Digital twin with automatic disturbance detection for real-time optimization of a semi-autogenous grinding (SAG) mill

TL;DR

The paper addresses the challenge of real-time optimization for a semi-autogenous grinding (SAG) mill by developing a three-module digital twin that combines fuzzy logic-based expert control, a discrete-time state-space regulator, and a NARX-based SAG mill predictor. An automatic disturbance detection mechanism continuously evaluates predictive accuracy and retrains the regulator and mill models when drift is detected, while keeping the expert controller fixed. Trained on 68 hours of historical operation and validated on 8 hours, the twin forecasts the controlled variables $y_1$ (bearing pressure) and $y_2$ (motor power) over a horizon of 2.5 minutes at a 30-second sampling rate, achieving maximum errors of about 5% and 1% for longer and shorter horizons respectively. This approach demonstrates a viable path toward supervisory optimization (RTO) of SAG milling with the potential for industrial validation and real-time optimization integration, adapting to changing feed conditions and disturbances through automatic retraining.

Abstract

This work describes the development and validation of a digital twin for a semi-autogenous grinding (SAG) mill controlled by an expert system. The digital twin consists of three modules emulating a closed-loop system: fuzzy logic for the expert control, a state-space model for regulatory control, and a recurrent neural network for the SAG mill process. The model was trained with 68 hours of data and validated with 8 hours of test data. It predicts the mill's behavior within a 2.5-minute horizon with a 30-second sampling time. The disturbance detection evaluates the need for retraining, and the digital twin shows promise for supervising the SAG mill with the expert control system. Future work will focus on integrating this digital twin into real-time optimization strategies with industrial validation.

Figures (8)

• Figure 1: Proposed supervisory system scheme including a closed-loop system, where $\mathbf{u}:=[u_{1}, u_{2}, u_{3}]^T, \mathbf{u^{SP}}:= [u_{1}^{SP}, u_{2}^{SP}, u_{3}^{SP}]^T, \mathbf{y^{LIM^{*}}}:=[y_{1}^{LIM^{*}},y_{2}^{LIM^{*}}]^T, \mathbf{y}:=[y_{1},y_{2}]^T$.
• Figure 2: Digital twin structure.
• Figure 3: expert control system model description.
• Figure 4: Diagram of the learning detection algorithm
• Figure 5: Diagram of the digital twin integrated with the learning detection algorithm.