A stochastic model approach for modeling SAG mill production and power through bayesian networks: a case study of the chilean copper mining industry

Abstract

Semi-autogenous (SAG) milling represents one of the most energy-intensive and variable stages of copper mineral processing. Traditional deterministic models often fail to capture the nonlinear dependencies and uncertainty inherent in industrial operations such as granulometry, solids percentage in the feeding or hardness. This work develops and validates a stochastic model based on Discrete Bayesian networks (BNs) to represent the causal relationships governing SAG Production and SAG Power under uncertainty or partial knowledge of explanatory variables. Discretization is adopted for methodological reasons as well as for operational relevance, since SAG plant decisions are typically made using threshold-based categories. Using operational data from a Chilean mining operation, the model fitted integrates expert-guided structure learning (Hill-Climbing with BDeu/BIC scores) and Bayesian parameter estimation with Dirichlet priors. Although validation indicators show high predictive performance (R2 ≈ 0.85—0.90, RMSE < 0.5 bin, and micro- AUC ≈ 0.98), the primary purpose of the BN is not exact regression but explainable causal inference and probabilistic scenario evaluation. Sensitivity analysis identified water feed and solids percentage as key drivers of throughput (SAG Production), while rotational speed and pressure governed SAG Power behavior. The BN framework effectively balances accuracy and interpretability, offering an explainable probabilistic representation of SAG dynamics. These results demonstrate the potential of stochastic modeling to enhance process control and support uncertainty-aware decision making.