A points estimation and series approximation method for uncertainty analysis

X. F. Zhang; Y. E. Zhao; Y. M. Zhang; X. Z. Huang; H. Li

doi:10.1243/09544062JMES1229

A points estimation and series approximation method for uncertainty analysis

X. F. Zhang, Y. E. Zhao, Y. M. Zhang, X. Z. Huang, H. Li

Research output: Journal Publication › Article › peer-review

11 Citations (Scopus)

Abstract

The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram-Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.

Original language	English
Pages (from-to)	1997-2007
Number of pages	11
Journal	Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume	223
Issue number	9
DOIs	https://doi.org/10.1243/09544062JMES1229
Publication status	Published - 1 Sept 2009
Externally published	Yes

Keywords

C-type Gram-Charlier series
Moment method
Orthogonal polynomial
Point estimation
Probability density function

ASJC Scopus subject areas

Mechanical Engineering

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10.1243/09544062JMES1229

Cite this

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abstract = "The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram-Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.",

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AU - Zhang, X. F.

AU - Zhao, Y. E.

AU - Zhang, Y. M.

AU - Huang, X. Z.

AU - Li, H.

PY - 2009/9/1

Y1 - 2009/9/1

N2 - The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram-Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.

AB - The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram-Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.

KW - C-type Gram-Charlier series

KW - Moment method

KW - Orthogonal polynomial

KW - Point estimation

KW - Probability density function

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DO - 10.1243/09544062JMES1229

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VL - 223

SP - 1997

EP - 2007

JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

IS - 9

ER -

A points estimation and series approximation method for uncertainty analysis

Abstract

Keywords

ASJC Scopus subject areas

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