Hybrid modelling of hot-rolling force prediction based on PSO-optimised physical parameters and SSA-BP neural network

Accurate rolling force prediction is critical for hot-rolling control, yet conventional models are oversimplified and data-driven approaches lack interpretability. Hybrid methods, despite their potential, remain constrained by the accuracy of key physical parameters. To address this, the present study proposes a double-layer optimisation framework for hot-rolling force prediction. In the first layer, particle swarm optimisation is used to calibrate the deformation resistance K and the stress state coefficient Q _p of the mechanistic rolling-force model, thereby reducing the systematic error associated with empirically determined physical parameters. In the second layer, the optimised physical parameters, together with the process variables, are introduced as inputs into a backpropagation neural network whose hyperparameters are further tuned by the sparrow search algorithm. This arrangement improves the accuracy and physical consistency of the mechanistic features in the first layer while allowing the data-driven layer to capture the residual nonlinear relationships that the analytical model cannot represent. The results show that the proposed model achieves higher prediction accuracy and robustness compared to traditional hybrid and theoretical models. Further analysis indicates that the optimised deformation resistance varies only slightly, whereas the stress state coefficient changes more noticeably when temperature effects are considered. By introducing a temperature correction term, the interpretability and adaptability of the stress state coefficient model are effectively improved, providing a more reliable tool for rolling force prediction under varying operating conditions.