An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

Abstract

In uncertainty analysis and reliability-based multidisciplinary design and optimization (RBMDO) of engineering structures, the saddlepoint approximation (SA) method can be utilized to enhance the accuracy and efficiency of reliability evaluation. However, the random variables involved in SA should be easy to handle. Additionally, the corresponding saddlepoint equation should not be complicated. Both of them limit the application of SA for engineering problems. The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments. However, the traditional moment matching method is not very accurate generally. In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization, a fourth-moment saddlepoint approximation (FMSA) method is introduced into RBMDO. In FMSA, the approximate cumulative generating functions are constructed based on the first four moments of the limit state function. The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function. Furthermore, the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment, which is based on the performance measure approach strategy. Two engineering examples are introduced to verify the effectiveness of proposed method.

Study on reliability of emergency braking performance of high-speed and heavy-load monorail crane

“…Du et al [5,6] proposed the first-order saddlepoint approximation (FOSPA) method to solve the non-linear problem caused by the transformation of the standard normal space of random variables, which first linearizes the performance function and then approximates its PDF using SPA. In addition to deriving an approximate performance function using a Taylor expansion of the limit state function at the Most Likelihood Point (MLP), an approximate cumulative generating function (CGF) for the performance function can be constructed based on statistical moments and then approximated its cumulative distribution function (CDF) using SPA [11]. Zhou et al [33] used an adaptive trivariate dimensional decomposition method to calculate the first six-order moments of the performance function, SPA method based on the first six-order moments was proposed to estimate the failure probability of the system for its high accuracy and validity.…”