重力坝多失效模式相关层间抗滑稳定体系的可靠性分析
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摘要
提出了基于Copula函数的重力坝多失效模式相关体系的可靠性分析方法。运用多元Copula函数建立了重力坝层间抗滑稳定相关体系的联合分布模型,从理论上推导了基于Copula函数求解体系相关可靠度的计算式;然后采用非参数估计方法确定了相应Copula函数中的待定参数。通过算例,验证了基于Copula函数的相关性可靠度分析模型的合理性,接着对某重力坝多失效模式相关的层间抗滑稳定体系进行了可靠性分析,并与传统方法的计算结果进行了对比。算例结果表明,Clayton Copula函数可以作为表征重力坝串联体系可靠性中失效模式间相关结构的最优Copula函数,基于Copula函数的相关性可靠度模型计算结果克服了基于独立性假设的一阶、二阶区间估计等方法的局限性,且仍在Ditlevsen二阶界限区间估计值的范围内,能够满足工程问题的精度要求。
System reliability analysis method for multiple failure patterns of gravity dam is put forward based on the Copula function.The joint distribution model is established using Copula function of stability between layers of gravity dam,and the computational formula of this system reliability analysis method is deduced theoretically.Then,the parameters in the Copula are determined using the parameter estimation method.The reasonableness of the reliability analysis model is verified through a case study,and then the related sliding stability system reliability between layers is analyzed and also compared with the calculation results of the traditional method.The results show that Clayton Copula function can be characterized as a series of gravity dam system reliability failure mode of the correlation between the optimal structure Copula function,based on the correlation of Copula function reliability model calculation results overcome the limitations of the first and second order interval estimation methods based on the assumption of the independence, and it can satisfy the precision requirement of engineering problems because the result is still in the range of estimate value of the Ditlevsen method.
System reliability analysis method for multiple failure patterns of gravity dam is put forward based on the Copula function.The joint distribution model is established using Copula function of stability between layers of gravity dam,and the computational formula of this system reliability analysis method is deduced theoretically.Then,the parameters in the Copula are determined using the parameter estimation method.The reasonableness of the reliability analysis model is verified through a case study,and then the related sliding stability system reliability between layers is analyzed and also compared with the calculation results of the traditional method.The results show that Clayton Copula function can be characterized as a series of gravity dam system reliability failure mode of the correlation between the optimal structure Copula function,based on the correlation of Copula function reliability model calculation results overcome the limitations of the first and second order interval estimation methods based on the assumption of the independence, and it can satisfy the precision requirement of engineering problems because the result is still in the range of estimate value of the Ditlevsen method.
引文
[1]唐家银,何平,宋东利.基于Copula函数的失效相关构件可靠度计算[J].机械强度,2010,32(5):740-744.
[2]陈进,黄薇.重力坝系统可靠度研究方法探讨[J].长江科学院院报,1997,14(1):21-24.
[3]唐小松,李典庆,周创兵,等.基于Copula函数的基桩荷载-位移双曲线概率分析[J].岩土力学,2012,33 (1):171-178.
[4]Cornell.Bounds on the reliability of structural systems[J].J.Struct.Div.,ASCE,1967,93(STI):171-200.
[5]Ditlevsen O.Narrow reliability bounds for structural system[J].J.Struct.Meth.,1979,7(4):453-472.
[6 J Rackwitz R,Flessler B.Structural reliability under combined random load sequence[J].Computers & Structures, 1979,9(5):489-494.
[7]Ma H-F,Ang A H-S.Reliability Analysis of Redundant Ductile Structural Systems[M].Urbana Champain, University of Illinois,1981.
[8]李刚,程耿东.灾害荷载下结构体系失效模式的相关性及可靠度计算[J].工程力学,2001,18(3):1-9.
[9]喻天翔,宋笔锋,万方义,等.机械零件多失效模式相关可靠度算法研究[J].机械强度,2006,28(4): 508-511.
