## 4 Model Prediction Performance Discussion
### Performance Analysis of the Prediction Model for the Maximum Tunnel Uplift Displacement  
As shown in Figures 10-13, the distributions of the predicted and measured \(S_{\text{max}}\) values for the SVM model, CART model, XGBoost model, and BO-XGBoost model were given. The scatter plots, which were closer to the diagonal line P = A, indicated the superior prediction results. The performances of the four established models were analyzed using the evaluation metrics. It is worth stating that model performance was evaluated based on the learning ability and prediction ability corresponding to the training and test sets, respectively. Figure 10a,b shows the prediction results for the training and test sets using the SVM model. The predictions exhibited a clear tendency: the prediction was generally large for smaller measured \(S_{\text{max}}\) values and smaller for larger measured \(S_{\text{max}}\) values. The RMSE, MAE and R\({}^{2}\) values were 20.0142, 15.0773, and 0.7126 for the training set and 25.4354, 21.0216, and 0.6172 for the test set, respectively. This indicated that the prediction results of the SVM model deviated significantly from the measured \(S_{\text{max}}\) values, and thus, they were not reliable. The \(S_{\text{max}}\) value predicted by the CART model is plotted in Figure 11. Compared with the SVM model, the CART model could predict a wider range of measured \(S_{\text{max}}\) values more accurately. The RMSE, MAE and R\({}^{2}\) values of the SVM model for the training set were 10.8984, 9.4908, and 0.9148, respectively, indicating that the predicted values for the entire training set were closer to the measured \(S_{\text{max}}\) value. However, the deviation of the CART model was still relatively large for the test set (RMSE = 16.5961 and MAE = 14.6490). The prediction results using the unoptimized XGBoost model and the BO-XGBoost model are respectively shown in Figures 12 and 13. For the training set, the RMSE, MAE and R\({}^{2}\) values were 3.5153, 3.2277, and 0.9916, respectively, for the XGBoost model and 5.8232, 4.9647, and 0.9763, respectively, for the BO-XGBoost model, and they both demonstrated excellent learning abilities for the data. Figures 12a and 13a show the scatter distributions over the range of 0.8 to 1.2 for the accuracy of the P = A line. For the test set, the RMSE and MAE values were reduced from 13.8493 and 11.9235 to 10.9808 and 9.2765, respectively,  
Figure 12: Prediction results for the XGBoost model: (**a**) training set, and (**b**) test set. Figure 13: Prediction results for the BO-XGBoost model: (**a**) training set, and (**b**) test set. after the hyperparameters of the XGBoost model were optimized by the Bayesian algorithm. The prediction accuracy of the XGBoost model evaluated by the RMSE and MAE values had improved by 20% and 22%, respectively. The metrics of the different models evaluated on the training and test sets are summarized in Figure 14 to compare their performances more visually. The models were ranked according to their learning ability on the training set from lowest to highest, as follows: SVM \(<\) CART \(<\) BO-XGBoost \(<\) XGBoost, and, similarly, for their predictive ability on the test set, they were ranked as follows: SVM \(<\) CART \(<\) XGBoost \(<\) BO-XGBoost. Unexpectedly, the BO-XGBoost model showed a lower performance on the training set compared to the unoptimized XGBoost model, but it achieved a better prediction performance on the test set (XGBoost: R\({}^{2}\) = 0.8865 and BO-XGBoost: R\({}^{2}\) = 0.9287). This could be explained by the fact that the unoptimized XGBoost model tended to overfit the training data, highlighting the importance of hyperparameter optimization for the XGBoost model.