北京航空航天大学学报 ›› 2016, Vol. 42 ›› Issue (3): 421-425.doi: 10.13700/j.bh.1001-5965.2015.0181

• 论文 • 上一篇    下一篇

基于降维算法和Edgeworth级数的结构可靠性分析

孟广伟, 冯昕宇, 李锋, 周立明   

  1. 吉林大学机械科学与工程学院, 长春 130025
  • 收稿日期:2015-03-30 出版日期:2016-03-20 发布日期:2015-10-15
  • 通讯作者: 李锋,Tel.:0431-85095843 E-mail:fengli@jlu.edu.cn E-mail:fengli@jlu.edu.cn
  • 作者简介:孟广伟 男,博士,教授,博士生导师。主要研究方向:疲劳与断裂,结构可靠性。Tel.:0431-85095834 E-mail:mgw@jlu.edu.cn;冯昕宇 女,博士研究生。主要研究方向:结构可靠性。Tel.:0431-85095834 E-mail:fxy120884766@163.com;李锋 男,博士,副教授。主要研究方向:疲劳与断裂。Tel.:0431-85095834 E-mail:fengli@jlu.edu.cn
  • 基金资助:
    吉林省科技厅基金(201205001,201215048);国家重大科学仪器设备开发专项(2012YQ030075)

Structural reliability analysis based on dimensionality reduction and Edgeworth series

MENG Guangwei, FENG Xinyu, LI Feng, ZHOU Liming   

  1. School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China
  • Received:2015-03-30 Online:2016-03-20 Published:2015-10-15
  • Supported by:
    Foundation of Jilin Provincial Science & Technology Department (201205001, 201215048);National Key Scientific Instrument and Equipment Development Projects of China (2012YQ030075)

摘要: 针对工程实际中存在功能函数为隐式或高维非线性的复杂结构,本文提出了一种基于降维算法和Edgeworth级数的可靠性分析方法。利用降维算法将n维函数展开为n个一维函数,经变量转换后变量都相互独立且服从均值为0、方差为0.5的正态分布,再结合Gauss-Hermite积分方法计算出一维函数的原点矩,从而得到结构功能函数的中心矩,将所得的矩信息应用到Edgeworth级数展开式中,给出功能函数的累积分布函数表达式,计算得到结构的失效概率。该方法避免了功能函数对变量梯度的要求,仅需少量的确定性重分析计算。数值算例结果表明了本方法的有效性和正确性。

关键词: 结构可靠性, 降维算法, Gauss-Hermite数值积分, Edgeworth级数, 矩方法

Abstract: A reliability analysis method based on the dimension reduction algorithm and the Edgeworth series was proposed to treat the complicate structures with implicit and high dimensional nonlinear limit state functions in practical engineering. By utilizing the dimension reduction method, the n-dimensional function was expanded to n unidimensional functions and the random variable were made to subject to the independent normal distribution with mean value being zero and variance deviation being 0.5 by means of the variable transformation. The origin moments of the unidimensional functions were obtained after the Gauss-Hermite integration. In this case, the central moments of the limit state function of the structure were achieved successfully and applied to the Edgeworth series expanding expressions, from which the cumulative distribution function of the limit state function could be generated and finally the probability of failure could be obtained. Avoiding gradient computation, the proposed method requires less definite reanalysis and is proved to be effective and correct via numerical examples.

Key words: structural reliability, dimension reduction method, Gauss-Hermite numerical integration, Edgeworth series, moment method

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