## 4 Experimental Validation on Public Datasets
### Remaining Useful Life (RUL) Prediction  
To validate the effectiveness of the proposed method in this paper, a portion of the test set data was utilized for prediction, and the prediction results were subsequently evaluated. The training and validation data were divided in a 70% to 30% ratio, with specific allocations detailed in Table 6. The prediction results are illustrated in Figure 16. Upon examining these results, it is evident that the health indicators constructed using the proposed method demonstrate superior accuracy in predicting the RUL of bearings. The generated RUL prediction curve closely aligns with the actual life trajectory, effectively capturing the degradation process of the bearing. To further establish the superiority of the proposed method, a quantitative comparative analysis was conducted between this method and the CNN-BiGRU [26; 27] and TCN-BiGRU [28; 29] approaches, with the results of the analysis presented in Table 6.  
Table 7 presents the quantitative evaluation metrics for the RUL prediction of the test set, employing three distinct methods. The mean values of the root mean square error (RMSE) and mean absolute error (MAE) for the life prediction results of the proposed method are 0.0504 and 0.0239, respectively, both of which are lower than those obtained from the conventional CNN-BiGRU and TCN-BiGRU methods. Additionally, the average score of 0.867 surpasses that of the other two life prediction methods. The experimental results indicate that the health indicators constructed by the proposed method more ef \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bearing Number** & **Number of Samples** & **Training Data** & **Validation Data** \\ \hline
1-4 & 1428 & 1000 & 428 \\ \hline
2-5 & 2311 & 1618 & 693 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Data allocation. Figure 15: Performance comparison of health indicators/%. (**a**) Correlation; (**b**) monotonicity; (**c**) robustness. fectively characterize the degradation trend of bearings, thereby achieving superior life prediction performance. We comprehensively evaluated the overhead of experimental data on the same hardware platform (NVIDIA RTX 3090, manufactured by NVIDIA Corporation, headquartered in Santa Clara, CA, USA), and the specific information is shown in Table 8:  
Based on experimental findings, this study concludes that TCN-BiGRU incurs the highest computational burden, primarily due to the increased complexity of dilated convolution operations in TCN compared to standard CNN computations. Although the proposed method introduces a moderate computational overhead over CNN-BiGRU through its gating-based dimensionality reduction mechanism, which is reflected in a 4.12% increase in parameter count, the substantial gains in predictive accuracy justify this trade-off. In the aspect of signal processing methodology, this paper addresses the issue of signal detail loss during the analysis of rolling bearing vibration signals by enhancing  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test Bearings**} & \multicolumn{2}{c}{**Methods of This Article**} & \multicolumn{2}{c}{**CNN-BiGRU**} & \multicolumn{2}{c}{**TCN-BiGRU**} \\ \cline{2-10}  & **RMSE** & **MAE** & **Score** & **RMSE** & **MAE** & **Score** & **RMSE** & **MAE** & **Score** \\ \hline
1-4 & 0.0479 & 0.0236 & 0.89 & 0.0563 & 0.0345 & 0.82 & 0.0568 & 0.0312 & 0.83 \\ \hline
1-5 & 0.0566 & 0.0245 & 0.81 & 0.0632 &  
the U-Net model with adaptive convolution kernels to improve signal quality. Structural optimizations are achieved through the incorporation of time-domain dilated convolution and multi-resolution feature pyramid modules, which significantly enhance signal processing performance. Comparative experiments with WGAN and DCGAN models demonstrate that the processed signals achieve average increases in the signal-to-noise ratio (SNR) of 33.33% and 14.06%, respectively, while the root mean square error (RMSE) decreases by averages of 27.16% and 27.89%, confirming a substantial improvement in signal quality.