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Research Papers

A Hybrid Reliability Approach Based on Probability and Interval for Uncertain Structures

[+] 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 City 410082, P. R. Chinajiangchaoem@yahoo.com.cn

X. Han1

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering,  Hunan University, Changsha City 410082, P. R. Chinahanxu@hnu.edu.cn

W. X. Li, J. Liu, Z. Zhang

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

1

Corresponding author.

J. Mech. Des 134(3), 031001 (Feb 18, 2012) (11 pages) doi:10.1115/1.4005595 History: Received September 30, 2010; Revised December 02, 2011; Published February 17, 2012; Online February 18, 2012

Traditional reliability analysis generally uses probability approach to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. In this paper, a new reliability analysis technique is developed based on a hybrid uncertain model, which can deal with problems with limited information. All uncertain parameters are treated as random variables, while some of their distribution parameters are not given precise values but variation intervals. Due to the existence of the interval parameters, a limit-state strip enclosed by two bounding hyper-surfaces will be resulted in the transformed normal space, instead of a single hyper-surface as we usually obtain in conventional reliability analysis. All the limit-state strips are then summarized into two different classes and corresponding reliability analysis models are proposed for them. A monotonicity analysis is carried out for probability transformations of the random variables, through which effects of the interval distribution parameters on the limit state can be well revealed. Based on the monotonicity analysis, two algorithms are then formulated to solve the proposed hybrid reliability models. Three numerical examples are investigated to demonstrate the effectiveness of the present method.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Transformation of the limit-state function with different types of interval distribution parameters

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Figure 4

Identification of the interval translation parameter on the limit-state bounds

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Figure 5

Reliability analysis process for the second form of limit-state strip

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Figure 6

The limit-state strip caused by the interval parameters for the first case

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Figure 7

The limit-state strip caused by the interval parameters for the second case

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Figure 8

A cantilever beam [37]

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Figure 9

An automobile frame structure

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Figure 1

Two forms of limit-state strip caused by the interval parameters

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Figure 2

Transformation of the limit-state function with an interval distribution parameter in the CDF of Xi

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