Modelling of the cold rolling process for mild steel using physics-constrained neural network

Abstract Modelling the cold rolling process to predict rolling force is a challenging task, particularly for online applications that demand both rapid and accurate results. For this purpose, several well-established modelling techniques have been investigated in the past. Numerical techniques, such as finite element methods (FEM), provide high accuracy but are computationally expensive. In contrast, analytical models based on slab theory offer quick results but rely on simplifications and require extensive calibration typically conducted through parametric FEM simulation studies. Data-driven models like artificial neural networks (ANN) are fast and flexible; however, they necessitate large datasets, and being black box models, the learned correlations may not necessarily align with the physical laws governing the process. This work introduces a novel approach to modelling a reversible cold rolling process using a physics-constrained neural network (PCNN). It integrates known relationships from Siebel’s slab theory into the ANN framework to address the limitations of other modelling methods. A PCNN model has been developed specifically for DC04 steel and validated against experiments conducted on a Bühler VRW-400 universal rolling mill. The validation results indicate strong agreement with experimental data, achieving a maximum relative error of 5.63% in predicting the rolling force and a computation time of 0.054 s. In comparison to other modelling approaches, the proposed approach can provide more accurate and faster force predictions without requiring extensive calibration or large training datasets.