Failure Surface Frontier for Reliability Assessment on Expensive Performance Function

[+] Author and Article Information
Songqing Shan

Department of Mechanical & Manufacturing Engineering, The University of Manitoba, Winnipeg, MB, Canada, R3T 5V6

G. Gary Wang

Department of Mechanical & Manufacturing Engineering, The University of Manitoba, Winnipeg, MB, Canada, R3T 5V6gary_wang@umanitoba.ca

J. Mech. Des 128(6), 1227-1235 (Jan 06, 2006) (9 pages) doi:10.1115/1.2337311 History: Received June 20, 2005; Revised January 06, 2006

This work proposes a novel concept of failure surface frontier (FSF), which is a hyper-surface consisting of the set of non-dominated failure points on the limit states of a failure region. Assumptions, definitions, and benefits of FSF are described first in detail. It is believed that FSF better represents the limit states for reliability assessment (RA) than conventional linear or quadratic approximations on the most probable point. Then, a discriminative sampling based algorithm is proposed to identify FSF, based on which the reliability can be directly assessed for expensive performance functions. Though an approximation model is employed to approximate the limit states, it is only used as a guide for sampling and a supplementary tool for RA. Test results on well-known problems show that FSF-based RA on expensive performance functions achieves high accuracy and efficiency, when compared with the state-of-the-art results archived in literature. Moreover, the concept of FSF and proposed RA algorithm are proved to be applicable to problems of multiple failure regions, multiple most probable points, or failure regions of extremely small probability.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

An illustration of the failure surface and failure regions

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Figure 2

Tangent line to g(u)=0 in the U space

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Figure 3

A problem with 2 failure regions and many limit state surfaces

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Figure 4

An illustration of fitness function values

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Figure 5

Soil profile for Problem 5

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Figure 6

Evaluated sampling points for Problem 2

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Figure 7

Reliability assessment from 104 sample points for Problem 2

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Figure 8

Convergence history of two criteria for Problem 1



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