Reduced order modelling for spatial-temporal temperature and property estimation in a multi-stage hot sheet metal forming process

A concise approach is proposed to determine a reduced order control design oriented dynamical model of a multi-stage hot sheet metal forming process starting from a high-dimensional coupled thermo-mechanical model. The obtained reduced order nonlinear parametric model serves as basis for the design of an Extended Kalman filter to estimate the spatial-temporal temperature distribution in the sheet metal blank during the forming process based on sparse local temperature measurements. To address modeling and approximation errors and to capture physical effects neglected during the approximation such as phase transformation from austenite to martensite a disturbance model is integrated into the Kalman filter to achieve joint state and disturbance estimation. The extension to spatial-temporal property estimation is introduced. The approach is evaluated for a hole-flanging process using a thermo-mechanical simulation model evaluated using LS-DYNA. Here, the number of states is reduced from approximately 17 000 to 30 while preserving the relevant dynamics and the computational time is 1000 times shorter. The performance of the combined temperature and disturbance estimation is validated in different simulation scenarios with three spatially fixed temperature measurements.