Application of surrogate models to FE simulation for a sizing press in a hot rolling mill

Abstract In steel production plants, finite element (FE) simulations are widely used to develop plastic deformation processes such as rolling and forging. However, these simulations are large-scale and highly nonlinear, and therefore require long computation times, which makes systematic optimization of process conditions difficult. In this study, a POD-based non-intrusive reduced order model (NIROM), which is used here as a surrogate model, is applied to FE simulations of a sizing press in a hot rolling mill to address this challenge. The method combines Proper Orthogonal Decomposition (POD) with machine-learning-based regression to learn from existing simulation results and predict unknown process conditions. Gaussian process regression (GPR) is employed as the regression model. This approach accelerates computations while preserving the relevant physical characteristics of the solution. For slab displacement, POD-based NIROM with Gaussian process regression as developed in this study achieves a relative root mean square error (RMSE) of approximately 5 % across all nodes at each time step, although periodic error growth is observed during initial slab–die contact. Excluding the initial contact phase, relative RMSE values in all directions remain under 1 % relative to the characteristic lengths of the slab in the conveyance, thickness, and width directions. While one FE simulation requires about 20 hours on the target computational environment, the surrogate model produces predictions within a few seconds, resulting in a significant reduction in computation time. The results demonstrate that POD-based NIROM with Gaussian process regression is effective for predicting displacement even in simulations involving complex plastic deformation such as sizing press operations. Furthermore, the method provides sufficient accuracy and speed for process development in steel production, indicating its practical applicability. To the best of the authors’ knowledge, this is the first reported application of a POD-based NIROM to FE simulation models involving large-scale plastic deformation in industrial steel production processes.