On the choice of basis in proper orthogonal decomposition-based surrogate models

Abstract

To reduce scrap in metal forming processes, one should aim for robustness by means of optimization, control or a combination of both. Due to the high computational costs, a Finite Element (FE) model of a metal forming process cannot be used in optimization routines or control algorithms directly. Alternatively, a surrogate model of the process response to certain variables can be created that enables efficient control or optimization algorithms. When the process response is more than a scalar function only, reduction methods such as Proper Orthogonal Decomposition (POD) can be applied to obtain a surrogate model. In this work, the results of a set of FE analyses are decomposed using a single and separated snapshot matrices using different preprocessing methods. Additionally, a new method for projecting in different parts of the snapshot matrix is proposed. The bases obtained using different preprocessing methods are compared. Thereafter, the surrogate models of the process are built by interpolating the amplitudes obtained in different bases. The accuracy of all surrogate models is assessed by comparing the reduced results with the results from the FE analyses.