Developing Metamodels for Fast and Accurate Prediction of the Draping of Physical Surfaces

In this paper, the use of methods from the meta- or surrogate modeling literature, for building models predicting the draping of physical surfaces, is examined. An example application concerning modeling of the behavior of a variable shape mold is treated. Four different methods are considered for this problem. The proposed methods are difference methods assembled from the methods kriging and proper orthogonal decomposition (POD) together with a spline-based underlying model (UM) and a novel patchwise modeling scheme. The four models, namely kriging and POD with kriging of the coefficients in global and local variants, are compared in terms of accuracy and numerical efficiency on data sets of different sizes for the treated application. It is shown that the POD-based methods are vastly superior to models based on kriging alone, and that the use of a difference model structure is advantageous. It is demonstrated that patchwise modeling schemes, where the complete surface behavior is modeled by a collection of locally defined smaller models, can provide a good compromise between achieving good model accuracy and scalability of the models to large systems.