Recent Advances on Surrogate Modeling for Robustness Assessment of Structures with Respect to Crashworthiness Requirements

Due to the inherent nonlinearity, crashworthiness is one of the most demanding design cases for vehicle structures. Recent developments have enabled very accurate numerical simulations and corresponding optimizations. Therefore, structural concepts are now much better adapted to the specific requirements. This has led to designs in which redundancies are reduced and highly effective car concepts have been derived. Important questions are then the reliability and the robustness of designs. Reliability addresses probabilities that constraints are violated and robustness assures that performance loss is small due to unavoidable variations. Because there is neither consensus on the precise definitions of robustness and reliability in the field of crashworthiness nor is there a unique understanding of the appropriate numerical methods, this paper first clarifies these aspects. Further an overview of recent research results from PhD theses supervised by the first author is presented. Hereby, special focus is laid on physical surrogate models for robustness assessments. Physical surrogates enable robustness investigations in early design phases considering mainly uncertainties related to lack of knowledge (changes, which occur later in the development process). Solution spaces derived by simplified models, here surrogate models based on lumped mass approaches, allow decoupled development of components. Robustness is achieved here by maximizing these solution spaces, resulting in high design flexibility. Further, an approach for robust design optimization is presented for later development phases based on a trust region and multi-fidelity approach. Low-fidelity models (physical surrogates using equivalent static loads) are used in the explorative phase of the analysis. Manufacturing or load case uncertainties are considered. Special criteria are established to switch to high-fidelity models (nonlinear transient finite element models) whenever necessary during optimization. It is hence possible to include robustness into the optimization with reduced numerical effort.