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.

Three approaches for construction of a surrogate model of a result field consisting of multiple physical quantities are presented. The first approach uses direct interpolation of the result space on the input space. In the second and third approaches a Singular Value Decomposition is used to reduce the model size. In the reduced order surrogate models, the amplitudes corresponding to the different basis vectors are interpolated. A quality measure that takes into account different physical parts of the result field is defined. As the quality measure is very cheap to evaluate, it can be used to efficiently optimize hyperparameters of all surrogate models. Based on the quality measure, a criterion is proposed to choose the number of basis vectors for the reduced order models. The performance of the surrogate models resulting from the three different approaches is compared using the quality measure based on a validation set. It is found that the novel criterion can effectively be used to select the number of basis vectors. The choice of construction method significantly influences the quality of the surrogate model.

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.