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.
Highlights
Computational Fluid Dynamics (CFD) and Finite Element (FE) analyses are powerful tools to solve engineering problems for which no analytical solution can be found
Different approaches in surrogate model construction are presented. Two of these approaches are based on different preprocessing methods of the snapshot matrix and two approaches are based on decomposition of different parts of the snapshot matrix
In this work four different approaches for interpolation of field data from FE simulations are presented
Summary
Computational Fluid Dynamics (CFD) and Finite Element (FE) analyses are powerful tools to solve engineering problems for which no analytical solution can be found. Constructing different surrogate models The general steps to construct a POD-based surrogate model are: obtaining a training set, preprocessing the snapshot matrix, reducing the output, interpolating the amplitudes and lastly post-processing the approximation. Zero centering In the construction of non-intrusive POD-based surrogate models it is common practice to subtract the mean result from the snapshot matrix before decomposing [33]. As pointed out by Skillicorn [33] dividing by the standard deviation will ensure that most of the values in each row will fall in the range − 1 to + 1 It has been found in previous work [36] that this is not beneficial for the quality of the surrogate model because the variation of the variables with relatively small variations will be amplified, and these variables get a larger contribution to the basis vectors. Scaling each row is left out of consideration in this paper
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