## 5 Results and Discussion
### Model Performance Evaluation  
This section provides a detailed performance evaluation of all ML models using the training and test sets. Firstly, the model performance is illustrated using regression graphs. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Models** & \multicolumn{3}{c}{**Hyperparameters**} \\ \hline ANN & n\_layers: [2]; n\_units: [123]; activation function: [’Relu’]; a\_solver: [’lbfgs’]; alpha: [5.3660 \(\times\) 10\({}^{-4}\)] \\ \hline MLP & n\_layers: [6]; n\_units: [91; 31; 76; 13; 79; 18]; activation function: [’Relu’]; a\_solver: [’lbfgs’]; alpha: [1.4721 \(\times\) 10\({}^{-4}\)]; batch\_size: [128]; i\_learning rate: [2.0767 \(\times\) 10\({}^{-5}\)]; max\_iter: [810] \\ \hline DT & max\_depth: [12]; min\_sample\_split: [2]; min\_sample\_leaf: [1] \\ \hline GBDT & Loss function: [’huber’]; n\_estimators: [188]; max\_depth: [5]; min\_sample\_split: [9]; min\_sample\_leaf: [3]; learning rate: [1.3497 \(\times\) 10\({}^{-1}\)]; subsample ratio: [6.8284 \(\times\) 10\({}^{-1}\)] \\ \hline KNN & n\_neighbors: [4]; weight function: [’uniform’]; p: [1] \\ \hline XGBoost & n\_estimators: [100, 1000]; max\_depth: [3; 10]; learning\_rate: [0.01, 0.3]; subsample ratio: [’0.5, 1.0]; subsample\_bytree: [0.5, 1.0]; gamma: [0.0, 1.0]; reg\_alpha: [0.0, 1.0]; reg\_lambda: [0.0, 1.0] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The optimal hyperparameters for each prediction model. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**The Ratio of Training Set to Test Set**} \\ \cline{2-4}
**Models** & **60:40** & **70:30** & **80:20** \\ \hline ANN & 1231 s & 1201 s & 2277 s \\ DT & 123 s & 115 s & 119 s \\ GBDT & 2019 s & 823 s & 929 s \\ KNN & 89 s & 41 s & 84 s \\ MLP & 3483 s & 4229 s & 12,970 s \\ XGBoost & 604 s & 380 s & 501 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time consumption of each model using three types of data allocation methods. Figure 7: Iteration plots for various prediction models: (**a**) ANN; (**b**) DT; (**c**) GBDT; (**d**) KNN; (**e**) MLP; (**f**) XGBoost. As shown in Figure 8, the prediction accuracy of each model in the training phase can be illustrated using the distribution of data points. It can be seen that the GBDT, DT, and XGBoost models exhibit a strong correlation between the predicted and actual values, indicating high predictive accuracy. In other words, the points in the above three models are closely aligned along the diagonal line. This alignment suggests that the DT, GBDT, and XGBoost models are effectively capturing the underlying patterns in the training set. In contrast, other models, including ANN, KNN, and MLP, show a greater dispersion of points around the diagonal, reflecting lower prediction accuracy than the DT, GBDT, and XGBoost models. It can be observed that the ANN, KNN, and MLP models exhibit a higher degree of variance and less precision in predicted values. It also means that ANN, KNN, and MLP models may not be as effective in modeling the complex relationships between the input features and predictive targets. Additionally, Table 5 provides a quantitative assessment of each model's performance on the training set using five evaluation indices, MSE, RMSE, MAE, MAPE, and R\({}^{2}\), offering detailed insight into each model's accuracy and reliability. The quantitative results corroborate the visual analysis from Figure 8. It can be observed that the DT, GBDT, and XGBoost models show exceptionally low MSE and RMSE values, along with high R\({}^{2}\) values close to 1, indicating a perfect prediction in the training phase. In particular, the DT model achieves the best performance represented by all indices, followed by the XGBoost model. The GBDT also performs well but with slightly higher error indices compared to the DT and XGBoost models. On the other hand, the KNN model exhibits the highest MSE, RMSE, MAE, and MAPE values among all models, indicating a poor performance in capturing the underlying data patterns.