## 4 Discussion  
To effectively predict the remaining useful life (RUL) of condition monitoring data, this paper proposed a multi-stage RUL prediction method. First, real-time signals of the monitoring data were preprocessed using path weight selection. The purpose of path weight selection was to choose the most representative and important features from the monitoring signals in order to better reflect the degradation state of the equipment. As shown in Table 4, the ablation experiment results indicated that after applying path weight selection, compared to (base + EM-NET), the performance improved across all bearing data, with an average reduction of 20% in MAE and 15% in RMSE. This improvement suggested that path weight selection effectively optimized the data features, thereby enhancing the model's prediction accuracy. Additionally, this paper introduces an improved attention mechanism module, which strengthens the traditional attention mechanism to capture more degradation information and preserve more detailed features. The features processed by this module were then input into the RNN, which effectively captured long-term dependencies in the time series [19, 47], allowing the model to better learn the degradation patterns and trends of the equipment. By combining path weight selection with the dual attention mechanism, the model was able to focus more on regions containing more degradation information, helping it emphasize features that were crucial for prediction. This integrated approach further improved the model's accuracy and robustness. Finally, the MS-DAN model demonstrated significant performance improvements on the PHM-bearing dataset. As shown in Table 5, the MS-DAN model, compared to newer models, reduced RMSE by an average of 13.51% and MAE by an average of 10.14%. These results indicated that the MS-DAN model exhibited notable improvements in both prediction accuracy and generalization ability, providing a more reliable solution for condition monitoring and RUL prediction.  
Multiscale selected the top K patch sizes for combination to adapt to different time series samples. As shown in Figure 9, the impact of different K values on the prediction result was evaluated in Figure 9. The results showed that performance with K = 2 and K = 3 outperformed K = 1 and K = 6, highlighting the advantage of adaptively modeling critical multi-scale features to enhance accuracy. Furthermore, different time series samples benefited from feature extraction using various patch sizes, but not all patch sizes were equally effective. These findings highlighted the adaptability of the model, emphasizing its ability to identify and apply optimal combinations of patch sizes to address the diverse periodic and trend patterns present in the samples.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**Evaluated Metrics**} \\ \cline{2-3}  & **MAE** & **RMSE** \\ \hline TCN + Hybrid Attention Mechanism & 0.095 & 0.109 \\ Patch + PAS + Multiscale & 0.093 & 0.105 \\ DMW-Trans & 0.099 & 0.137 \\ MLP + Transformer & 0.111 & 0.140 \\ Ours & 0.089 & 0.105 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of classification performance on Bearings 1–3.  
Table 4 presents the hyperparameter settings for model training across six different experiments, with all experiments using 50 epochs. Comparing Exp2 and Exp4, it could be observed that, with other parameters held constant, a larger batch size led to better model performance. Comparing Exp1, Exp3, and Exp4, it was evident that using SGD or RMSprop as optimizers was less efficient in complex tasks compared to Adam. Finally, comparing Exp4 and Exp6, it could be seen that using a smaller learning rate allowed for more precise model adjustments and prevented skipping over optimal weights.