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Research Papers: Design Automation

A Vine-Copula-Based Reliability Analysis Method for Structures With Multidimensional Correlation

[+] 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, China
e-mail: jiangc@hnu.edu.cn

W. Zhang, X. Han, B. Y. Ni, L. J. Song

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

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 24, 2014; final manuscript received March 8, 2015; published online April 16, 2015. Assoc. Editor: Xiaoping Du.

J. Mech. Des 137(6), 061405 (Jun 01, 2015) (13 pages) Paper No: MD-14-1512; doi: 10.1115/1.4030179 History: Received August 24, 2014; Revised March 08, 2015; Online April 16, 2015

This paper proposed a vine-copula-based structural reliability analysis method which is an effective approach for performing a reliability analysis on complex multidimensional correlation problems. A joint probability distribution function (PDF) among multidimensional random variables was established using a vine copula function, based on which a reliability analysis model was constructed. Two solution algorithms were proposed to solve this reliability analysis model: one was based on Monte Carlo simulation (MCS) and another one was based on the first-order reliability method (FORM). The former method provides a generalized computational method for a reliability analysis based on vine copula functions and can provide so-called “precise solutions”; the latter method has high computational efficiency and can be used to solve actual complex engineering problems. Finally, three numerical examples were provided to verify the effectiveness of the method.

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Figures

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Fig. 1

A four-variable D-vine model

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Fig. 2

The scatter plots of the random variables (numerical example 1)

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Fig. 3

A comparison of reliability analysis results under different thresholds (numerical example 1)

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Fig. 4

Performance function in standard normal space (numerical example 1)

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Fig. 5

10-bar truss structure

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Fig. 6

The scatter plots of the random variables (10-bar truss)

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Fig. 7

A comparison of reliability analysis results under different thresholds (10-bar truss)

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Fig. 8

Reliability analysis results under different Kendall correlation parameters (10-bar truss)

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Fig. 9

The scatter plots in standard uniform space (Pile settlement analysis problem)

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Fig. 10

The effect of tail dependence coefficient on reliability results (Pile settlement analysis problem)

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