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Technical Brief

Some Important Issues on First-Order Reliability Analysis With Nonprobabilistic Convex Models

[+] Author and Article Information
C. Jiang

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha 410082, China
e-mail: jiangc@hnu.edu.cn

G. Y. Lu, R. G. Bi

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha 410082, China

X. Han

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha 410082, China
e-mail: hanxu@hnu.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 6, 2012; final manuscript received December 4, 2013; published online January 10, 2014. Assoc. Editor: Wei Chen.

J. Mech. Des 136(3), 034501 (Jan 10, 2014) (5 pages) Paper No: MD-12-1012; doi: 10.1115/1.4026261 History: Received January 06, 2012; Revised December 04, 2013

Compared with the probability model, the convex model approach only requires the bound information on the uncertainty, and can make it possible to conduct the reliability analysis for many complex engineering problems with limited samples. Presently, by introducing the well-established techniques in probability-based reliability analysis, some methods have been successfully developed for convex model reliability. This paper aims to reveal some different phenomena and furthermore some severe paradoxes when extending the widely used first-order reliability method (FORM) into the convex model problems, and whereby provide some useful suggestions and guidelines for convex-model-based reliability analysis. Two FORM-type approximations, namely, the mean-value method and the design-point method, are formulated to efficiently compute the nonprobabilistic reliability index. A comparison is then conducted between these two methods, and some important phenomena different from the traditional FORMs are summarized. The nonprobabilistic reliability index is also extended to treat the system reliability, and some unexpected paradoxes are found through two numerical examples.

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References

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Figures

Grahic Jump Location
Fig. 1

Determination of the linearization point in the design-point method

Grahic Jump Location
Fig. 2

Absolute errors of the two methods for numerical example 1

Grahic Jump Location
Fig. 4

Absolute errors of the two methods for numerical example

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