## 4 Experiment Study
### Results and Discussion for RUL Prediction
#### 4.3.1 Results and Discussion for Initial Degradation Detection
The reconstruction results based on DACAEN and DCAE for the frequency spectrum from two samples are shown in Figure 5. The cyan line represents the frequency spectrum in the model's input, the green line represents the reconstructed frequency spectrum via DACAEN, and the blue represents the DCAE. It can be seen that, although DACAEN and DCAE did not completely restore the frequency spectrum at the time of input, the reconstruction of DACAEN was better than that of DCAE. This is attributed to the introduction of an adversarial mechanism strategy into DCAE. (3) Comparison with Popular HIs  
To demonstrate the advantage of the proposed RAPP from DACAEN in constructing the HI, some popular and commonly used health indicators such as rectified average value, root mean square, root amplitude, waveform index, and average frequency are selected for comparison [31]. Take Bearing 1-1 as an example. The detailed results and the partial enlarged view are shown in Figure 6, in which the blue line represents the proposed HI, the green line represents the rectified average value, the cyan line represents the root mean square, the magenta line represents the root amplitude, the black line represents the waveform index, and the yellow line represents the average frequency. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Functions**} & \multirow{2}{*}{**Model Name**} & \multicolumn{2}{c}{**Ablation Name**} \\  & & **Adversarial** & **RAPP** \\  & & **Mechanism** & **RAPP** \\ \hline Reconstruction ability & DCAE & No & No \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Details of the comparison. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Bearings**} & \multirow{2}{*}{**Results of IDD**} & \multicolumn{2}{c}{**Total Number of**} & \multicolumn{2}{c}{**Number of**} \\  & & **Samples** & **Degraded Samples** \\ \hline Bearing 1-1 & 1451 & 2803 & 1352 \\ Bearing 1-2 & 828 & 871 & 43 \\ Bearing 1-3 & 1267 & 2375 & 1108 \\ Bearing 1-4 & 1087 & 1428 & 341 \\ Bearing 1-5 & 2443 & 2463 & 20 \\ Bearing 1-6 & - & 2448 & - \\ Bearing 1-7 & 2206 & 2259 & 53 \\ Bearing 2-1 & 877 & 911 & 34 \\ Bearing 2-2 & 388 & 797 & 409 \\ Bearing 2-3 & 1946 & 1955 & 9 \\ Bearing 2-4 & - & 751 & \(-\) \\ Bearing 2-5 & - & 2311 & - \\ Bearing 2-6 & 687 & 701 & 14 \\ Bearing 2-7 & 225 & 230 & 5 \\ Bearing 3-1 & 493 & 515 & 22 \\ Bearing 3-2 & 1610 & 1637 & 27 \\ Bearing 3-3 & 420 & 434 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of IDD for IEEE PHM bearings. Figure 5 shows that the proposed RAPP and average frequency display a low and stable value during the early stages of degradation. As serious performance degradation occurs in the bearings, the amplitude of HI increases significantly and exhibits a monotonic trend until the bearings fail. Although both the proposed RAPP and the average frequency effectively represent the degradation trend, it is noticed from Figure 5b that the average frequency shows more fluctuations in the healthy stages and the early stages of degradation, making it difficult to calculate the health threshold for determining abnormal points. As serious performance degradation occurs in the bearings, the amplitude of HI increases significantly and exhibits a monotonic trend until the bearings fail. However, the remaining three methods show the opposite phenomenon, with sharp burrs and large amplitude during the whole process. As an excellent indicator of degradation trends, the root mean square and root amplitude show more fluctuations in the healthy stages, making them less convenient for determining abnormal points. The waveform index suffers from poor monotonic trends and significant fluctuations throughout the process, making it difficult to accurately complete the IDD.