Combining Copula Theory and Machine Learning for Prediction of Ground Vibrations Induced by Tunnel Blasting

To effectively predict and control the peak particle velocity (PPV) induced by tunnel blasting, this study investigates the Qinhuangdao Jiaoshan Tunnel as a case study. This study first proposes an Improved Particle Swarm Optimization (IPSO) algorithm through theoretical derivation. Building upon IPSO, a further enhanced algorithm, termed CIPSO, is developed by integrating a dependency model derived from Copula theory. The CIPSO algorithm is then employed to optimize a Support Vector Regression (SVR) model, establishing the final CIPSO-SVR prediction framework. Copula theory was employed to quantify the correlation between PPV and surface cumulative settlement (S). A regularization term incorporating Kullback-Leibler (KL) divergence was then embedded into the SVR objective function. The Hyperparameters of the CIPSO-SVR model were optimized using fixed-step rolling cross-validation. The model’s predictive performance was rigorously compared against CIPSO-optimized Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) models, as well as against SVR, CNN, and LSTM models optimized by the Grey Wolf Optimizer (GWO) and Moth-Flame Optimization (MFO) algorithms. The results show that the CIPSO-SVR model achieves superior accuracy and robustness on the test set (R2= 0.9569) in predicting PPV compared to the alternative models. Crucially, the model effectively captures the inherent nonlinear relationships of complex engineering problems, even with small-sample data.OPEN ACCESS Received: 18/08/2025 Accepted: 17/10/2025 Published: 23/01/2026