Structural Reliability Evaluation Using Enhanced HDMR

Abstract

This paper presents a new computational tool for predicting failure probability of randomly parametered structural/mechanical systems based on high dimensional model representation (HDMR) generated from low order function components. HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. When first-order HDMR approximation of the original high dimensional implicit limit state/performance function is not adequate to provide desired accuracy to the predicted failure probability, this paper presents an enhanced HDMR (eHDMR) method to represent the higher order terms of HDMR expansion by expressions similar to the lower order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input-output samples without directly invoking the determination of second- and higher order HDMR terms. This study aims to assess how accurately and efficiently eHDMR approximation technique can capture complex model output uncertainty. As a part of this effort, the efficacy of HDMR approximation, which is recently applied to reliability analysis, is also demonstrated. Once the approximate form of implicit response function is defined using HDMR/eHDMR, the failure probability can be obtained by statistical simulation.