Reliability-Based Design Optimization of Uncertain Stochastic Systems: Gradient-Based Scheme

A method to carry out reliability-based optimization of uncertain structural systems under stochastic excitation is presented in this paper. The approach is based on a nonlinear interior point algorithm and a line search strategy. The associated reliability problems to be solved during the optimization process are high-dimensional (thousands or more random variables). An advanced Monte Carlo simulation is adopted for the purpose of estimating the corresponding failure probabilities. The gradients of the failure probability functions needed during the design process are estimated by an approach based on the local behavior of the normalized demand functions that define the failure domains. Numerical results show that only a small number of reliability estimates has to be performed during the entire design process. By construction, the design scheme is monotonically convergent; that is, it generates a sequence of steadily improved feasible designs. Example problems that consider a resistant element of a shear building model under ground motion and a nonlinear 11-story building model under earthquake excitation are presented to illustrate the effectiveness and feasibility of the approach reported in this paper.