基于Latin方抽样和修正的Latin方抽样的可靠性灵敏度估计及其方差分析
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摘要
运用Latin方抽样(Latin hypercube sampling)方法和经统计相关减小方程修正后的Latin方抽样(updated Latin hypercube sampling)方法对结构进行可靠性灵敏度估计及其方差分析。单模式和多模式的数值及工程算例说明,可靠性灵敏度分析的Latin方抽样和修正的Latin方抽样在样本容量较小时都可以得到比Monte Carlo抽样方法更稳定的估计结果。采用Latin方抽样可以得到可靠性灵敏度的无偏估计,而修正的Latin方抽样方法在样本容量较小的情况下得到的可靠性灵敏度估计值的方差的分散性较Latin方抽样有进一步的减小。Latin方抽样和修正的Latin方抽样方法对基本变量的分布形式和相关性等均无限定,是适用于结构可靠性灵敏度分析的一种有效而实用的小样本抽样方法。
Latin hypercube sampling (LHS) and updated Latin hypercube sampling (ULHS) by statistical correlation reducing equation are employed to analyze structural reliability sensitivity and its variance. Numerical and engineering examples with single failure mode and with multiple failure modes are used to demonstrate the advantage of the LHS and ULHS based reliability sensitivity methods. The results of the illustrations show that the reliability sensitivity estimates based on the LHS and the ULHS are more robust than that on the Monte Carlo simulation in case of small sampling size. The unbiased estimate of the reliability sensitivity can be obtained by use of LHS. The variance of the sensitivity estimation based on ULHS can be reduced more than that based on LHS in small sampling size. The LHS and ULHS based structural reliability sensitivity method are independent of the distribution form and correlative characteristics of the basic random variable,thus they are effective and practicable for reliability sensitivity in small sampling size.
Latin hypercube sampling (LHS) and updated Latin hypercube sampling (ULHS) by statistical correlation reducing equation are employed to analyze structural reliability sensitivity and its variance. Numerical and engineering examples with single failure mode and with multiple failure modes are used to demonstrate the advantage of the LHS and ULHS based reliability sensitivity methods. The results of the illustrations show that the reliability sensitivity estimates based on the LHS and the ULHS are more robust than that on the Monte Carlo simulation in case of small sampling size. The unbiased estimate of the reliability sensitivity can be obtained by use of LHS. The variance of the sensitivity estimation based on ULHS can be reduced more than that based on LHS in small sampling size. The LHS and ULHS based structural reliability sensitivity method are independent of the distribution form and correlative characteristics of the basic random variable,thus they are effective and practicable for reliability sensitivity in small sampling size.
引文
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[2]Helton J C,Davis FJ.Latin hypercube sampling andthe propagation of uncertaintyin analysis of complex systems[J].Reliability Engineering and SystemSafety,2003,81:23-69.
[3]张令心,江近仁.Latin超立方采样技术及其在结构可靠性分析中的应用[J].世界地震工程.1997,13(4):1-6.ZHANGLingXin,JIANGJinRen.Latin hypercube sampling and its ap-plication tostructural reliability analysis[J].WorldInformation on Earth-quake Engineering,1997,13(4):1-6(In Chinese).
[4]Olsson A,Sandberg G.,DahlblomO.On Latin hypercube samplingfor structural reliability analysis[J].Structural Safety,2003,25:47-68.
[5]Ales Florian.An efficient sampling scheme:Updated Latin hypercube sampling[J].Probabilistic Engineering Mechanics,1992,7:123-30.
[6]Wu Y-T,Sitakanta Monhanty.Variable screeningandranking usingsam-pling-based sensitivity measures[J].Reliability Engineering and System Safety,2006,91(6):634-647.
[7]Ding Keqin,Zhou Zegong,Liu Chuntu.Latin hypercube sampling used inthe calculation of the fracture probability[J].Relaibility Engineering and SystemSafety,1998,59:239-242.
[8]Iman RL,Conover WJ.Small sample sensitivity analysis techniques to risk assessment[J].Commun.Statist.,1980,A9:1749-1842.
[9]Huntington D E,Lyrintzis C S.Improvements to andlimitations of Latin hypercube sampling[J].Prob.Engng.Mech,1998,13(4):245-253.
[10]宋笔锋.结构体系失效概率计算方法研究[D].西安:西北工业大学,1994:75-78.SONG BiFeng.Study of probability calculating method for systemstruc-ture[D].Xi′an:Northwestern Polytechnical University,1994:75-78(In Chinese).
[2]Helton J C,Davis FJ.Latin hypercube sampling andthe propagation of uncertaintyin analysis of complex systems[J].Reliability Engineering and SystemSafety,2003,81:23-69.
[3]张令心,江近仁.Latin超立方采样技术及其在结构可靠性分析中的应用[J].世界地震工程.1997,13(4):1-6.ZHANGLingXin,JIANGJinRen.Latin hypercube sampling and its ap-plication tostructural reliability analysis[J].WorldInformation on Earth-quake Engineering,1997,13(4):1-6(In Chinese).
[4]Olsson A,Sandberg G.,DahlblomO.On Latin hypercube samplingfor structural reliability analysis[J].Structural Safety,2003,25:47-68.
[5]Ales Florian.An efficient sampling scheme:Updated Latin hypercube sampling[J].Probabilistic Engineering Mechanics,1992,7:123-30.
[6]Wu Y-T,Sitakanta Monhanty.Variable screeningandranking usingsam-pling-based sensitivity measures[J].Reliability Engineering and System Safety,2006,91(6):634-647.
[7]Ding Keqin,Zhou Zegong,Liu Chuntu.Latin hypercube sampling used inthe calculation of the fracture probability[J].Relaibility Engineering and SystemSafety,1998,59:239-242.
[8]Iman RL,Conover WJ.Small sample sensitivity analysis techniques to risk assessment[J].Commun.Statist.,1980,A9:1749-1842.
[9]Huntington D E,Lyrintzis C S.Improvements to andlimitations of Latin hypercube sampling[J].Prob.Engng.Mech,1998,13(4):245-253.
[10]宋笔锋.结构体系失效概率计算方法研究[D].西安:西北工业大学,1994:75-78.SONG BiFeng.Study of probability calculating method for systemstruc-ture[D].Xi′an:Northwestern Polytechnical University,1994:75-78(In Chinese).
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