This work presents the development and validation of a digital twin for a semi-autogenous grinding (SAG) mill controlled by an expert control system. The digital twin consists of three interconnected modules that emulate the behavior of a closed-loop system: (1) fuzzy logic for the expert control system, (2) a state-space model for the regulatory control, and (3) a recurrent neural network (RNN) for the SAG mill process. The model was trained with data corresponding to 68 hours of operation and validated with 8 hours of test data. The digital twin predicts the dynamic behavior of the mill's bearing pressure, motor power, tonnage, solids percentage, and rotational speed within a 2.5-minute horizon with a 30-second sampling time. The RNN comprises two serial modules for detection and training. The disturbance detection evaluates the need for training by comparing the recent prediction error with the expected error using hypothesis tests for mean, variance, and probability distribution. If the detection module is activated, the parameters of the neural model are re-estimated with recent data. The detection module was configured with test data to eliminate false positives. Results indicate that the digital twin can satisfactorily supervise the SAG mill, which is operated with the expert control system. Future work will focus on integrating this digital twin into real-time optimization strategies with industrial validation.

翻译：本研究提出并验证了一种由专家控制系统控制的半自磨机数字孪生。该数字孪生由三个相互关联的模块组成，用于模拟闭环系统的行为：(1) 专家控制系统的模糊逻辑模块，(2) 调节控制的状态空间模型，以及 (3) 用于半自磨机过程建模的循环神经网络。模型使用对应68小时运行的数据进行训练，并用8小时的测试数据进行验证。该数字孪生能以30秒采样时间、2.5分钟预测时域，预测磨机轴承压力、电机功率、处理量、固体百分比和转速的动态行为。该循环神经网络包含用于检测和训练的两个串联模块。扰动检测模块通过假设检验比较近期预测误差与期望误差的均值、方差和概率分布，以评估重新训练的必要性。若检测模块被触发，则使用近期数据重新估计神经模型的参数。检测模块已通过测试数据配置以消除误报。结果表明，该数字孪生能有效监控由专家控制系统运行的半自磨机。未来工作将集中于将该数字孪生集成到实时优化策略中并进行工业验证。