[10]李典庆,周创兵.考虑多失效模式相关的岩质边坡体系可靠度分析[J].岩石力学与工程学报,2009,28 (3):541-551.
[11]江胜华,侯建国,何英明.基于加权响应面法的重力坝深层抗滑稳定体系可靠度分析[J].水利学报,2011,42 (3):337-343.
[12]Nelson R B.An Introduction to Copulas[M].Springer:New York,2006.
[13]范书立,陈健云,范武强,等.地震作用下碾压混凝土重力坝的可靠度分析[J].岩石力学与工程学报, 2008,27(3):564-571.
[14]Nelsen N B.An Introduction to Copulas.Lectures Notes in Statistics[M].NewYork:Spring Verlag,1999.
[15]Embrechts P,Mcneil A J,Straumann D.Correlation and Dependence in Risk Management:Properties and Pitfalls [M].Dempster M.Risk Management:Value at Risk and Beyond,Cambridge University Press,1999:176-223.
[16]Akaike H.A new look at the statistical model identification[J].IEEE Transactions on Automatic Control,1974, 19(6):716-723.
[17]李云贵,赵国藩.结构体系可靠度的近似计算方法[J].土木工程学报,1993,26(5):70-76.
[18]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.
[19]傅旭东,邓建刚.土性参数随机场的模拟和随机场的离散[J].工业建筑,2002,32(1):32-36.
[2]陈进,黄薇.重力坝系统可靠度研究方法探讨[J].长江科学院院报,1997,14(1):21-24.
[3]唐小松,李典庆,周创兵,等.基于Copula函数的基桩荷载-位移双曲线概率分析[J].岩土力学,2012,33 (1):171-178.
[4]Cornell.Bounds on the reliability of structural systems[J].J.Struct.Div.,ASCE,1967,93(STI):171-200.
[5]Ditlevsen O.Narrow reliability bounds for structural system[J].J.Struct.Meth.,1979,7(4):453-472.
[6 J Rackwitz R,Flessler B.Structural reliability under combined random load sequence[J].Computers & Structures, 1979,9(5):489-494.
[7]Ma H-F,Ang A H-S.Reliability Analysis of Redundant Ductile Structural Systems[M].Urbana Champain, University of Illinois,1981.
[8]李刚,程耿东.灾害荷载下结构体系失效模式的相关性及可靠度计算[J].工程力学,2001,18(3):1-9.
[9]喻天翔,宋笔锋,万方义,等.机械零件多失效模式相关可靠度算法研究[J].机械强度,2006,28(4): 508-511.
[10]李典庆,周创兵.考虑多失效模式相关的岩质边坡体系可靠度分析[J].岩石力学与工程学报,2009,28 (3):541-551.
[11]江胜华,侯建国,何英明.基于加权响应面法的重力坝深层抗滑稳定体系可靠度分析[J].水利学报,2011,42 (3):337-343.
[12]Nelson R B.An Introduction to Copulas[M].Springer:New York,2006.
[13]范书立,陈健云,范武强,等.地震作用下碾压混凝土重力坝的可靠度分析[J].岩石力学与工程学报, 2008,27(3):564-571.
[14]Nelsen N B.An Introduction to Copulas.Lectures Notes in Statistics[M].NewYork:Spring Verlag,1999.
[15]Embrechts P,Mcneil A J,Straumann D.Correlation and Dependence in Risk Management:Properties and Pitfalls [M].Dempster M.Risk Management:Value at Risk and Beyond,Cambridge University Press,1999:176-223.
[16]Akaike H.A new look at the statistical model identification[J].IEEE Transactions on Automatic Control,1974, 19(6):716-723.
[17]李云贵,赵国藩.结构体系可靠度的近似计算方法[J].土木工程学报,1993,26(5):70-76.
[18]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.
[19]傅旭东,邓建刚.土性参数随机场的模拟和随机场的离散[J].工业建筑,2002,32(1):32-36.
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