A hierarchical kriging approach for multi-fidelity optimization of automotive crashworthiness problems

Abstract

Multi-fidelity optimization schemes enriching expensive high-fidelity functions with cheap-to-evaluate low-fidelity functions have gained popularity in recent years. In the present work, an optimization scheme based on a hierarchical kriging is proposed for large-scale and highly non-linear crashworthiness problems. After comparison to other multi-fidelity techniques an infill criterion called variable-fidelity expected improvement is applied and evaluated. This is complemented by two innovative techniques, a new approach regarding initial sampling and a novel way to generate the low-fidelity model for crash problems are suggested. For the former, a modified Latin hypercube sampling, pushing samples more towards design space boundaries, increases the quality of sampling selection. For the latter, a projection-based non-intrusive model order reduction technique accelerates and simplifies the low-fidelity model evaluation. The proposed techniques are investigated with two application problems from the field of automotive crashworthiness—a size optimization problem for lateral impact and a shape optimization problem for frontal impact. The use of a multi-fidelity scheme compared to baseline single-fidelity optimization saves computational effort while keeping an acceptable level of accuracy. Both suggested modifications, independently and especially combined, increase computational performance and result quality in the presented examples.