Worst-case design in head impact crashworthiness optimization

This paper describes the solution of a worst-case design optimization problem of head impact in automotive design. The worst-case design process uses an optimization algorithm that can locate saddlepoints: points in the design space where the objective function is maximized with respect to some design variables (worst case) while it is minimized with respect to other design variables simultaneously. The worst-case design methodology is rst tested using two analytic functions. Both functions contain saddlepoints, while the second one also has a random analytic noise component and an integer variable. Thereafter, the methodology is applied to the worst-case design of a crashworthiness head impact problem. The head impact problem contains both numerical noise and an integer variable. For the rst analytical case, the e ect of separability of the maximization and minimization variables is investigated by rotating the design variable axes. For the second analytical case, analytical noise in the form of a modi ed Griewank function and an integer variable is added. For the head impact problem, cases are presented where maximization and minimization are rst performed separately, and then in a combined fashion to locate the saddle point. The case studies illustrate the power of this approach in the automotive occupant safety design eld