## 5 Rotor Temperature Modeling and Prediction
### Rotor Temperature Prediction Experiment Under Medium-Sized Samples
\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 \\  & Total & Runtime & 52.9506 & 51.3548 & 4.9756 \\ \hline \multirow{8}{*}{SMA-RF} & \multirow{8}{*}{Train} & RMSE & 1.7814 & 1.7963 & 0.2987 \\  & & MSE & 3.2625 & 3.2269 & 1.0684 \\  & & MAE & 0.7109 & 0.7136 & 0.0706 \\  & & MSE & 0.0456 & 0.0463 & 0.0364 \\  & & R-squared & 0.9940 & 0.9942 & 0.0020 \\  & & RMSE & 2.2036 & 2.0456 & 0.3157 \\  & & MSE & 4.9554 & 4.1855 & 1.4704 \\  & & MAE & 0.9034 & 0.8913 & 0.0705 \\  & & MSE & 0.0689 & 0.0787 & 0.0936 \\  & & R-squared & 0.9909 & 0.9923 & 0.0027 \\  & Total & Runtime & 28.3762 & 28.5778 & 1.8633 \\ \hline \multirow{8}{*}{SO-BiGRU} & \multirow{8}{*}{Train} & RMSE & 1.9903 & 2.0787 & 0.4596 \\  & & MSE & 4.1726 & 4.3210 & 2.0399 \\ \cline{1-1}  & & MAE & 1.4642 & 1.4852 & 0.3535 \\ \cline{1-1}  & & MSE & \(-0.0946\) & \(-0.0334\) & 0.4265 \\ \cline{1-1}  & & R-squared & 0.9923 & 0.9920 & 0.0037 \\ \cline{1-1}  & & RMSE & 4.4236 & 3.4068 & 3.1639 \\ \cline{1-1}  & & MSE & 29.5780 & 11.6067 & 47.3067 \\ \cline{1-1}  & & MAE & 1.6525 & 1.6125 & 0.3797 \\ \cline{1-1}  & & MSE & \(-0.0933\) & \(-0.0437\) & 0.4356 \\ \cline{1-1}  & & R-squared & 0.9457 & 0.9785 & 0.0867 \\ \cline{1-1}  & Total & Runtime & 302.5257 & 297.2967 & 17.3790 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of rotor temperature prediction experiment with medium-sized samples. high computational efficiency. However, SMA-RF's overall performance in both training and testing is inferior to RIME-XGBoost. EO-SVR exhibits similar prediction performance and computational efficiency to SMA-RF. However, its MBE is larger, indicating a higher positive prediction bias. The test set results are relatively stable, but their prediction accuracy is weaker than that of SMA-RF. SO-BiGRU is the worst-performing hybrid model overall. Its average modeling time is significantly longer than that of RIME-XGBoost (approximately 5.7 times). While the training set R-squared is high, the predictions show a negative bias. During testing, all of the error metrics increase, indicating poor generalization ability. The standard deviation results suggest instability in the prediction process. Furthermore, as shown in Figure 4, although all hybrid models achieve low errors on the training set, the three methods, excluding RIME-XGBoost, have limitations. For example, SMA-RF struggles to provide accurate predictions at low temperatures and fails to fit sudden temperature drops. SO-BiGRU cannot predict fluctuating data in the low-temperature region. EO-SVR is unable to accurately learn fluctuating data in both high- and low-temperature regions, resulting in minor errors between the predicted and actual values. A half-violin plot using the MAE of the test set is shown in Figure 5. The horizontal axis represents the models, and the vertical axis represents the MAE. It is visually evident that RIME-XGBoost is the most stable method, while SO-BiGRU has the largest error distribution. In terms of average values, RIME-XGBoost is the lowest. SMA-RF is a moderately performing model. However, in one out of the twenty tests, an anomaly occurred, which increased the overall prediction error and variability. The MAE distribution of EO-SVR shows a bimodal pattern, indicating two concentrated forms of prediction errors. This suggests that the model's learning ability varies depending on the randomly selected training data.