Investigating the influence of design and operational parameters on SAG mill energy spectra: A DEM and SHAP-based sensitivity analysis

This study uses a Discrete Element Modelling (DEM) based data-driven approach to identify and quantify the key variables influencing energy distribution in a Semi-Autogenous Grinding (SAG) mill, which is critical for balancing grinding efficiency and liner wear. A set of 36 conditions was simulated using the Discrete Element Method (DEM). Seven input variables were investigated: percentage of critical speed, number of lifters, two variables for lifter geometry (face angle, height), and three variables for charge composition (relative ball diameter and the filling levels for rocks and balls). The resulting energy spectra for two collision types (Rock-Ball and Rock-Belly) were analysed using regression models and SHAP (SHapley Additive exPlanations) to provide insights into variable importance and interactions. The analysis revealed that ball-related variables (percentage fill and diameter) and critical speed are the dominant factors governing collision energies. The SHAP analysis quantified complex, non-linear relationships and competing influences; for instance, the number of lifters significantly impacted Rock-Belly collisions, while lifter angle was more influential on Ball-Belly collisions. To explore the trade-offs identified by this analysis, three types of surrogate models were trained on the pre-wear dataset. Surrogate models exhibiting varying levels of predictive accuracy were subsequently coupled with the NSGA-II genetic algorithm to generate multi-objective Pareto fronts, illustrating the inherent trade-off between maximising Rock–Ball energy (grinding efficiency) and minimising Rock–Belly energy (liner wear).This study presents a detailed sensitivity analysis that quantifies the non-linear influence of key parameters, offering insights to guide future large-scale optimisation studies. • Uses PCA and SHAP to rank nonlinear effects of design and operational drivers. • Demonstrates DNN surrogate superiority over GPR for sparse DEM datasets. • Optimises Rock-Ball vs. Rock-Belly energy trade-offs via NSGA-II.