吉林大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (1): 174-179.doi: 10.13229/j.cnki.jdxbgxb201701026

• 论文 • 上一篇    下一篇

基于降维算法的结构可靠性分析

孟广伟, 冯昕宇, 周立明, 李锋   

  1. 吉林大学 机械科学与工程学院,长春 130022
  • 收稿日期:2015-11-06 出版日期:2017-01-20 发布日期:2017-01-20
  • 通讯作者: 李锋(1977-),男,副教授,博士.研究方向:疲劳与断裂.E-mail:fengli@jlu.edu.cn
  • 作者简介:孟广伟(1959-),男,教授,博士生导师.研究方向:疲劳与断裂.E-mail:mgw@jlu.edu.cn
  • 基金资助:

    国家重大科学仪器设备开发专项项目(2012YQ030075); 吉林省科技发展计划项目(201205001,201215048).

Structural reliability analysis based on dimension reduction algorithm

MENG Guang-wei, FENG Xin-yu, ZHOU Li-ming, Li Feng   

  1. College of Mechanical Science and Engineering,Jilin University,Changchun 130022,China
  • Received:2015-11-06 Online:2017-01-20 Published:2017-01-20

摘要:

为解决工程实际中功能函数为高维非线性的可靠性分析问题,提出了基于降维算法的一种新型的直接结构可靠度的分析方法。利用降维算法,建立了新的n个一维函数模型近似替代原n维功能函数,借助于泰勒级数和统计矩理论,求解结构功能函数的前四阶矩信息,并通过Edgeworth级数拟合结构功能函数的累积分布函数,结合可靠性理论可计算得到结构的失效概率。与传统方法相比,本文方法无需积分求解功能函数的统计矩,也无需迭代搜索最可能失效点。数值算例结果表明本文方法具有较高的计算精度和较好的适应性。

关键词: 工程力学, 可靠性分析, 降维算法, 泰勒级数, Edgeworth级数, 矩方法

Abstract:

Considering the high-dimensional non-linear performance functions of complex structures, a new structural reliability analysis method based on dimension reduction algorithm was proposed. The n one-dimensional approximate functions were established to substitute the n dimensional performance function by using dimension reduction algorithm. With the help of Taylor series and statistical moment theory, the first four order moments of the performance function were solved. The cumulative distribution function of the performance function was fitted by Edgeworth series and the failure probability of the structure was obtained based on the reliability theory. Compared with the traditional methods, the new method does not need to use integral method to solve the statistical moments of the performance function, and not need to search the most possible failure point iteratively. Numerical results indicate that the proposed method has high precision and good adaptability.

Key words: engineering mechanics, reliability analysis, dimension reduction method, Taylor series, Edgeworth series, moment method

中图分类号: 

  • TB114.3
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