## 1 Introduction
Certain features might have been critical to the degradation process at specific stages, yet traditional methods often fail to dynamically weight or focus on features based on the changing degradation stages, leading to the neglect of key features. Secondly, the models lacked adaptability, as many traditional models relied on fixed parameters or feature extraction methods, making it challenging to flexibly adjust to varying degradation stages or environmental conditions. Although attention mechanisms could capture long-term dependencies, they might have still lacked sufficient adaptability in adjusting focus points. To address these issues, this paper proposed a time-series analysis method based on multi-scale feature extraction and path weight selection. As shown in Figure 1, this method employed Discrete Fourier Transform (DFT) [27] to extract periodic components from time-series data and used a TopK selection mechanism [28] to retain the most critical path weights. This allowed the importance of feature paths to be dynamically adjusted based on the degradation stage of the equipment. In the healthy stage, when degradation signs were not yet apparent, the path weight selection mechanism automatically reduced the influence of paths with lower contributions. In the degradation stage, when key features became more critical, the mechanism enhanced the weights of these paths, improving the extraction rate of degradation-related information. After extracting path features, the model first utilized the proposed attention model, EM-Net, to extract initial features, ensuring an effective representation of the data in the feature space. Subsequently, the model employed a recurrent neural network (RNN) [29] to progressively capture the temporal dependencies of the signals. Finally, the processed features were passed to the RUL prediction module,which incorporated activation functions and dropout regularization to prevent overfitting, ultimately generating accurate RUL predictions to provide precise lifespan estimations for the equipment. This study made significant contributions to effectively capturing information during the equipment degradation process, extracting key information, and enhancing the model's robustness against interference. Compared to existing methods, our model demonstrated superior prediction accuracy and generalization capability. In particular, by integrating path weight selection with an innovative approach based on one-dimensional convolution and spatial attention mechanisms, the model further improved its ability to predict the degradation process of bearings. The path weight selection mechanism dynamically adjusted the weights of feature paths according to different stages of bearing degradation, enabling more precise capture of degradation information. Experimental results showed that the proposed method outperformed other existing methods on both the PHM 2012 [30] bearing dataset and real-world equipment data, validating its effectiveness and superiority. The main contributions of this paper were as follows:  
1. A path weight selection mechanism was proposed, which could dynamically adjust the weights of feature paths according to different stages of bearing degradation, thereby capturing degradation information more accurately;
2. A dual attention mechanism was constructed, capable of flexibly capturing dependencies between channels and automatically adjusting the importance of each channel, which effectively enhanced the model's feature representation capability;
3. The MS-DAN prediction method was proposed, which enhanced the feature extraction capability during the equipment degradation process and demonstrated excellent performance in prediction accuracy.