Probabilistic Prediction of Rock Mass Deformation Modulus Using Vine Copula-SVR Fusion Model
摘要
Accurate estimation of the rock mass deformation modulus (Em) is essential for reliable analysis and design in rock engineering. This study proposes a fusion framework that integrates Vine Copula and Support Vector Regression (SVR) for Em uncertainty quantification based on six input indicators: Depth, uniaxial compressive strength (UCS), rock quality designation (RQD), discontinuity density (DD), discontinuity condition (DC), and rock mass rating (RMR). A publicly available dataset comprising 60 samples was utilized. Ten candidate marginal distributions were evaluated for each indicator. Subsequently, a Vine Copula model was constructed to capture the joint dependency structure among the indicators. The SVR model was then trained to characterize the nonlinear mapping between the input indicators and Em. Taylor diagram confirmed that the SVR model achieves satisfactory predictive performance. A total of 10,000 synthetic input samples were generated via Monte Carlo simulation and isoprobabilistic transformation, and then propagated through the trained SVR model to obtain the probabilistic prediction of Em. The predicted Em exhibits a smooth probability distribution approximated by Gaussian kernel density estimation. Sensitivity analysis further indicates that Depth and UCS are the dominant influential indicators affecting Em. The proposed Vine Copula–SVR fusion framework provides a robust, data-driven approach to probabilistic prediction and uncertainty analysis of Em, enhancing risk-informed decision-making in rock engineering projects.