Kriging modelization in predicting metal sheet elongation

Modern industries are increasingly replacing real experiments with non-stochastic simulation models due to their restrained costs and growing reliability. The non-stochastic simulator used in this paper is the Finite Element simulation code (FEM), a widely used numerical technique for the engineering problems modeled by a system of partial differential equations defined on a time-space domain. In such a context, it is common practice to provide a metamodel, a global approximation of the FEM experiment response on the design space to capture local minima/maxima. We use the most popular metamodel, the Kriging model, applied to an industrial instance: prediction of bend deduction. Metal sheet bending is a manufacturing process in which there is a plastic deformation of the workpieces over an axis. This is a metal forming process, similar to other processes where bending changes the shape of the workpieces. The work focuses on the construction of an optimal initial design in order to achieve a good accuracy of the metamodel at an acceptable computational cost, the theoretical study of this model, and the understanding of how it could be conformed to the bend deduction prediction. The correlation structure, mandatory in a Kriging model, was evaluated by means of the variogram, allowing to refine the correlation specification naturally improving the Kriging predictions. The empirical variograms for each input variable brought to light unusual behaviors. This suggested that the bending angle could be related to the bend deduction according to 2 different models. It is clear that there is a discontinuity in the relationship between the models, but its exact location is not known. The accuracy achieved was then evaluated using different indicators of robustness and the uncertainty of the “leave-one-out” methods.