## 5 Rotor Temperature Modeling and Prediction
### Rotor Temperature Modeling and Prediction Under Small 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} & & RMSE & 0.0068 & 0.0068 & 0.0004 \\  & & MSE & 0.0000 & 0.0000 & 0.0000 \\  & Train & MAE & 0.0050 & 0.0050 & 0.0003 \\  & & MSE & \(1.23\times 10^{-6}\) & \(\begin{matrix}-1.04\times\\ 10^{-6}\end{matrix}\) & \(7.08\times 10^{-6}\) \\  & & 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 \\  & Test & MAE & 0.4020 & 0.4015 & 0.0429 \\  & & MSE & 0.0149 & 0.0180 & 0.0748 \\  & & R-squared & 0.9491 & 0.9455 & 0.0107 \\  & Total & Runtime & 47.4799 & 47.3804 & 1.5684 \\ \hline \multirow{8}{*}{SMA-RF} & & RMSE & 0.6295 & 0.5911 & 0.1417 \\  & & MSE & 0.4163 & 0.3494 & 0.2044 \\  & Train & MAE & 0.3941 & 0.3716 & 0.0773 \\  & & MSE & 0.0322 & 0.0217 & 0.0382 \\  & & R-squared & 0.9427 & 0.9504 & 0.0273 \\  & & RMSE & 0.8937 & 0.8773 & 0.2180 \\  & & MSE & 0.8463 & 0.7697 & 0.4081 \\  & Test & MAE & 0.6043 & 0.5951 & 0.1177 \\  & & MSE & 0.0508 & 0.0241 & 0.1763 \\  & & R-squared & 0.8865 & 0.8941 & 0.0486 \\  & Total & Runtime & 47.0174 & 46.6430 & 6.1770 \\ \hline \multirow{8}{*}{SO-BiGRU} & & RMSE & 0.7036 & 0.6963 & 0.0818 \\  & & MSE & 0.5018 & 0.4849 & 0.1143 \\  & Train & MAE & 0.5591 & 0.5705 & 0.0754 \\  & & MSE & 0.0014 & 0.0008 & 0.0030 \\  & & R-squared & 0.9302 & 0.9294 & 0.0165 \\  & & RMSE & 0.8069 & 0.7890 & 0.0914 \\  & & MSE & 0.6594 & 0.6225 & 0.1459 \\  & Test & MAE & 0.6409 & 0.6314 & 0.0734 \\  & & MSE & 0.0087 & 0.0150 & 0.1145 \\  & & R-squared & 0.9119 & 0.9146 & 0.0214 \\  & Total & Runtime & 176.0875 & 176.1744 & 1.4659 \\ \hline \multirow{8}{*}{EO-SVR} & & RMSE & 0.5598 & 0.5539 & 0.0282 \\  & & MSE & 0.3142 & 0.3068 & 0.0318 \\ \cline{1-1}  & Train & MAE & 0.4820 & 0.4756 & 0.0286 \\ \cline{1-1}  & & MSE & \(-0.0647\) & \(-0.0602\) & 0.0339 \\ \cline{1-1}  & & R-squared & 0.9588 & 0.9582 & 0.0066 \\ \cline{1-1}  & & RMSE & 0.6777 & 0.6722 & 0.0639 \\ \cline{1-1}  & & MSE & 0.4634 & 0.4519 & 0.0908 \\ \cline{1-1}  & Test & MAE & 0.5435 & 0.5429 & 0.0377 \\ \cline{1-1}  & & MSE & \(-0.0631\) & \(-0.0637\) & 0.0992 \\ \cline{1-1}  & & R-squared & 0.9458 & 0.9495 & 0.0109 \\ \cline{1-1}  & Total & Runtime & 6.2627 & 6.2731 & 0.6984 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of rotor temperature prediction experiment under small-sample conditions. By combining the standard deviations of the error metrics, the stability of each model across the 20 consecutive prediction experiments is compared. Although RIME-XGBoost shows some fluctuations on the test set, its high R-squared value and low standard deviation indicate good stability. EO-SVR also demonstrates good stability. However, SMA-RF and SO-BiGRU have higher standard deviations, indicating greater variability in their predictions. A two-dimensional scatter plot of all hybrid models on the training and test sets is shown in Figure 6. The horizontal axis represents the true values, and the vertical axis represents the predicted values. The diagonal line in the plot represents perfect prediction, where predicted values equal true values. RIME-XGBoost performs well overall, with only a few predicted values slightly lower than the true values near 92 \({}^{\circ}\)C. SMA-RF exhibits a clear bias in the temperature range of 78, 86\({}^{\circ}\)C, where predicted values are generally higher than the true values. In higher temperature ranges, SMA-RF performs better. Figure 6: _Cont._  
In Figure 6, SO-BiGRU's predictions do not show a clear unidirectional bias. However, overall observations reveal that some predicted values are higher than the true values, while others are lower. There is a lack of consistency between the predicted and true values, resulting in larger overall errors.