinery in actual working environments. They play a very critical role in overall equipment operation [1, 2]. However, due to sustained loads under complex conditions, bearings are prone to a variety of failures, and the traditional scheduled maintenance model cannot effectively prevent economic losses caused by unforeseen failures. Prognostic and health management (PHM) delivers a transformative solution for bearing maintenance strategies through real-time monitoring and degradation analysis [3]. RUL prediction serves as a critical technology within PHM [4], which enables quantification of the time span from the current state to bearing functional failure. Accurate RUL prediction facilitates a paradigm shift from 'post-failure management' to 'pre-failure intervention', providing critical engineering value for normal operation and periodic maintenance programs for industrial equipment. Currently, RUL prediction methods for rolling bearings are internationally categorized into three well-defined parts: physically based models, statistically based models, and artificial intelligence-based models. Among them, RUL prediction methods based on statistical and artificial intelligence models are categorized as data-driven methods. Another approach, which we call the physics-based approach (such as the Paris law theory), requires an understanding of the failure mechanism of the bearing itself before modeling. However, the causes of bearing degradation are usually not homogeneous (such as load, lubrication, and material defects). These factors seriously affect the generalizability of the model ([PERSON] et al., 2018). Data-driven approaches directly model degradation trends using sensor data (such as vibration, temperature, etc. ), avoiding the need for complex physical assumptions, making them more suitable for real-world industrial environments. Shallow machine learning techniques rely on manual feature engineering and are limited in handling nonlinear degradation patterns ([PERSON] et al., 2018). [PERSON] et al. (2018) utilized optimized support vector regression for the prediction of bearing degradation, which concludes with a novel multi-population fruit fly optimization algorithm by introducing multi-population mechanism to choose the parameters of SVR. [PERSON] et al. (2018) proposed an adaptive time-varying ensemble Gaussian process regression-driven method for degradation prediction of rolling bearings. These shallow machine learning techniques are unable to autonomously extract features of the signal and generally depend on manually crafted features to perform RUL prediction. Deep learning methods can automatically extract temporal and spatial features, which significantly enhances prediction accuracy, and are increasingly adopted with the advancement of artificial intelligence technologies. For example, [PERSON] et al. (2018) proposed a multi-scale deep convolutional neural network (MS-DCNN) with robust feature extraction capabilities for integrating vibration signals, enabling more accurate degradation stage identification. [PERSON] et al. (2018) designed a convolutional long short-term memory fusion network. This network combines data from multiple sensors for modeling and prediction. [PERSON] et al. (2018) utilized BiTCN, which subsequently isolates bidirectional features and feeds them into a bidirectional gated recurrent unit (BiGRU) to predict the RUL of rolling bearings. [PERSON] et al. (2018) proposed a novel convolutional transformer. This network incorporates an attention mechanism to fully discover and capture important feature information. Local dependency modeling capability is used to predict bearings more accurately during convolution operation. [PERSON] et al. (2018) proposed a spectral graph convolutional method.