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工程力学  2013 

联合分布函数构造的Copula函数方法及结构可靠度分析

DOI: 10.6052/j.issn.1000-4750.2012.08.0603

Keywords: 联合分布函数,不完备概率信息,相关性,Copula,失效概率

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Abstract:

不完备概率信息条件下变量联合分布函数的确定及其对结构可靠度的影响还缺少系统地研究。为此,提出了基于Copula函数的变量联合概率分布函数构造方法,并分析了不同Copula函数类型对结构可靠度的影响规律。首先,简要介绍了基于Copula函数的变量联合分布函数构造方法。其次,提出了构件失效概率计算的直接积分方法。最后以构件可靠度问题为例研究了Copula函数的类型对结构可靠度的影响规律。结果表明:不完备概率信息条件下构件可靠度是不唯一的,表征变量间相关性的Copula函数类型对构件可靠度具有明显的影响,不同Copula函数计算的构件失效概率存在明显的差别,这种差别随构件可靠指标的增大(或失效概率的减小)而增大。Copula函数尾部相关性对结构可靠度具有重要的影响。当功能函数的失效区域位于Copula函数尾部时,计算的失效概率明显比没有尾部相关性的Copula函数的失效概率大。基于功能函数的均值和标准差计算的可靠指标不能反映Copula函数的类型对结构可靠度的影响,而基于功能函数实际分布求得的失效概率则可以有效反映不同Copula函数对结构可靠度的影响。

References

[1]  Ghosh S. Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighbouring meteorological subdivisions using copula [J]. Hydrological Processes, 2010, 24(24): 3558―3567.
[2]  Sklar A. Fonctions de r#x000e9;partition #x000e0;n dimensions et leurs marges [J]. Publications de l#x02019;Institut de Statistique de l#x02019;Universit#x000e9; de Paris, 1959, 8: 229―231.
[3]  Goda K. Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands [J]. Structural Safety, 2010, 32(2): 112―123.
[4]  Leira B J. Probabilistic assessment of weld fatigue damage for a nonlinear combination of correlated stress components [J]. Probabilistic Engineering Mechanics, 2011, 26(3): 492―500.
[5]  Low B K. Reliability analysis of rock slopes involving correlated nonnormals [J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 922―935.
[6]  Li D Q, Chen Y F, Lu W B, et al. Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables [J]. Computers and Geotechnics, 2011, 38(1): 58―68.
[7]  Li D Q, Tang X S, Phoon K K, et al. Bivariate simulation using copula and its application to probabilistic pile settlement analysis [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(6): 597―617.
[8]  Dutfoy A, Lebrun R. Practical approach to dependence modeling using copulas [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2009, 223(4): 347―361.
[9]  吴帅兵, 李典庆, 周创兵. 二维联合分布函数构造方法及其对结构可靠度的影响分析[J]. 工程力学, 2012, 29(7): 69―74.
[10]  Wu Shuaibing, Li Dianqing, Zhou Chuangbing. Bivariate construction methods and its effect on structural reliability [J]. Engineering Mechanics, 2012, 29(7): 69―74. (in Chinese)
[11]  吴帅兵, 李典庆, 周创兵. 联合分布函数蒙特卡罗模 及结构可靠度分析[J]. 工程力学, 2012, 29(9): 68―74.
[12]  Wu Shuaibing, Li Dianqing, Zhou Chuangbing. Monte Carlo simulation of multivariate distribution and its application to structural reliability analysis [J]. Engineering Mechanics, 2012, 29(9): 68―74. (in Chinese)
[13]  李典庆, 吴帅兵, 周创兵, 方国光. 二维联合概率密度函数构造方法及结构并联系统可靠度分析[J]. 工程力学, 2013, 30(3): 37―45.
[14]  Li Dianqing, Wu Shuaibing, Zhou Chuangbing, Phoon Kok kwang. Bivariate distribution construction method and its application to structural parallel system reliability analysis [J]. Engineering Mechanics, 2013, 30(3): 37―45. (in Chinese)
[15]  吴帅兵, 李典庆, 周创兵. 结构可靠度分析中变量相关时三种变换方法的比较[J]. 工程力学, 2011, 28(5): 41―48.
[16]  Wu Shuaibing, Li Dianqing, Zhou Chuangbing. Comparison among three transformation methods for structural reliability analysis with correlated variables [J]. Engineering Mechanics, 2011, 28(5): 41―48. (in Chinese)
[17]  Lebrun R, Dutfoy A. A generalization of the Nataf transformation to distributions with elliptical copula [J]. Probabilistic Engineering Mechanics, 2009, 24(2): 172―178.
[18]  Lebrun R, Dutfoy A. An innovating analysis of the Nataf transformation from the copula viewpoint [J]. Probabilistic Engineering Mechanics, 2009, 24(3): 312―320.
[19]  Nelsen R B. An introduction to copulas [M]. New York: Springer, 2006: 214―216.
[20]  Cherubini U, Luciano E, Vecchiato W. Copula methods in finance [M]. Chichester: John Wiley Sons, 2004: 49―93.

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