## 6 Conclusions  
To enhance real-time monitoring capabilities in industrial processes and achieve accurate and efficient predictions of rolling bearing remaining useful life (RUL), this study proposes a prediction method based on an improved U-Net architecture coupled with a multi-dimensional hybrid gated attention mechanism (MHGAM). Utilizing the IEEE PHM 2012 Data Challenge dataset, along with a self-constructed dataset derived from engineering tests, we draw the following conclusions:  
1. The improved U-Net model effectively removes noise from vibration signals while preserving essential detail features in the time-frequency domain, utilizing depthwise separable convolutions and residual skip connections. The processed signals demonstrate an average increase in the signal-to-noise ratio (SNR) of 23.69% and a reduction in the root mean square error (RMSE) of 27.53% when compared to the WGAN and DCGAN methods.  
Figure 18: RUL prediction results. (**a**) Bearing 4-A; (**b**) Bearing 4-B.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test Bearings**} & \multicolumn{3}{c}{**Methods of This Article**} & \multicolumn{3}{c}{**CNN-BiGRU**} & \multicolumn{3}{c}{**TCN-BiGRU**} \\ \cline{2-10}  & **RMSE** & **MAE** & **Score** & **RMSE** & **MAE** & **Score** & **RMSE** & **MAE** & **Score** \\ \hline
4-A & 0.0684 & 0.0472 & 0.84 & 0.0745 & 0.0578 & 0.79 & 0.0786 & 0.0564 & 0.77 \\ \hline
4-B & 0.0731 & 0.0554 & 0.82 & 0.0789 & 0.0624 & 0.75 & 0.0767 & 0.0658 & 0.74 \\ \hline Mean & 0.0708 & 0.0513 & 0.83 & 0.0767 & 0.0601 & 0.77 & 0.0777 & 0.0611 & 0.755 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of life prediction results by different methods.  
2. The multi-dimensional hybrid gated attention mechanism (MHGAM) employs a spatial-channel parallel network architecture to dynamically allocate multi-dimensional fusion weights. This approach effectively addresses the information loss commonly encountered in traditional feature dimensionality reduction and fusion processes. The health indices generated by the proposed method show substantial enhancements in correlation, monotonicity, and robustness, thereby exhibiting superior comprehensiveness.
3. Experimental validation conducted on the IEEE PHM 2012 Data Challenge dataset demonstrates that the proposed method achieves reductions of 7.8% in RMSE and 14.6% in MAE compared to the CNN-BiGRU and TCN-BiGRU benchmark models, respectively. In terms of overall prediction performance scores, the proposed method exhibits average improvements of 7.8% and 9.3 percentage points, significantly enhancing prediction accuracy.
4. Validated by engineering test data, the proposed method demonstrates strong robustness and generalization capabilities under varying operating conditions, thereby providing an innovative technical approach for remaining useful life (RUL) prediction.  
Conceptualization, H.W. and A.S.; methodology, H.W. and A.S.; software, H.W.; validation, H.W. and A.S.; formal analysis, H.W.; investigation, A.S.; resources, H.W.; data curation, H.W. and A.S.; writing--original draft preparation, A.S.; writing--review and editing, H.W.; visualization, A.S.; supervision, H.W.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Ningbo City Unveiled Project (2023T016). This work was supported by the Key Research and Development Program of Ningbo City and the \"Unveiling the List and Appointing the Commander\" Project (2023Z006).  
Not applicable.  
The data used to support the findings of this study are available from the corresponding author upon request.