## 4 Implementation of RUL Prediction Based on Proposed Method
### Experimental Verification and Analysis
#### 4.4.3 Comparison of Different Models  
To verify the superiority of the proposed combined model, single models such as GRU, Transformer, and TCN were selected as comparison models, and a comparative experiment was conducted using MAE and RMSE as evaluation metrics. Additionally, the results were compared with those from similar studies [6; 43]. The prediction results for Experiment Group 1 are shown in Figure 18, and the results for all experimental groups are presented in Table 9. As shown in Figure 18, during the early stage of prediction, all models failed to predict accurately, but the Transformer-GRU model provided results closer to the true values. In the middle stage, all four models exhibited some lag. In the later stages, GRU still showed a lagging issue, while TCN performed better, although some lag occurred in the final stage. The Transformer model underestimated the actual values, which could lead to unnecessary actions in predictive maintenance. In contrast, the Transformer-GRU model's predictions aligned closely with the true RUL. According to Table 9, the proposed combined model reduced the average MAE by 24.9% and the average RMSE by 19.36% compared to GRU; reduced the average MAE by 29.4% and the average RMSE by 29.5% compared to TCN; and reduced the average MAE by 16.0% and the average RMSE by 15.4% compared to Transformer. These comparative results demonstrate that the proposed model achieved higher prediction accuracy. It can be concluded that the combined model proposed in this study achieved the highest prediction accuracy. Single models can only extract useful information from features from a single dimension, while the combined model proposed in this study allows the encoder  
Figure 17: Late comparison diagram of life prediction of different feature sets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluating Indicator** & **Sensitive Feature Set** & **Optimal Feature Set** \\ \hline MAE & 0.0259 & 0.0187 \\ RMSE & 0.0312 & 0.0232 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The later evaluation index of life prediction of different feature sets. part to extract local variation information from the degradation features by capturing the dependencies across time steps. GRU, on the other hand, can capture the macro trend information that evolves over time in different feature samples. This enables more efficient mining of the bearing degradation patterns and consequently improves the model's prediction performance. Compared with the improved models [43] and combined models [6] in the literature, the model proposed in this study achieved the best prediction performance with the lowest average error. In contrast to the approach in reference [6], which uses TCN, LSTM, and Transformer models to extract features from input data and then simply concatenates the features extracted by the different models, the combined model proposed in this study concatenates two models in series. By deepening the network, GRU further extracts features from the encoder's output, thereby obtaining more advanced features and endowing the model with stronger expressive power. Reference [43] improves TCN by introducing attention mechanisms and multi-scale mechanisms. In comparison, the multi-head attention mechanism in the encoder of our model not only mines the dependencies across different time steps but also assigns greater weight to key time steps. The Transformer and GRU extract information from different dimensions, which, compared to multi-scale information, carries more comprehensive and rich information. Additionally, based on the experimental results of this study and those in the literature [43; 44; 45], it can be observed that the prediction error for Bearing 1-3 was the smallest, further confirming that the prediction of gradual-change bearings is less challenging than that of sudden-change bearings.