Probabilistic Constrained Physics-Informed Neural Networks for Blasting Vibration: From Mechanism Unveiling to Risk-Based Decision Support

Blast-induced ground vibrations constitute a critical hazard in open-pit mining, threatening adjacent structures and environments. Current prediction methodologies face limitations regarding data dependency, rock mass heterogeneity characterization, and the absence of robust uncertainty quantification. To address these challenges, this paper proposes a Probabilistic Constrained Physics-Informed Neural Network (PC-PINN). Embedded within a Bayesian deep learning framework, the model integrates the cylindrically symmetric damped wave equation via a dual-branch architecture to simultaneously perform vibration prediction and uncertainty quantification. An adaptive weighting strategy is employed to balance physics-based and data-driven loss components. Validated using 161 field datasets from the Kemerburgaz quarry, Turkey, the model incorporates seven critical parameters identified via feature selection, effectively synergizing physical mechanisms with data adaptability. Furthermore, SHAP analysis elucidates the coupled influence of key parameters to guide design adjustments. Ablation studies confirm the architecture's efficacy, achieving an \((R^2)\) of 0.92 and significantly outperforming classical machine learning algorithms in error minimization. Engineering case applications demonstrate high predictive accuracy (\((R^2=0.91)\)), supporting safety control in complex rock masses. Notably, the integrated parameter optimization framework reduces engineering risk probability by over 5%, providing a quantitative decision-making basis for hazard prevention and cost optimization.