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Second-Order Reliability Method With First-Order Efficiency

[+] Author Affiliations
Xiaoping Du

Missouri University of Science and Technology, Rolla, MO

Junfu Zhang

Xihua University, Chengdu, Sichuan, China

Paper No. DETC2010-28178, pp. 973-984; 12 pages
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 36th Design Automation Conference, Parts A and B
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4409-0 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME


The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

Copyright © 2010 by ASME
Topics: Reliability



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