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

Wanxin He

,
Wanxin He

Department of Engineering Mechanics,

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian 116024,

e-mail: hewanxin_dlut@mail.dlut.edu.cn

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: hewanxin_dlut@mail.dlut.edu.cn

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Gang Li

,
Gang Li

Department of Engineering Mechanics,

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian 116024,

e-mail: ligang@dlut.edu.cn

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: ligang@dlut.edu.cn

1

1

Corresponding author.
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Peng Hao

,
Peng Hao

Department of Engineering Mechanics,

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian 116024,

e-mail: haopeng@dlut.edu.cn

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: haopeng@dlut.edu.cn

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Yan Zeng

Yan Zeng

Department of Engineering Mechanics,

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian 116024,

e-mail: zengyan@dlut.edu.cn

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: zengyan@dlut.edu.cn

Search for other works by this author on:

Wanxin He

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
1

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: ligang@dlut.edu.cn

Peng Hao

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: haopeng@dlut.edu.cn

Yan Zeng

State Key Laboratory of Structural Analysis for Industrial Equipment,

Dalian University of Technology

,Dalian 116024,

China

e-mail: zengyan@dlut.edu.cn

1

Corresponding 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*. Oct 2019, 141(10): 101405 (13 pages)

**Published Online:**July 19, 2019

Article history

Received:

September 13, 2018

Revision Received:

May 1, 2019

Accepted:

May 4, 2019

Citation

He, W., Li, G., Hao, P., and Zeng, Y. (July 19, 2019). "Maximum Entropy Method-Based Reliability Analysis With Correlated Input Variables via Hybrid Dimension-Reduction Method." ASME. *J. Mech. Des*. October 2019; 141(10): 101405. doi: https://doi.org/10.1115/1.4043734

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