Abstract
This study presents the analysis and modeling of the thermal regime of a furnace lining at an industrial copper smelting facility using a combined approach based on neural network (NN) technologies and the finite element method (FEM). Experimental temperature data were collected from a laboratory setup equipped with three thermocouples (TP-2488/1 and TCRosemount 0065), with a sampling frequency of 1 Hz over a total duration of 5 hours, resulting in 18,000 measurement points. The measurement uncertainty of the thermocouples did not exceed ±1.5 °C. These data were used both for model development and for validating the numerical FEM simulations. A feedforward neural network was trained using 70% of the dataset, while 15% and 15% were used for validation and testing, respectively. The prediction error of the neural network remained within 3% with a 95% confidence interval of [2.6%, 3.4%]. The results show that the proposed hybrid approach improves temperature prediction accuracy and reduces static control error by 15% when combined with a proportional-integral controller. The methodology demonstrates significant potential for improving thermal process stability and reducing energy consumption in high-temperature metallurgical systems.