基于Bootstrap方法的岩土体参数联合分布模型识别

小样本容量岩土体参数最优联合概率分布模型的识别是一个富有挑战性的问题。基于Bootstrap提出了小样本容量岩土体参数最优边缘分布函数和最优Copula函数识别方法。简要介绍了岩土体参数联合概率分布函数构造的Copula方法,采用AIC准则识别最优的边缘分布函数和Copula函数。将识别结果表示为不同备选边缘分布函数和Copula函数为最优边缘分布和最优Copula的权重系数集合,以基桩荷载-位移双曲线参数试验数据为例证明了所提方法的有效性。结果表明:基于小样本容量岩土体参数试验数据估计的样本均值、标准差和相关系数具有较大的离散性,这种离散性进一步导致了统计量AIC值存在较大变异性。提出的基于Bootstrap的最优边缘分布函数和最优Copula函数识别方法不仅可以有效地考虑统计量AIC值的变异性,而且能够综合地反映不同备选边缘分布函数和Copula函数为最优边缘分布和最优Copula函数的概率,为小样本容量岩土体参数最优边缘分布函数和最优Copula函数的识别提供了一条有效的途径。

Bootstrap method for joint probability distribution identification of correlated geotechnical parameters

Identification of the best-fit joint probability distribution for a small set of samples is a challenging problem. Based on the Bootstrap method, an optimum marginal distribution function and an optimum Copula function for identifying the geotechnical parameters with a small sample size are proposed. The Copula method for constructing the joint probability distribution function (PDF) for correlated geotechnical parameters is briefly introduced, and then the Akaike Information Criterion (AIC) is adopted to identify the optimum marginal distribution function and Copula function. The identification results are represented by a collection of the weight factors such that each candidate marginal distribution function and copula function become the optimum (best-fit). Four measured datasets of the hyperbolic load-settlement curve-fitting parameters of piles are used to demonstrate the validity of the proposed method. The results indicate that the sample mean, sample standard deviation and sample correlation coefficient derived from the geotechnical parameters with a small sample size are relatively scattering, leading to a higher variation in the AIC values associated with the fitted marginal distributions and Copulas. The proposed bootstrap method can effectively consider the variation of the AIC values of the fitted marginal distributions function and Copulas function. It can also account for the possibilities that each candidate marginal distribution function and Copula function become the optimum. The bootstrap method provides a general and practical tool for identifying the best-fit marginal distribution function and Copula function with a small sample size.