Saddlepoint Approximation for Sequential Optimization and Reliability Analysis

Abstract

A good balance between accuracy and efficiency is essential for reliability-based design (RBD). For this reason, sequential-loops formulations combined with the first-order reliability method (FORM) are usually used. FORM requires a nonlinear non-normal-to-normal transformation, which may increase the nonlinearity of a probabilistic constraint function significantly. The increased nonlinearity may lead to an increased error in reliability estimation. In order to improve accuracy and maintain high efficiency, the proposed method uses the accurate saddlepoint approximation for reliability analysis. The overall RBD is conducted in a sequence of cycles of deterministic optimization and reliability analysis. The reliability analysis is performed in the original random space without any nonlinear transformation. As a result, the proposed method provides an alternative approach to RBD with higher accuracy when the non-normal-to-normal transformation increases the nonlinearity of probabilistic constraint functions.