Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations

Abstract

Surrogate modelling is a powerful tool to replace computationally expensive nonlinear numerical simulations, with fast representations thereof, for inverse analysis, model-based control or optimization. For some problems, it is required that the surrogate model describes a complete output field. To construct such surrogate models, proper orthogonal decomposition (POD) can be used to reduce the dimensionality of the output data. The accuracy of the surrogate models strongly depends on the (pre)processing actions that are used to prepare the data for the dimensionality reduction. In this work, POD-based surrogate models with Radial Basis Function interpolation are used to model high-dimensional FE data fields. The effect of (pre)processing methods on the accuracy of the result field is systematically investigated. Different existing methods for surrogate model construction are compared with a novel method. Special attention is given to data fields consisting of several physical meanings, e.g. displacement, strain and stress. A distinction is made between the errors due to truncation and due to interpolation of the data. It is found that scaling the data per physical part substantially increases the accuracy of the surrogate model.