Data-driven Temperature Estimation for a Multi-Stage Press Hardening Process

In a multi-stage press hardening process with a sheet material in a progressive die the material is first rapidly austenitized, pre-cooled, stretch-formed, and finally die bent. The product properties result from the thermo-mechanical history. With the aim to estimate and subsequently to directly control these properties a data-driven estimation of the spatial-temporal temperature distribution in the sheet is developed in this work. Therefore a data-driven dynamical model is designed via the Dynamic Mode Decomposition (DMD) using a Finite Element (FE) simulation as data basis. This model is extended to a parameter-dependent formulation (parametric DMD) capturing the process parameters stroke rate, blank holder force, and austenitization temperature, which serve as inputs to the model. The approach is verified by a comparison of the data-driven model with the original FE model. To estimate the temperature distribution a discrete time system representation is formulated, where the stage dependent and hence time varying output matrix is constructed for thermocouples integrated into the individual stages. Based on this a Kalman filter is designed and evaluated in simulation.