## 1 Introduction  
Rotating machinery is one of the most widely used equipment in the industrial field [1]. As an important part of rotating machinery equipment, rolling bearings play a vital role in ensuring the normal operation of equipment. However, due to the harsh operating environment of the equipment and the highly variable workload, rolling bearing faces inevitable risks of wear and failure [2]. The prediction of equipment's remaining useful life is one of the key technologies in fault prediction and health management (PHM) [3]. If the rolling bearing degrades to the required threshold, the machine will fail. How to accurately determine the RUL of rolling bearing based on monitoring data is crucial for developing a reasonable maintenance plan and reducing downtime and cost losses [4]. For RUL prediction of rolling bearing under strong background noise, due to the complex degradation characteristics of vibration signals and the difficulty in extracting key features, it is difficult to obtain accurate prediction results based on non-stationary vibration signals. Therefore, it is necessary to explore RUL prediction methods based on multi-domain features, which have important practical significance in equipment maintenance management. Currently, the remaining useful life (RUL) prediction methods for rolling bearing equipment can be mainly divided into two types: traditional methods based on physical models and data-driven methods [5]. The remaining useful life prediction method based on physical models [6] relies on degradation mechanisms, expert rules, and empirical knowledge, resulting in limited applicability of the model. In recent years, with the advancement of sensor technology and the development of deep learning [7], data-driven remaining useful life prediction models have received widespread attention [8]. This type of model learns degradation features and trends from data for prediction, reducing the need for prior knowledge and complex physical models. It can adapt to changes in different systems and environments, and has strong adaptability and scalability. Data-driven methods can be further divided into shallow machine learning-based methods and deep learning-based methods. Methods based on shallow machine learning include statistical regression analysis [9], support vector machines [10, 11], neural networks [12, 13, 14], and so on. However, the hierarchical structure of shallow machine learning-based methods is relatively simple, which limits the model's ability to extract deep-level structures and abstract features from the data. Life prediction methods based on deep learning typically perform better in feature extraction on large-scale data and can automatically learn feature representations that are suitable for tasks. The model-building process of this method generally requires three major steps: signal denoising, feature extraction and health indicator construction, and prediction model. Signal noise reduction is an important prerequisite for predicting the remaining useful life prediction of rolling bearings. [PERSON] et al. [15] proposed a denoising network model based on convolutional denoising autoencoder. The noise component was removed from the original data by stacking convolutional autoencoders, and the RUL of rolling bearings was predicted by the bidirectional long short-term memory network model. [PERSON] et al. [16] use a wavelet packet algorithm to denoise the direct current component of the gear pump pressure signal and then extract state evaluation indexes to predict the remaining useful life of the gear pump. [PERSON] et al. [17] proposed a joint denoising algorithm based on adaptive white noise complete set empirical mode decomposition and improved adaptive wavelet threshold to address the issue of wavelet threshold denoising algorithms not being able to adaptively select decomposition levels and wavelet bases. The processed intrinsic mode functions (IMF) components were reconstructed to better extract signal features from noisy signals. [PERSON] et al.