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 PublicationArticlepeer-review

10 Citations (Scopus)


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 languageEnglish
Pages (from-to)1997-2007
Number of pages11
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Issue number9
Publication statusPublished - 1 Sept 2009
Externally publishedYes


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

ASJC Scopus subject areas

  • Mechanical Engineering


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