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Research Papers

A Second-Order Reliability Method With First-Order Efficiency

[+] Author and Article Information
Junfu Zhang

School of Mechanical Engineering, Xihua University, Chengdu 610039, P.R. Chinazhangjun@mst.edu

Xiaoping Du1

Department of Mechanical and Aerospace Engineering,Missouri University of Science and Technologydux@mst.edu

1

Corresponding author.

J. Mech. Des 132(10), 101006 (Oct 04, 2010) (8 pages) doi:10.1115/1.4002459 History: Received April 09, 2010; Revised August 07, 2010; Published October 04, 2010; Online October 04, 2010

The 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 to identify 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 by a quadratic function. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied in 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.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flowchart of SORM-FOE

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Figure 2

Information used for approximation

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Figure 4

Contours of the limit-state function in the X-space

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Figure 5

Contours of the limit-state function in the U-space

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Figure 6

Crank-slider mechanism

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Figure 7

pf over θ2=[10 deg,90 deg]

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Figure 8

A cantilever beam

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