Order statistics approach to structural optimization considering robustness and confidence of responses

A method for the worst-case analysis of structures is presented based on a random sampling approach and order statistics. The approximate worst value of the response is obtained with pre-assigned accuracy using the distribution-free tolerance interval of order statistics. A multi-objective optimization formulation is presented for robust design relating the order of response to the robustness level. Some recent studies linked a robust design optimization or a reliability-based design optimization with non-parametric order statistics. The chapter considers the uncertainty in seismic loads to ensure high robustness. It investigates the applicability of robust optimal design based on order statistics when there are uncertain properties in the phase spectrum, layer thickness and shear wave velocity of the surface ground. The Pareto optimal solutions with various levels of robustness can be obtained by solving the multi-objective optimization problem of minimizing the representative responses with various orders.