Probabilistic Sensitivity Analysis for Novel Second-Order Reliability Method (SORM) Using Generalized Chi-Squared Distribution

1. Abstract Reliability-based design optimizations (RBDO) require evaluation of sensitivities of probabilistic constraints. To develop RBDO utilizing the recently proposed novel second-order reliability method (SORM) that improves the conventional SORM in terms of accuracy, the sensitivities of the probabilistic constraints at the most probable point (MPP) are required. Thus, this study presents the sensitivity analysis of the novel SORM at MPP for more accurate RBDO. During the analytic derivation in this study, it is assumed that the Hessian matrix does not change due to change of distribution parameter. The calculation of the sensitivity based on the analytic derivation requires evaluation of probability density function (PDF) of a linear combination of non-central chi-square variables, which is obtained by utilizing general chi-squared distribution. In terms of accuracy, the proposed probabilistic sensitivity analysis is compared with the finite difference method (FDM) using the Monte Carlo simulation (MCS) through numerical examples. The numerical examples demonstrate that the analytic sensitivity of the novel SORM agrees very well with the sensitivity obtained by FDM using MCS when a performance function is quadratic in U-space and input variables are normally distributed. It is further tested that sensitivity of a higher order performance function in terms of how the proposed assumption – the Hessian is constant – affects the accuracy of the sensitivity. 2.