## 1 Introduction  
Rolling bearings are widely used in industrial production and life, such as aerospace, engines, mining machinery, agricultural machinery, and other fields, and they are known as 'industrial joints'. The primary failure modes of rolling bearings include rolling contact fatigue, wear, corrosion, electrical erosion, plastic deformation, cracking, and fracture. These failures are mainly attributed to material fatigue and inadequate lubrication [1]. Operating rolling bearings under rated conditions and applying appropriate types and amounts of lubricant at regular intervals can significantly reduce the likelihood of failures caused by factors other than fatigue [2]. As one of the key components of mechanical equipment, a good running state is very important for the normal operation of mechanical equipment [3]. Bearing failures can lead to outcomes ranging from unplanned downtime to complete system breakdowns, resulting in substantial economic losses and even potential safety hazards [4]. Therefore, research on accurate prediction methods for the remaining useful life (RUL) of rolling bearings holds significant practical importance. The RUL of a rolling bearing is defined as the time interval from the current moment to the point of failure [5]. Currently, RUL prediction methods for rolling bearings can be broadly classified into two categories [6]: physics-based methods and data-driven methods. Physics-based approaches aim to build accurate mathematical models by deeply analyzing the operating mechanisms, degradation processes, and failure modes of equipment. Common models include the Paris model [7], the Forman crack growth model [8], and the Palmgren-Miner linear damage accumulation model [9]. These methods offer strong interpretability and reliable prediction accuracy without requiring large datasets. However, with the increasing complexity and integration of modern industrial systems, accurate physical modeling has become extremely challenging, which significantly limits the practical applicability of physics-based approaches. With advances in signal processing and artificial intelligence, data-driven methods have emerged as a research hotspot for the RUL prediction of rolling bearings [10]. These methods can be further divided into statistical learning, shallow machine learning, and deep learning approaches. Statistical learning methods often depend heavily on prior knowledge and high-quality data; shallow machine learning models tend to struggle with complex tasks and high-dimensional data. In contrast, deep learning methods can autonomously learn degradation patterns from large volumes of historical data without requiring expert knowledge, making them a focal point in the data-driven domain. For the accurate RUL prediction of rolling bearings, two key challenges must be addressed [11]: (1) how to select an optimal feature set that effectively characterizes bearing degradation trends, and (2) how to choose an appropriate model to map degradation features to the remaining useful life. In terms of feature selection, several studies [12; 13; 14] have proposed constructing composite indicators based on specific criteria to identify features that are beneficial for bearing RUL prediction. While such indicators can effectively filter features related to the degradation process, they often overlook the interrelationships among features. [PERSON] et al. [15] applied kernel principal component analysis to reduce multi-domain features, which helped to mitigate redundancy but lacked interpretability. [PERSON] et al. [16] proposed a dual-selection method combining mutual information with hierarchical clustering. Their experimental results demonstrated that this approach reduced feature redundancy and improved model classification performance. [PERSON] et al. [17] introduced an adaptive feature selection algorithm that integrates the ideal point method with K-medoids clustering, enabling effective optimization of the feature set.