Abstract

Modern product development in engineering is highly driven by computational approaches using finite element simulations and data analysis. Nevertheless, simulations in automotive applications are still very time and resource consuming. This results in a high need for accurate surrogate models that are cheap to evaluate, can be analysed easily with machine learning, and can be efficiently used, for example, in optimization studies. However, changes in input parameters can result in bifurcations in the simulation results, especially in highly nonlinear applications such as crash simulation. Often, these bifurcations cannot be represented adequately by a single surrogate model. To improve in such a case the prediction quality of the surrogate model, a preceding clustering of the simulations is very promising. We propose a workflow in which one first clusters the simulations obtained for different input parameter combinations according to the similarity of the results and secondly selectively uses these clusters to obtain separate surrogate models. The approach identifies global similarities using dimensionality reduction, where then simulations forming a cluster are automatically identified. Since simulations inside a similarity based cluster vary in a much more uniform way as outside the clusters, constructing surrogate models using clusters is much more accurate. In our study, design of experiments is employed to generate simulation snapshots. These are used for constructing two types of surrogate models, a standard proper orthogonal decomposition (POD) and our approach. The POD is used as a baseline for comparison and the same set of simulation snapshots is used for the POD and for our cluster-based approach. In particular, we employ a metamodeling approach using a kernel method, namely radial basis functions (RBF), to improve the prediction quality especially for highly nonlinear crash simulation results. Both types of surrogate model approaches are applied without the preceding clustering which results in rather poor prediction accuracy for specific parameter combinations, and next with the preceding clustering leading to large improvements in the prediction results. The approach is demonstrated for several CAE applications in metal forming and for crash simulation. For the studied methods the constructed surrogate models are evaluated using different type of metrics for comparison. The results clearly demonstrate the advantages of the proposed methodology especially in the presence of bifurcations.