Han, Xiaofei; Li, Kang; Wang, Chuan; Zhang, Jiayang; Hu, Yukun; (2025) Transient heat conduction modelling for real-time operation and control of steel-making reheating furnaces - a physics-informed knowledge distillation-assisted EngGeneNet approach. Control Engineering Practice , 164 , Article 106472. 10.1016/j.conengprac.2025.106472.

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Abstract

Accurate and fast transient temperature distribution prediction is a long-standing technically challenging open problem in real-time operation and control of many energy-intensive industrial processes involving massive heat conduction. The powerful fitting capabilities of deep learning models to perform parallel computations make them ideal surrogate models to meet the requirements for real-time applications. However, collecting and processing a large amount of labelled data is tedious and challenging if not possible. Furthermore, most neural models are black-box models, hence suffer from a few well-known problems such as poor generalization performance and slow convergence speed. This paper proposes a physics-informed deep learning modelling framework, namely EngGeneNet to capture the salient features and functional relationships of system variables to predict the transient temperature distribution of large-scale intermediate steel products in reheating furnaces. The network can learn a mapping between the current and the future transient 2D temperature field at a given ambient temperature, equivalent to solving the partial differential equations in real-time. The heat conduction governing equations and the boundary conditions are formulated as the loss function to guide the accurate and efficient training of the proposed EngGeneNet model. Then, an ‘Eng-Gene’ module is embedded into the deep learning model to accelerate the training convergence and enhance generalization performance. The ‘Eng-Gene’ is the salient physical relationship among variables that are extracted from the first-principle knowledge of the target system. Furthermore, the knowledge distillation approach is adopted, where a computationally expensive but more accurate numerical method namely alternating direction implicit (ADI) is applied to generate sufficient training data for training the deep learning models. To improve the adaptability of the EngGeneNet model to varying product batches, transfer learning is adopted to mitigate the dataset feature space variations under different operating conditions. The proposed method has been validated on a pilot-scale walking-beam furnace with a range of steel bloom batches under different operating conditions. The results suggest that the EngGeneNet framework can effectively improve the generalization and convergence performance of the deep learning model. In terms of processing time for predicting each frame of the heat distribution map, the proposed model achieves an improvement of approximately 96% in computational efficiency with comparable accuracy of the conventional method used in real-life applications, paving the way for real-time applications in many energy-intensive engineering processes.

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