## 5 Conclusions  
This study proposed the XGBoost model in a machine learning algorithm to predict the maximum uplift displacement of an underlying shield tunnel vault caused by an excavation. Meanwhile, the Bayesian optimization algorithm was applied to optimize the XGBoost model's hyperparameters, and the best prediction model was established, namely, the BO-XGBoost model. The RMSE, MAE, and R\({}^{2}\) values were selected as metrics for quantitatively evaluating the prediction performances of the SVM, CART, XGBoost, and BO-XGBoost models. The main conclusions were as follows:  
1. Among the four algorithmic models for \(S_{\text{max}}\) prediction, the SVM model's predicted results deviated the most from the measured values (RMSE = 25.4354, MAE = 21.0216, and R\({}^{2}\) = 0.6172). The highest prediction accuracy was achieved by the BO-XGBoost model. In addition, compared to the unoptimized XGBoost model, the RMSE and MAE values of the BO-XGBoost model improved from 13.8493 and 11.9235 to 10.9808 and 9.2765, respectively.
2. According to the prediction results for the test set, the prediction errors of the four models showed tendencies to grow larger as \(S_{\text{max}}\) values grew larger in certain time periods. These tendencies were particularly reflected in the SVM and CART models. The maximum prediction error of the SVM-based model was more than \(-\)60 mm, whereas it was near \(-\)50 mm for the CART model. However, the maximum prediction error of the BO-XGBoost model was controlled to within \(\pm\)2 mm for most time periods, which was superior to the \(\pm\)31 mm error of the XGBoost model.
3. The BO-XGBoost model had better interpretability, including its ability to visualize the decision trees and calculate the feature importance. According to the weights of the characteristic importance elements, the three measures of the excavation enclosure, in order of the SWM, BP, and DW, were the most critical factors in predicting the maximum tunnel uplift displacement.
4. Expanding a dataset is beneficial for improving the prediction accuracy of a model. Currently, cases of actual projects with excavations over existing tunnels are insufficient. Apart from this, the input parameters of the training prediction model were still divided in inadequate detail. These play vital roles in achieving higher levels of accuracy for predictive models.  
Figure 18: Feature importance of the BO-XGBoost model.  
**Author Contributions:** Conceptualization, H.Z.; methodology, H.Z., Y.W. and P.G.; software, H.Z. and Y.W.; data curation, H.Z.; visualization, X.L.; writing--original draft, H.Z.; writing--review and editing, H.Z. and H.L.; funding acquisition, Y.W. and P.G.; supervision, Y.W. and H.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This paper was supported by the National Natural Science Foundation of China grant number 42077249 and 42107082, the opening project of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology), grant number KFJJ23-05M, and the Fundamental Research Funds for the Central Universities, grant number JZ2023 HIGA0193 and JZ2023 HIGQA0094.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data will be made available upon request.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.