Tail Modeling in Reliability-Based Design Optimization for Highly Safe Structural Systems

This paper presents an approach for the reliability–based design optimization of highly safe structural systems where a tail–model is used for computing the reliability constraint during design optimization. It is generally accepted that using central models (e.g., moment– based method or stochastic response surfaces) for estimating large percentiles such as those required in reliability constraint calculations can lead to significant inaccuracies in the result. The tail–model is an adaptation of a powerful result from extreme value theory in statistics related to the distribution of exceedances. The conditional excess distribution above a certain threshold is approximated using the generalized Pareto distribution (GPD). The shape and scale parameters in the GPD are estimated using the least–square method. The tail–modeling technique is utilized to approximate the performance measure in inverse reliability analysis. The accuracy and convergence properties are studied using an analytical function. The effectiveness and efficiency of the proposed approach are demonstrated using benchmark problems in structural design under uncertainty.