Interpretable machine learning for rockburst intensity prediction in deep underground engineering using Schrödinger optimization and SHAP analysis

To address the limitations of existing empirical and machine learning methods in nonlinear relationship characterization, hyperparameter optimization, and model interpretability, this study proposes an integrated machine learning framework that combines Schrödinger optimization algorithm (SRA)-based hyperparameter tuning, multi-level rockburst prediction, and SHAP-based interpretation. A database containing 121 unique rockburst cases was established, and SMOTE was applied exclusively to the training set to alleviate the class imbalance problem. The SRA was employed to optimize nine representative machine learning algorithms, which were subsequently applied to four-class rockburst intensity prediction and binary risk warning (N+L vs M+S). The results demonstrate that SRA improved the average classification accuracy of the investigated models by 9.84%. In 50 repeated stratified data splitting experiments, SRA-XGBoost achieved an average accuracy of 93.49%, with a 95% confidence interval ranging from 89.79% to 97.18%, indicating that the model maintained strong overall predictive capability under different data partitioning conditions. SHAP analysis revealed that the interaction between the stress concentration factor ( SCF ) and the elastic energy index ( W et ) was one of the most significant feature interactions influencing model predictions, suggesting a strong association between their combined variations and predicted rockburst intensity. Independent validation using 18 field cases from the Jiangbian Hydropower Station showed good agreement between the predicted and observed rockburst grades, providing preliminary engineering evidence for the applicability of the proposed model under the specific conditions of this project. Overall, the proposed framework integrates prediction optimization, risk assessment, and interpretability analysis into a unified rockburst prediction system, providing a theoretical reference for rockburst risk prediction, evaluation, and explainable intelligent assessment.