SEQUENTIAL MULTIDISCIPLINARY DESIGN OPTIMIZATION AND RELIABILITY ANALYSIS USING AN EFFICIENT THIRD-MOMENT SADDLEPOINT APPROXIMATION METHOD

摘要

In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBMDO method using Third-Moment Saddlepoint Approximation (TMSA) is proposed in this study. TMSA can construct a concise CGF using the first three statistical moments of a limit state function easily, and then express the probability density function and cumulative distribution function of the limit state function approximately using this concise CGF. To further improve the efficiency of RBMDO, a sequential optimization and reliability analysis strategy is also utilized and a formula of RBMDO using TMSA within the framework of SORA is proposed. Two examples are given to show the effectiveness of the proposed method.