An order statistics approach to multiobjective structural optimization considering robustness and confidence of responses

A design method is proposed for reducing the worst value of representative response of structure under random variation of structural parameters. To reduce the computational cost for finding the worst value, the requirement of ‘worst’ is relaxed to the value corresponding to the specified quantile of the distribution function. The order statistics is used for defining the level of robustness of the approximate worst response value for specified confidence. Obviously, a larger estimate of response is required for ensuring larger robustness with the same confidence. Therefore, a trade-off relation exists between the order of response generated by random parameter values and the robustness in estimation of the worst response. A multiobjective optimization problem is formulated to minimize the representative responses with various order; thus, the solutions with various levels of robustness are simultaneously obtained. A numerical example of a 20-story shear frame is presented for minimizing the maximum interstory drift against seismic motions under constraint on the total amount of damping coefficient, where uncertainty is considered in the story stiffness and the floor mass as well as the damping coefficient that is also the design variable. It is shown that the distribution of additional damping coefficients depends on the level of robustness in estimation of the worst response value.