## 5 Rotor Temperature Modeling and Prediction
### Performance Comparison Between RIME-XGBoost and Baseline XGBoost
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Number of Trees** & **Tree Depth** & **Learning Rate** \\ \hline XGBoost-Alpha & 50 & 5 & 0.05 \\ XGBoost-Beta & 300 & 15 & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Hyperparameter settings for two typical baseline XGBoost models. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Stage** & **Error** & **Average** & **Median** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline \multirow{8}{*}{RIME-XGBoost} & \multirow{8}{*}{Train} & RMSE & 0.0068 & 0.0068 & 0.0004 \\  & & MSE & 0.0000 & 0.0000 & 0.0000 \\  & & MAE & 0.0050 & 0.0050 & 0.0003 \\  & & MSE & \(1.23\times 10^{-6}\) & \(-1.04\times 10^{-6}\) & \(7.08\times 10^{-6}\) \\  & & R-squared & 0.9999 & 0.9999 & \(1.09\times 10^{-6}\) \\  & & RMSE & 0.6010 & 0.5960 & 0.0741 \\  & & MSE & 0.3667 & 0.3553 & 0.0913 \\  & & MAE & 0.4020 & 0.4015 & 0.0429 \\  & & MSE & 0.0149 & 0.0180 & 0.0748 \\  & & R-squared & 0.9491 & 0.9455 & 0.0107 \\  & & Runtime & 47.4799 & 47.3804 & 1.5684 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Performance evaluation based on error metrics of RIME-XGBoost and baseline models on Group B (small-scale). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Stage** & **Error** & **Average** & **Median** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline \multirow{8}{*}{RIME-XGBoost} & \multirow{8}{*}{Train} & RMSE & 0.0440 & 0.0442 & 0.0016 \\  & & MSE & 0.0019 & 0.0020 & 0.0001 \\  & & MAE & 0.0318 & 0.0321 & 0.0013 \\  & & MSE & \(2.84\times 10^{-5}\) & \(9.42\times 10^{-6}\) & \(5.53\times 10^{-5}\) \\  & & R-squared & 0.9999 & 0.9999 & \(2.17\times 10^{-7}\) \\  & & RMSE & 1.1555 & 1.0298 & 0.4079 \\  & & MSE & 1.5016 & 1.0605 & 1.1670 \\  & & MAE & 0.4864 & 0.4782 & 0.0410 \\  & & MSE & \(-0.0227\) & \(-0.0185\) & 0.0478 \\  & & R-squared & 0.9972 & 0.9981 & 0.0021 \\  & & Runtime & 52.9506 & 51.3548 & 4.9756 \\ \hline \hline \multirow{8}{*}{XGBoost-Alpha} & \multirow{8}{*}{Train} & RMSE & 2.3286 & 2.3308 & 0.0623 \\  & & MSE & 5.4261 & 5.4325 & 0.2887 \\  & & MAE & 1.9056 & 1.9028 & 0.0614 \\  & & MSE & 1.3008 & 1.3051 & 0.0903 \\  & & R-squared & 0.9900 & 0.9901 & 0.0005 \\  & & RMSE & 2.7128 & 2.6569 & 0.2273 \\  & & MSE & 7.4084 & 7.0594 & 1.2525 \\  & & MAE & 2.0269 & 2.0355 & 0.0432 \\  & & MSE & 1.2814 & 1.3351 & 0.1039 \\  & & R-squared & 0.9863 & 0.9870 & 0.0023 \\  & Total & Runtime & 0.5361 & 0.3879 & 0.6124 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance evaluation based on error metrics of RIME-XGBoost and baseline models on Group A (medium-scale). By comparing baseline models using different empirical parameters, we can see RIME-XGBoost's pros and cons. It still has lower errors in small samples, which proves the effectiveness of RIME in hyperparameter optimization. Optimizing the number of trees, tree depth, and learning rate enhances learning ability and reduces overfitting. The limitations of RIME-XGBoost are the need to design additional regularization strategies or optimize regularization parameters to further balance prediction accuracy, generalization, and computational efficiency. For example, regularization parameters and early-stopping have to be introduced to expand RIME-XGBoost. In addition, the operation logic of RIME-XGBoost can be changed. Using GPU parallel computing can shorten its Runtime.