High-dimensional model representation for structural reliability analysis

• Published in: Communications in numerical methods in engineering Vol. 25; no. 4; pp. 301 - 337
• Main Authors: Chowdhury, Rajib, Rao, B. N., Prasad, A. Meher
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.04.2009; Wiley
• Subjects: Computational techniques; Exact sciences and technology; failure probability; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); high-dimensional model representation; Mathematical methods in physics; moving least squares; Physics; response surface; Solid mechanics; Structural and continuum mechanics; structural reliability; Monte Carlo method; Statistical analysis; Probabilistic approach; Rupture; moving least squares; Structural reliability; Modeling; high-dimensional model representation; System with n degrees of freedom; Least squares method; Mechanical system; Random load; Response surface; Implicit function theorem; failure probability; Non linear effect; Random medium; Quantitative analysis; Structural analysis; Input output model
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1118

This paper presents a new computational tool for predicting failure probability of structural/mechanical systems subject to random loads, material properties, and geometry. The method involves high‐dimensional model representation (HDMR) that facilitates lower‐dimensional approximation of the original high‐dimensional implicit limit state/performance function, response surface generation of HDMR component functions, and Monte Carlo simulation. 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. It is a very efficient formulation of the system response, if higher‐order variable correlations are weak, allowing the physical model to be captured by the first few lower‐order terms. Once the approximate form of the original implicit limit state/performance function is defined, the failure probability can be obtained by statistical simulation. Results of nine numerical examples involving mathematical functions and structural mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of the probability of failure. Copyright © 2008 John Wiley & Sons, Ltd.