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Research Papers: Design Automation

Maximum Entropy Method-Based Reliability Analysis With Correlated Input Variables via Hybrid Dimension-Reduction Method

[+] Author and Article Information
Wanxin He

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: hewanxin_dlut@mail.dlut.edu.cn

Gang Li

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: ligang@dlut.edu.cn

Peng Hao

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: haopeng@dlut.edu.cn

Yan Zeng

Department of Engineering Mechanics,
State Key Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China
e-mail: zengyan@dlut.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received September 13, 2018; final manuscript received May 1, 2019; published online July 19, 2019. Assoc. Editor: Xiaoping Du.

J. Mech. Des 141(10), 101405 (Jul 19, 2019) (13 pages) Paper No: MD-18-1690; doi: 10.1115/1.4043734 History: Received September 13, 2018; Accepted May 04, 2019

The estimation of the statistical moments is widely involved in the industrial application, whose accuracy affects the reliability analysis result considerably. In this study, a novel hybrid dimension-reduction method based on the Nataf transformation is proposed to calculate the statistical moments of the performance function with correlated input variables. Nataf transformation is intrinsically the Gaussian copula, which is commonly used to transform the correlated input variables into independent ones. To calculate the numerical integration of the univariate component function in the proposed method, a normalized moment-based quadrature rule is employed. According to the statistical moments obtained by the proposed method, the probability density function of the performance function can be recovered accurately via maximum entropy method. Six examples are tested to illustrate the accuracy and efficiency of the proposed method, compared with that of Monte Carlo simulation, the conventional univariate dimension-reduction method, and the bivariate dimension-reduction method. It is confirmed that the proposed method achieves a good tradeoff between accuracy and efficiency for structural reliability analysis with correlated input variables.

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Figures

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Fig. 1

Flowchart of reliability analysis via MEM based on the HDRM

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Fig. 2

A cantilever beam under vertical and lateral bending

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Fig. 3

Comparison of PDF of Y1 obtained by different methods: (a) ρ12 = 0.9 and (b) ρ12 = −0.9

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Fig. 4

Comparison of PDF of Y2 obtained by different methods: (a) ρ56 = 0.9, (b) ρ56 = 0.5, (c) ρ56 = −0.5, and (d) ρ56 = −0.9

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Fig. 5

Comparison of PDF of Y3 obtained by different methods: (a) ρ = 0.9 and (b) ρ = −0.9

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Fig. 6

Comparison of PDF of Y4 obtained by different methods (ρ23 = 0.9)

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Fig. 7

Schematic view of aircraft stiffened shell problem

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Fig. 8

Comparison of PDF of critical buckling load obtained by different methods

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Fig. 9

Simplified model of the underwater vehicle with two nonlinear connections

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Fig. 10

Comparison of PDF of critical buckling load obtained by different methods

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