Moment-Based Importance Analysis of Structure Performance Functions under Mixed Uncertainties

Abstract

In this paper, a novel strategy for the importance analysis of structural performance models under both aleatory and epistemic uncertainties is presented. Random variables and fuzzy numbers are adopted for the representation of the two types of uncertainty respectively. Based on the statistical moments of the model outputs, two categories of importance measures are proposed under a hybrid framework composed of probability theory and fuzzy logic. The first category is for the input factors with aleatory uncertainty, while the other is for the input factors with epistemic uncertainty. In order to depict the credibility of the important measures of the random factors, a stability indicator is further introduced. Under the hybrid framework, the statistical moments of the performance outputs are fuzzy membership functions instead of deterministic values. Therefore, the importance measures are defined based on the area differences between conditional and unconditional membership functions. For the estimation of the proposed importance measures and stability indicator, a uniform discretization of the fuzzy membership function is first performed to combine the fuzzy factors with the random samples. Then, the Monte Carlo simulation (MCS) and Gorman and Seo's three-point estimates (GSP) are employed as uncertainty propagation methods to address the statistical moments of the performance outputs. Finally, the proposed importance measures and stability indicator are studied through two numerical examples by MCS and GSP comparatively for demonstrating their benefits in stability, applicability, and efficiency.