Real-Time Power Prediction of Ball Mill Using Explicit Mathematical Formulas

Grinding accounts for a relatively high proportion of the total electrical energy consumption in a mineral processing plant, and research on mill operating power constitutes a key basis for realizing intelligent control and energy conservation of the grinding process. Based on the SAB (semi-autogenous grinding followed by ball mill) circuit of a mineral processing plant, this study developed three sets of explicit mathematical models for ball mill power prediction using multivariate adaptive regression splines (MARS): an initial version containing 105 terms, an advanced version with 21 terms, and a reduced version with 11 terms. The prediction results show that the reduced version, using only 11 terms, attains a coefficient of determination R2 = 0.7989 (MAE = 8.96 kW, MAPE = 0.41%), comparable to the accuracy of the initial version (R2 = 0.8166). Moreover, the reduced model can be directly embedded into a PLC or an Excel spreadsheet to achieve mill power prediction at the millisecond scale. The proposed explicit model enables real-time prediction of ball mill operating power, allowing the plant to adjust mill operation promptly and reduce operating costs; it also holds important significance for the intelligent control of the grinding process.