Reliability Analysis of Stochastic System using Stochastic Spectral Embedding based Probability Density Evolution Method

Abstract

This study presents a reliability analysis of stochastic system using the probability density evolution method (PDEM). The PDEM is formulated according to the principle of probability conservation where generalized density evolution equations (GDEEs) are completely decoupled. To estimate the probability density function accurately, a set of representative points of random variables are generated using the GF-discrepancy scheme. A large number of representative points is needed to obtain satisfactory accuracy, which becomes computationally expensive. To reduce the computation burden, a stochastic spectral embedding (SSE) is used as a surrogate model which approximates the original response surface. To illustrate the proposed SSE-based PDEM, two numerical examples are investigated, including the reliability analysis of four-branch problem, and the reliability-based design optimization of a shape memory alloy based damped outrigger tall timber building. Numerical results show that the proposed SSE-based PDEM can estimate failure probability using a very small number of representative points without compromising accuracy compared with Monte Carlo simulation, which leads to a reduction in computational costs.