Distributionally robust hybrid energy management in smart mining using process-coupled primal-dual mirror descent

This study presents a process-centric hybrid energy management framework tailored for large-scale smart mining operations. The framework addresses three major challenges: (i) multi-source uncertainty propagation, (ii) cross-process energy coupling, and (iii) time-varying, safety-critical operational constraints. The energy scheduling problem is formulated as a process-constrained, multi-period optimization under uncertainty, explicitly modeling the spatio-temporal correlations among renewable power generation, ventilation loads, dewatering demands, and blasting energy requirements. To tackle high-dimensional uncertainties with non-Gaussian distributions, a Wasserstein metric-based distributionally robust optimization (DRO) model is constructed. The ambiguity set is dynamically refined through adaptive scenario generation and clustering, capturing worst-case energy supply-demand mismatches. The objective function jointly minimizes total energy cost, carbon emissions, and process-specific operational risks, subject to nonlinear thermodynamic process constraints, piecewise convex ventilation characteristics, and interdependent hydraulic-ventilation-thermal (HVT) processes. Mining safety regulations are integrated via chance constraints, embedding safety-critical margins related to pressure, airflow, and gas concentration. To alleviate the computational burden caused by nested risk formulations, a Primal-Dual Reformulated Distributionally Robust Process Scheduling (PDR-DRPS) algorithm is proposed. This method recursively updates process-coupled dual variables, enabling fast convergence within joint physical-energy feasible subspaces. The proposed framework is validated using a synthetic open-pit mining benchmark incorporating real-world meteorological data, empirical process dynamics, and regulatory thresholds. Numerical results indicate a 25.4% reduction in operational costs, a 31.2% cut in carbon emissions, and consistent adherence to safety constraints within a 3% tolerance under all uncertainty scenarios. Sensitivity analysis further highlights that process inertia and time delays significantly amplify uncertainty propagation, underscoring the necessity of process-aware robust energy scheduling in safety-critical industrial systems. The framework offers a generalizable paradigm applicable to smart mining, tunnel construction, and underground industrial infrastructures.