## 4 Implementation of RUL Prediction Based on Proposed Method
### Experimental Verification and Analysis
#### 4.4.2 Comparison Before and After Feature Clustering Reduction  
To validate the necessity and effectiveness of feature set reduction using hierarchical clustering, a comparison was conducted by inputting both the sensitive feature set and the optimal feature set into the model while keeping other experimental parameters and conditions constant. Taking Experiment Group 1 as an example, the prediction results are presented in Figure 16 and Table 6. As shown in Figure 16, in the early stages of prediction, neither feature set performed well in predicting the RUL. In the middle stages, the sensitive feature set demonstrated better prediction performance. In the later stages,  
Figure 15: Different bearing RUL prediction results. the optimal feature set not only provided more accurate predictions but also eliminated any prediction delay. According to the results in Table 6, although the MAE and RMSE values of the optimal feature set were similar to those of the sensitive feature set, this indicates that the optimal feature set contained a comparable amount of information to the sensitive feature set. The proposed method effectively removed redundant features from the feature set without losing useful information. Compared to the sensitive feature set, the optimal feature set resulted in an 8.61% reduction in model training time and a 23.26% reduction in model parameters. This demonstrates that by refining the sensitive feature set, the model's training efficiency was improved, and its complexity was reduced. The experimental results confirm that the proposed feature redundancy removal method is both necessary and effective for feature set construction. To verify the superiority of the proposed method, a comparative experiment was conducted between the proposed approach and the Max-Relevance Min-Redundancy method [42]. The experimental results are shown in the Table 7. It can be observed that the proposed method achieved smaller prediction errors, with a 13.13% reduction in model parameters and a 3.5% decrease in training time. This is because the Max-Relevance Min-Redundancy method emphasizes high correlation between the selected features and the target variable, but it still retains some redundant features. In contrast, the proposed method ensured a relatively high correlation with the target variable during the initial screening stage. Then, by employing hierarchical clustering to further eliminate redundancy within the feature set, a more optimal and compact feature subset was obtained. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluating Indicator** & **Sensitive Feature Set** & **Optimal Feature Set** \\ \hline MAE & 0.0433 & 0.0453 \\ RMSE & 0.0638 & 0.0632 \\ Number of model parameters & 294,400 & 225,908 \\ Training time (s) & 455.681 & 415.743 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The whole life evaluation index of the same feature set. Figure 16: Comparison diagram of whole life prediction of different feature sets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluating Indicator** & \multicolumn{2}{c}{**Max-Relevance**} & **Proposed Method** \\ \multicolumn{2}{c}{**Min-Redundancy Method**} & **Proposed Method** \\ \hline MAE & 0.0504 & 0.0453 \\ RMSE & 0.0682 & 0.0632 \\ Number of model parameters & 260,054 & 225,908 \\ Training time (s) & 430.674 & 415.743 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative analysis of various feature selection methods. Considering that the later stages of rolling bearing life are critical for bearing failure, a further analysis of the prediction performance of the two feature sets in the RUL prediction during the later stages was conducted. The prediction results for the two feature sets are shown in Figure 17 and Table 8. As depicted in Figure 17, the predictions using the optimal feature set were more aligned with the true RUL of the bearing, and no lagging phenomenon was observed.