## 4 Model Prediction Performance Discussion
### Performance Analysis of the Prediction Model for the Maximum Tunnel Uplift Displacement
The calculation results of the four algorithm models on the test set are shown in Figure 15. The maximum displacements of the tunnel vault uplift, i.e., the \(S_{\text{max}}\) values, were sorted from smallest to largest, and then the errors for the predicted and measured values were calculated using Equation (10):  
\[Error=S_{\text{max}P}-S_{\text{max}A}, \tag{10}\]  
where \(S_{\text{max}P}\) represents the predicted uplift displacement and \(S_{\text{max}A}\) represents the measured uplift displacement. Figure 16 shows the predicted errors corresponding to the four different algorithmic models. The positive values indicate that the predicted value of \(S_{\text{max}}\) was greater than the measured value while a negative value indicates the opposite. Figure 14: Model evaluation indexes: (**a**) RMSE, (**b**) MAE, and (**c**) R\({}^{2}\). Combining Figures 15 and 16, it can be noticed that the four models exhibited similar prediction patterns, with variations in their accuracy levels. Notably, the SVM model demonstrated the highest deviation from the measured \(S_{\text{max}}\) value, with the maximum error exceeding \(-60\) mm, particularly for the highest measured \(S_{\text{max}}\) value. This finding highlighted the unsuitability of the SVM model for projects where \(S_{\text{max}}\) values are expected to be relatively large, which could potentially compromise engineering safety. Compared with the SVM model, the prediction accuracy of the CART algorithm model for \(S_{\text{max}}\) values had improved, and the maximum prediction error was less than \(-50\) mm. The XGBoost algorithm model provided a more accurate prediction for the measured \(S_{\text{max}}\) values than the SVM and CART models, as evidenced by the maximum prediction error value of \(-31\) mm. Meanwhile, the maximum prediction error of the BO-XGBoost algorithm was further reduced to \(-26\) mm, and the absolute value of the maximum prediction error was controlled within \(20\) mm in most periods. Consequently, the BO-XGBoost algorithm demonstrated the highest prediction accuracy among the four models considered in this study. Summarizing the above analysis, the BO-XGBoost algorithm model performed better for generalization ability, with a higher prediction accuracy in predicting the maximum uplift displacement of the underlying tunnel vault caused by the excavation, and the prediction error of the maximum uplift displacement was only approximately \(\pm 10\) mm, which was suitable for practical projects. It is worth noting that for the prediction results of the BO-XGBoost model on the test set, two of the prediction errors exceeded \(-20\) mm and the predicted values were smaller than the measured values. Since the outliers of input  
Figure 16: Prediction error results for the four algorithmic models on the test set. Figure 15: Prediction comparison results for the four algorithmic models on the test set. variables can provide some extreme information to an established prediction model, the processing of a database in combination with field knowledge is necessary before training a model. However, the overall results demonstrated that the proposed BO-XGBoost model was effective at accurately predicting the maximum tunnel uplift displacement.