A Sequential Failure Probability Boundary Approximation Method for Reliability-Based Design Optimization

Reliability-Based Design Optimization (RBDO) provides an effective framework for addressing reliability constraints induced by uncertainties. Conventional RBDO approaches commonly employ the First-Order Reliability Method (FORM) for reliability estimation, which inevitably introduces first-order approximation errors. To overcome this limitation, this study proposes a Sequential Failure Probability Boundary Approximation (SFPBA) method, in which Monte Carlo Simulation (MCS) is employed to obtain accurate evaluations of failure probabilities, while the limit state surface is used to approximate the true failure probability boundary in the vicinity of the optimum. The proposed method effectively addresses the deficiencies of FORM in dealing with nonlinear problems, thereby enhancing the accuracy of solutions in nonlinear RBDO applications. The effectiveness and efficiency of the methodology are demonstrated through two numerical examples.