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Research Papers

A Random Field Approach to Reliability Analysis With Random and Interval Variables

[+] Author and Article Information
Zhen Hu

Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall,
400 West 13th Street, Rolla, MO 65409-0500
e-mail: zh4hd@mst.edu

Xiaoping Du

Professor Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall, 400 West 13th Street, Rolla, MO 65409-0500
e-mail: dux@mst.edu

Manuscript received May 26, 2014; final manuscript received October 10, 2014; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041005 (Oct 02, 2015) (11 pages) Paper No: RISK-14-1025; doi: 10.1115/1.4030437 History: Received May 26, 2014; Accepted April 27, 2015; Online October 02, 2015

Interval variables are commonly encountered in design, especially in the early design stages when data are limited. Thus, reliability analysis (RA) should deal with both interval and random variables and then predict the lower and upper bounds of reliability. The analysis is computationally intensive, because the global extreme values of a limit-state function with respect to interval variables must be obtained during the RA. In this work, a random field approach is proposed to reduce the computational cost with two major developments. The first development is the treatment of a response variable as a random field, which is spatially correlated at different locations of the interval variables. Equivalent reliability bounds are defined from a random field perspective. The definitions can avoid the direct use of the extreme values of the response. The second development is the employment of the first-order reliability method (FORM) to verify the feasibility of the random field modeling. This development results in a new random field method based on FORM. The new method converts a general response variable into a Gaussian field at its limit state and then builds surrogate models for the autocorrelation function and reliability index function with respect to interval variables. Then, Monte Carlo simulation is employed to estimate the reliability bounds without calling the original limit-state function. Good efficiency and accuracy are demonstrated through three examples.

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Figures

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Fig. 1

Limit-state function with interval variables

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Fig. 3

Responses with both random and interval variables

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Fig. 2

Random field thickness of a metal sheet

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Fig. 4

Flowchart of constructing surrogate models of β(y) and ρ(y,y′)

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Fig. 5

Surrogate model of β(y)

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Fig. 6

Surrogate model of ρ(y,y′)

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Fig. 8

Maximum von Mises stress of the tube for a given θ1 and θ2

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Fig. 9

Ten-bar aluminum truss

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