Unified uncertainty analysis using the maximum entropy approach and simulation

Abstract

Two types of uncertainty may exist in engineering. In this paper, a unified uncertainty (UUA) analysis method is proposed to handle the two types' uncertainties. The presented method involves three main steps: (1) sampling on both random variables and interval variables, (2) approximating the maximum entropy density function by using the first four moments, (3) determining the lower and upper bounds of the system probability of failure. The proposed method is found to be more efficient, robust and sometimes more accurate than the existing methods like the unified uncertainty analysis (UUA) based on the first order reliability method (FORM-UUA) for it requires neither the search of the most probable point (MPP) nor the non-normal variables to normal transformation. One mathematical example and one engineering example are presented to demonstrate the proposed method.