Nondeterministic multi-objective and multi-case discrete optimization of functionally-graded front-bumper structures for pedestrian protection

Pedestrian lower-leg protection and lower-speed crashworthiness often present two important yet competing criteria on the design of front-bumper structures. Conventional design optimization is largely focused on a single loading condition without considering multiple impact cases. Furthermore, design of front-bumper structures is usually discrete in engineering practice and impacting conditions are commonly random. To cope with such a sophisticated nondeterministic design problem, this study aimed to develop a successive multiple attribute decision making (MADM) algorithm for optimizing a functionally graded thickness (FGT) front-bumper structure subject to multiple impact loading cases. The finite element (FE) model of front-end vehicle was constructed and validated with the in-house experimental tests under the loads of both Flexible Pedestrian Legform Impactor (Flex-PLI) impact and lower-speed impact. In the proposed successive MADM algorithm, the order preference by similarity to ideal solution (TOPSIS) based upon relative entropy was coupled with the analytic hierarchy process (AHP) to develop a MADM model for converting multiple conflicting objectives into a unified single cost function. The presented optimization procedure is algorithmically iterated using the successive Taguchi method to deal with a large number of design variables and design levels. The results showed that not only the algorithm enabled to generate an optimal design efficiently, but also the robustness of Flex-PLI impact is significantly enhanced. The proposed algorithm can be potentially used for other engineering design problems with similar complexity. •A novel successive multiple attribute decision making (MADM) algorithm was developed.•The finite element (FE) model of front-end vehicle was constructed and experimentally validated.•Comparison of deterministic discrete optimization with robust discrete optimization.•The proposed algorithm can be potentially used of other engineering problems.