## 1 Introduction  
As a core component of rotating machinery, rolling bearings are widely used in important equipment in the fields of railway vehicles, the automobile industry, electric power equipment, etc., and their operating condition is decisive for the reliable operation of the whole system [1; 2]. In various application scenarios, rolling bearings are often subjected to high loads, high speeds, and corrosiveness. Under complex working conditions such as strong vibrations and impacts, it is easy to cause bearing failure [3; 4]. According to relevant research studies, about 30% of rotating equipment failures are caused by rolling bearings [5; 6]. When the equipment is in operation, if the rolling bearing fails, it will lead to equipment downtime maintenance, affecting the efficiency of the enterprise, or lead to disaster, causing great losses to the country and the people. Therefore, it is of great significance to take the rolling bearing as the research object, scientifically and reasonably establish the rolling bearing Remaining Useful Life (RUL) prediction model, and conduct real-time monitoring of the operation status of the rolling bearing [7; 8; 9; 10]. Currently, the RUL prediction method for rolling bearings can be broadly categorized into three main types: physical model-based methods, statistical model-based methods, and data-driven methods [11; 12; 13]. Some applications exist for physical and statistical model-based RUL prediction methods, but most of the parameter estimation methods for physical models are relatively complex and usually require extensive practical experience and guidance from domain experts [14]. Statistical model-based methods have the advantages of being easy to implement and easy to interpret in terms of the prediction results, but such methods can only respond to the commonality of the degradation of the same type of equipment, and the scope of application is narrower [15]. As industrial equipment tends to be more sophisticated and complex, data-driven methods based on data have gradually become mainstream. Deep learning has adaptive feature extraction capability and powerful generalizability, which can find the general law of degradation from messy and complicated data and is more suitable for modern mechanical equipment with massive data, complex structures, and many parameters [16; 17; 18]. CNN and GRU, as landmark networks in deep learning, are widely used in many fields such as fault diagnosis, life prediction, and target detection [19; 20]. [PERSON] [21] converted vibration signals into images and input them into CNN to successfully realize RUL prediction, but the data processing of this method is too complicated. [PERSON] [22] constructed the correlation between statistical features and time series by the HIs of bearings and input them into CNN to realize the RUL prediction of bearings, but the method requires a lot of prior knowledge and expert experience. [PERSON] [23] combined a residual network and an attention mechanism to effectively predict the RUL of bearings, but the method requires a large amount of training data. He [24] improved the GRU network and introduced the attention mechanism to weigh the processing and input the normalized time-frequency features into the network to achieve the RUL prediction of bearings, and the experiments show that the improved network can effectively predict the RUL trend of rolling bearings over time. [PERSON] [25] proposed a CNN-LSTM-based model that effectively combines the powerful feature extraction ability of CNN and the sequential processing capability of LSTM, and the results reveal its superiority and effectiveness in accurate RUL prediction.. [PERSON] [26] introduced a CNN-LSTM hybrid that utilizes a wide convolutional kernel for feature extraction, significantly enhancing noise robustness and diagnostic precision. The experimental results validate its superior performance in mixed-load scenarios. Utilizing the advantages of CNN and GRU, combining the two for more comprehensive modeling is another common processing method.