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High-order limit state functions in the response surface method for structural reliability analysis

Publication ,  Journal Article
Gavin, HP; Yau, SC
Published in: Structural Safety
March 1, 2008

The stochastic response surface method (SRSM) is a technique for the reliability analysis of complex systems with low failure probabilities, for which Monte Carlo simulation (MCS) is too computationally intensive and for which approximate methods are inaccurate. Typically, the SRSM approximates a limit state function with a multi-dimensional quadratic polynomial by fitting the polynomial to a number of sampling points from the limit state function. This method can give biased approximations of the failure probability for cases in which the quadratic response surface can not conform to the true limit state function's nonlinearities. In contrast to recently proposed algorithms which focus on the positions of sample points to improve the accuracy of the quadratic SRSM, this paper describes the use of higher order polynomials in order to approximate the true limit state more accurately. The use of higher order polynomials has received relatively little attention to date because of problems associated with ill-conditioned systems of equations and an approximated limit state which is very inaccurate outside the domain of the sample points. To address these problems, an algorithm using orthogonal polynomials is proposed to determine the necessary polynomial orders. Four numerical examples compare the proposed algorithm with the conventional quadratic polynomial SRSM and a detailed MCS. © 2006.

Duke Scholars

Published In

Structural Safety

DOI

ISSN

0167-4730

Publication Date

March 1, 2008

Volume

30

Issue

2

Start / End Page

162 / 179

Related Subject Headings

  • Civil Engineering
  • 4005 Civil engineering
  • 0905 Civil Engineering
 

Citation

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Gavin, H. P., & Yau, S. C. (2008). High-order limit state functions in the response surface method for structural reliability analysis. Structural Safety, 30(2), 162–179. https://doi.org/10.1016/j.strusafe.2006.10.003
Gavin, H. P., and S. C. Yau. “High-order limit state functions in the response surface method for structural reliability analysis.” Structural Safety 30, no. 2 (March 1, 2008): 162–79. https://doi.org/10.1016/j.strusafe.2006.10.003.
Gavin, H. P., and S. C. Yau. “High-order limit state functions in the response surface method for structural reliability analysis.” Structural Safety, vol. 30, no. 2, Mar. 2008, pp. 162–79. Scopus, doi:10.1016/j.strusafe.2006.10.003.
Gavin HP, Yau SC. High-order limit state functions in the response surface method for structural reliability analysis. Structural Safety. 2008 Mar 1;30(2):162–179.
Journal cover image

Published In

Structural Safety

DOI

ISSN

0167-4730

Publication Date

March 1, 2008

Volume

30

Issue

2

Start / End Page

162 / 179

Related Subject Headings

  • Civil Engineering
  • 4005 Civil engineering
  • 0905 Civil Engineering