Dimensional reduction for parametric projection‐based reduced‐order models in crash

Abstract

Modern car development regarding passive safety strongly relies on finite element simulations. Many simulations are required to assess the behavior of the design regarding minor parameter variations that occur naturally in hardware tests. This avoids costly revisions later in the design process when the first hardware tests are conducted. However, due to the immense computational costs, multiquery analyses such as robustness studies, optimization, and uncertainty quantification are currently not feasible for large simulation models. Reduced‐order modeling uses already generated data to accelerate future simulations. Using a data‐driven method, a low‐rank structure can be identified. The generated mapping subsequently expresses the governing equations regarding the reduced variables. Projection‐based model order reduction (MOR) is therefore physics‐based and has no black‐box character as classical machine learning models. The accuracy of the reduced‐order model (ROM) heavily relies on the dimensional reduction. Currently, proper orthogonal decompositionis most commonly used. However, this linear method is variance‐based and nonlinear correlation cannot be resolved requiring more dimensions in the approximation. Effective hyperreduction depends on the dimension of the ROM. Hence, we provide an overview of different strategies for parametric MOR in the context of highly nonlinear solid dynamics, discussing potential benefits and drawbacks. We show a successful application of the local reduced‐order bases approach to a crash problem and present first results of an autoencoder that is a nonlinear‐dimensional reduction.