结构可靠性分析的变量分解法

李金平; 焦生杰; 陈建军; 刘国梁; 徐信芯

doi:10.3969/j.issn.0258-2724.2014.01.013

结构可靠性分析的变量分解法

doi: 10.3969/j.issn.0258-2724.2014.01.013

李金平^1,2,
焦生杰^1,2, ,,
陈建军³,
刘国梁³,
徐信芯^1,2

基金项目:

中央高校基本科研业务费专项资金资助项目（CHD2009JC152，2013G3254015）

详细信息

通讯作者:
焦生杰（1955-），男，教授，博士，博士生导师，主要研究方向为工程机械机电液一体化、液压传动与控制，E-mail：jsj@chd.edu.cn

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- 文章访问数: 1134
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- PDF下载量: 605
- 被引次数: 0
出版历程
- 收稿日期: 2012-12-10
- 刊出日期: 2014-01-25

Dimension-Reduction Method for Structural Reliability Analysis

摘要

摘要: 针对隐式非线性极限状态的复杂结构可靠性预测，提出了一种变量分解方法.该方法利用双变量分解法将求解功能函数统计矩的多维积分转化为多个低维积分，并利用高斯-埃尔米特数值积分对低维积分进行求积.在获得功能函数的统计矩后，应用最大熵原理确定用于可靠性分析的功能函数的最佳概率密度函数.该方法只需进行一次结构功能函数的概率密度函数求解，就能获得不同极限状态值的可靠度.算例分析结果表明，该方法的结果与Monte Carlo法100万次模拟结果相比，其相对误差不超过0.5%，具有很好的计算精度.
- 结构可靠性 /
- 双变量分解法 /
- 最大熵原理 /
- 概率密度函数
Abstract: To predict the reliability of implicit and nonliear performance function for complex structures, a dimension-reduction method was presented. The multi-dimensional integration applied to calculate statistical moments of performance function is transformed into multiple low dimensional integrations using the bivariate dimension-reduction method, and the low dimensional integrations are then numerically calculated by the Gauss-Hermite integration. After obtaining the statistical moments, the maximum entropy principle (MEP) is used to determine the best probability density function of performance function for reliability analysis. The proposed method has the merit that the reliabilities at different limit-state values can be obtained readily by determining the probability density function of performance function simultaneously. The results of two examples show that the relative error of failure probability obtained by the proposed method is less than 0.5% compared with that derived by one million times simulations of the Monte Carlo method.
- structural reliability /
- bivariate dimension-reduction method /
- maximum entropy principle /
- probability density function

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参考文献(18)

李伦贵, 高波. 翼墙式隧道洞门可靠性分析[J]. 西南交通大学学报, 2002, 37(5): 496-499. LI Lungui, GAO Bo. Reliability analysis of wing wall tunnel portal[J]. Journal of Southwest Jiaotong University, 2002, 37(5): 496-499.

戴鸿哲, 王伟. 结构可靠性分析的拟蒙特卡罗方法[J]. 航空学报, 2009, 30(4): 666-671. DAI Hongzhe, WANG Wei. Quasi-Monte Carlo method for structural reliability analysis[J]. Acta Aeronautica Et Astronautica Sinica, 2009, 30(4): 666-671.

ENGELUND S, RACKWITZ R. A benchmark study on importance sampling techniques in structural reliability[J]. Structural Safety, 1993, 12(4): 255-276.

NIE J, ELLINGWOOD B R. Directional methods for structural reliability analysis[J]. Structure Safety, 2000, 22(3): 233-249.

NIE J, ELLINGWOOD B R. A new directional simulation method for system reliability. Part Ⅰ: application of deterministic point sets[J]. Probabilistic Engineering Mechanics, 2004, 19(4): 425-436.

NIEDERREITER H, SPANIER J. Monte Carlo and quasi-Monte Carlo methods[M]. Berlin: Springer, 2000: 44-45.

KIM S H, NA S W. Response surface method using vector projected sampling points[J]. Structural Safety, 1997, 19(1): 3-19.

GUAN X L, MELCHERS R E. Effect of response surface parameter variation on structural reliability estimates[J]. Structural Safety, 2001, 23(4): 429-444.

NAM M D, THANH T C. Approximation of function and its derivatives using radial basis function networks[J]. Applied Mathematical Modelling, 2003, 27(3): 197-220.

GOMES H M, AWRUCH A M. Comparison of response surface and neural network with other methods for structural reliability analysis[J]. Structural Safety, 2004, 26(1): 49-67.

李洪双, 吕震宙. 结构可靠性分析的支持向量机响应面法[J]. 计算力学学报, 2009, 26(2): 199-203. LI Hongshuang, LV Zhenzhou. A support vector machine response surface method for structural reliability analysis[J]. Chinese Journal of Computational Mechanics, 2009, 26(2): 199-203.

PENMETSA R C, GRANDHI R V. Adaptation of fast Fourier transformations to estimate structural failure probability[J]. Finite Elements in Analysis and Design, 2003, 39(5/6): 473-485.

陈建兵, 李杰. 基于概率密度演化方法的随机结构可靠度分析[J]. 计算力学学报, 2004, 21(3): 285-290. CHEN Jianbing, LI Jie. Reliability analysis of stochastic structures based on probability density evolution method[J]. Chinese Journal of Computational Mechanics, 2004, 21(3): 285-290.

雒卫廷, 陈建军, 张驰江, 等. 随机桁架结构可靠性分析的完全概率方法[J]. 安全与环境学报, 2005, 5(5): 35-38. LUO Weiting, CHEN Jianjun, ZHANG Chijiang, et al. Analysis of reliability of stochastic truss structure based on full-probability[J]. Journal of Safety and Environment, 2005, 5(5): 35-38.

王新刚, 张义民, 王宝艳. 涡轮转子随机结构的可靠性研究[J]. 航空动力学报, 2009, 24(6): 1316-1320. WANG Xingang, ZHANG Yimin, WANG Baoyan. Research on reliability of turbo-rotor with random structure[J]. Journal of Aerospace Power, 2009, 24(6): 1316-1320.

XU H, RAHMAN S. Decomposition methods for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2005, 20(3): 239-250.

XU H, RAHMAN S. A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics[J]. International Journal for Numerical Methods in Engineering, 2004, 61(12): 1992-2019.

李金平, 陈建军, 黄白, 等. 基于分解法的最大熵随机有限元法[J]. 振动与冲击, 2009, 28(7): 99-104. LI Jinping, CHEN Jianjun, HUANG Bai, et al. Maximum entropy stochastic finite element method based on dimension-reduction method[J]. Journal of Vibration and Shock, 2009, 28(7): 99-104.

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文章访问数: 1134
HTML全文浏览量: 46
PDF下载量: 605
被引次数: 0

结构可靠性分析的变量分解法

doi: 10.3969/j.issn.0258-2724.2014.01.013

通讯作者: 焦生杰（1955-），男，教授，博士，博士生导师，主要研究方向为工程机械机电液一体化、液压传动与控制，E-mail：jsj@chd.edu.cn

计量

出版历程

Dimension-Reduction Method for Structural Reliability Analysis

计量

出版历程

目录

通讯作者:
焦生杰（1955-），男，教授，博士，博士生导师，主要研究方向为工程机械机电液一体化、液压传动与控制，E-mail：jsj@chd.edu.cn