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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。
Small sample size The identification of the best joint probability distribution model for rock and soil parameters is a challenging issue. Based on Bootstrap, the optimal edge distribution function of rock mass parameters and the optimal Copula function identification method are proposed. The Copula method for constructing the joint probability distribution function of rock and soil parameters is briefly introduced. The AIC criterion is used to identify the optimal edge distribution function and Copula function. The recognition results are expressed as a set of weight coefficients with different edge distribution functions and Copula functions as the optimal edge distribution and the optimal Copula. The validity of the proposed method is illustrated with the experimental data of pile-load-displacement hyperbolic parameters. The results show that the sample mean, standard deviation and correlation coefficient estimated from the test data of rock and soil parameters based on small sample size have large discrepancy, which further leads to the large variability of the AIC value of the statistics. The proposed Bootstrap-based optimal edge distribution function and the optimal Copula function identification method can not only effectively consider the variability of the AIC values of the statistics, but also comprehensively reflect the optimal edge distributions and copula functions for different candidate edge distribution functions and Copula functions The probability of the optimal Copula function provides an effective way for the identification of the optimal edge distribution function and the optimal Copula function of rock mass parameters with small sample size.