## 4 Experimental Validation on Public Datasets
### Raw Data Processing  
The enhanced U-Net signal processing method was utilized to process and analyze Bearings 1-4 and 2-5 within the dataset. Figures 8 and 9 illustrate the time-domain and frequency-domain signal processing results for the entire lifespan of Bearing 1-4, while Figures 10 and 11 display the corresponding results for Bearing 2-5. The quality of the generated signals was assessed using the signal-to-noise ratio (SNR) and root mean square error (RMSE), where a lower RMSE and a higher SNR indicate superior signal quality. The calculation formulas are provided in Equations (18) and (19). The proposed method was compared with WGAN [22] and DCGAN [23]. The relevant numerical information pertaining to the signal data is presented in Table 2. Tables 3 and 4 present a comparison of the signal quality generated by various models. It is evident that the signal quality produced by WGAN and DCGAN is significantly inferior to that of the proposed method. This discrepancy is attributed to the requirement of GAN models for a substantial amount of data for effective learning; when data are limited, these models struggle to capture all relevant features. In this study, the selection and analysis of bearing datasets are guided by two primary criteria: the completeness of working  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & & **RMSE** & **SNR** \\ \hline WGAN & Average & 0.3145 & 9.4523 \\ \hline DCGAN & Average & 0.2585 & 10.4578 \\ \hline the method proposed in this paper & Average & 0.2046 & 11.3258 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Evaluation results of Bearing 2-5 generated by different models.  
Figure 11: The frequency-domain processing results of Bearing 2-5.  
Figure 10: The time-domain processing results of Bearing 2-5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Bearing Data** & **Number of Signal** & **Sampling** & **Sampling** & **Duration of** \\
**Serial Number** & **Data Points** & **Interval** & **Frequency** & **Each Sampling** \\ \hline Bearing 1-4 & 1427 & 10/s & 25.6 kHz & 0.1 s \\ \hline Bearing 2-5 & 2311 & 10/s & 25.6 kHz & 0.1 s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Signal-related information.  
The signal-to-noise ratio (SNR) formula [24] is:  
\[SNR=10\log_{10}\left(\begin{array}{c}\dfrac{1}{N}\sum\limits_{n=0}^{N-1}\left|x _{s}(n)\right|^{2}\\ \dfrac{1}{N}\sum\limits_{n=0}^{N-1}\left|x_{n}(n)\right|^{2}\end{array}\right) \tag{18}\]  
where \(X_{s}n\) denotes the separated useful signal component; \(X_{n}n\) denotes the noise component; and \(N\) denotes the number of signal points.  
The root mean square error (RMSE) formula [25] is:  
\[RMSE=\sqrt{\dfrac{1}{N}\sum\limits_{i=1}^{N}\left(X_{i}-\hat{X}_{i}\right)^{2}} \tag{19}\]  
where \(X_{i}\) denotes the \(i\)-th sampled value of the original signal; \(\hat{X}_{i}\) denotes the i-th sampled value of the processed signal; and \(N\) denotes the number of data points.  
The results presented in Tables 3 and 4 demonstrate that the proposed method achieves significant improvements in signal quality for both bearing types. Specifically, the signal-to-noise ratio (SNR) of the signals from Bearings 1-4 and 2-5 generated by our method shows respective enhancements of 46.44% and 20.21%, as well as 19.82% and 8.3%, when compared with the two baseline methods. Furthermore, the root mean square error (RMSE) values exhibit notable reductions of 32.11% and 22.2% for Bearing 1-4 and 34.94% and 20.85% for Bearing 2-5. These quantitative improvements indicate that the proposed methodology not only effectively suppresses noise interference but also better preserves essential information from the original signals. Consequently, this approach establishes a more reliable data foundation for subsequent lifespan prediction tasks by maintaining higher signal fidelity.