## 1 Introduction  
Accurate prediction of the remaining useful life (RUL) of rolling bearings is crucial for ensuring the safe operation of machinery and reducing maintenance costs [1, 2, 3]. Modern industrial equipment operates in complex and dynamic environments, where its reliability directly impacts production efficiency and safety [4, 5, 6]. Therefore, accurate reliability assessment was crucial. However, the actual structure of the equipment was influenced by various internal and external time-varying effects, complex operational disturbances, measurement noise, and other factors, making it challenging to ensure the accuracy of long-term predictions [7, 8]. To address this issue, this paper analyzed real operational data and developed new methods and tools for reliability evaluation. In recent years, deep learning has attracted widespread attention in fields such as natural language processing, transfer learning, and computer vision [9, 10, 11, 12]. [PERSON] et al. [13] proposed an improved time fusion Transformer method, which replaces the traditional long short-term memory (LSTM) [14] with a bidirectional long short-term memory (Bi-LSTM) encoder-decoder to enhance the ability to capture time-series features. This method integrates Bayesian optimization based on a tree-structured Parzen estimator for the state of health and RUL prediction of lithium batteries. [PERSON] et al. [15] developed a parallel neural network framework that employs multi-channel processing combined with Time Transformer [16], LSTM, and other methods to capture spatiotemporal dependencies, improving efficiency and accuracy in handling multidimensional features. [PERSON] et al. [17] proposed the TACT model constrained by L2 regularization for RUL prediction. The model combines multi-scale convolutional neural network CNN and Transformer to achieve simultaneous extraction of local and global features and introduces delayed prediction constraints to optimize training. [PERSON] et al. [18] introduced a nonlinear multi-stage degradation model based on the Wiener process, incorporating a stage division method to automatically determine the number of stages, change point locations, and drift model forms. Variational Bayesian methods were used to adaptively estimate parameters and derive RUL analytically. Traditional RUL prediction models [1,2] had inherent limitations in extracting critical information. They lacked the ability to effectively represent significant features, particularly when dealing with multi-directional data [19]. With the deepening research on equipment degradation processes, attention mechanisms have been gradually introduced into RUL prediction. This mechanism helps dynamically capture key features and improves the model's prediction performance in complex degradation processes. For example, [PERSON] et al. [20] proposed an algorithm that integrates an improved self-attention mechanism, temporal convolutional network (TCN) [21], and squeeze-and-excitation mechanism to weight the contributions of input features across both the time-step and channel dimensions, highlighting key features highly relevant to the RUL. [PERSON] et al. [22] proposed an RUL prediction method based on an improved Transformer model that integrates attention mechanisms and deep learning, comprehensively considering spatiotemporal characteristics and various operating conditions. [PERSON] et al. [23] designed a multi-scale convolution module [24] combined with the Swish activation function, embedding local feature learning into global sequence modeling. This approach simultaneously extracts local dependencies and global interaction information from raw time signals and transforms them into trainable class labels. [PERSON] et al. [25] proposed a novel gated attention mechanism called Capsule Neural Network [26]. These methods achieved significant results in equipment reliability assessment and RUL prediction but also exhibited some notable shortcomings. Firstly, the requirements for different features might have varied across different degradation stages.