## 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 |
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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 | |

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