唐小松, 李典庆, 周创兵, 方国光. 样本数目对岩土体参数联合分布模型识别精度的影响[J]. 工程力学, 2015, 32(2): 1-11. DOI: 10.6052/j.issn.1000-4750.2013.08.0740
引用本文: 唐小松, 李典庆, 周创兵, 方国光. 样本数目对岩土体参数联合分布模型识别精度的影响[J]. 工程力学, 2015, 32(2): 1-11. DOI: 10.6052/j.issn.1000-4750.2013.08.0740
TANG Xiao-song, LI Dian-qing, ZHOU Chuang-bing, PHOON Kok-kwang. EFFECT OF SAMPLE SIZE ON IDENTIFICATION OF A JOINT PROBABILITY DISTRIBUTION UNDERLYING CORRELATED GEOTECHNICAL PARAMETERS[J]. Engineering Mechanics, 2015, 32(2): 1-11. DOI: 10.6052/j.issn.1000-4750.2013.08.0740
Citation: TANG Xiao-song, LI Dian-qing, ZHOU Chuang-bing, PHOON Kok-kwang. EFFECT OF SAMPLE SIZE ON IDENTIFICATION OF A JOINT PROBABILITY DISTRIBUTION UNDERLYING CORRELATED GEOTECHNICAL PARAMETERS[J]. Engineering Mechanics, 2015, 32(2): 1-11. DOI: 10.6052/j.issn.1000-4750.2013.08.0740

样本数目对岩土体参数联合分布模型识别精度的影响

EFFECT OF SAMPLE SIZE ON IDENTIFICATION OF A JOINT PROBABILITY DISTRIBUTION UNDERLYING CORRELATED GEOTECHNICAL PARAMETERS

  • 摘要: 目前样本数目对岩土体参数联合概率分布模型识别精度的影响还缺少研究。该文提出了样本数目对岩土体参数联合分布模型识别精度的影响分析方法,给出了基于蒙特卡洛模拟的统计量AIC值变异性模拟步骤,定义了描述岩土体参数联合概率分布模型识别精度的正确识别概率,采用蒙特卡洛模拟方法分别研究了样本数目对岩土体参数最优边缘分布函数和最优Copula函数识别精度的影响规律。结果表明:基于有限岩土体参数数据估计的边缘分布函数和Copula函数的AIC值存在较大的变异性。岩土体参数样本数目对最优边缘分布函数和Copula函数的识别精度具有重要的影响,边缘分布函数和Copula函数的正确识别概率随样本数目的增加而增大。岩土体参数变异系数对最优边缘分布函数的识别精度影响相对较小,岩土体参数间相关系数对最优Copula函数的识别精度影响较大。此外,岩土体参数二维分布模型识别比一维边缘分布模型识别需要更多的数据。因此,为了提高岩土体参数联合概率分布模型的识别精度,建议尽可能多地收集岩土体参数试验数据。

     

    Abstract: This paper aims to study the effect of sample size on identification of a joint probability distribution which underlies multiple correlated geotechnical parameters. First, a method for constructing the joint probability density function (PDF) of correlated geotechnical parameters using copulas is introduced. Then, a Monte Carlo-based procedure is proposed to simulate the variation of the Akaike Information Criterion (AIC) values associated with the fitted margins and copulas. The identification accuracy is defined as the probability of correct identification of the true margins and copulas. Finally, the proposed Monte Carlo-based procedure is presented to demonstrate the effect of sample size on the identification accuracy. The results indicate that the AIC values associated with the fitted margins and copulas derived from the geotechnical parameters with a small sample size show large scatter. The sample size has a significant effect on the identification accuracy of the true margins and copulas underlying correlated geotechnical parameters. The probability of correct identification of the true margins and copulas increases with increasing sample size. The coefficient of variation (COV) of geotechnical parameters has a smaller influence on the identification accuracy of the true margins, whereas the correlation coefficient between geotechnical parameters has a larger influence on the identification accuracy of the true copulas. Generally, the correct identification of the true copulas is much more demanding in data than that of the true margins. It is recommended that as much data should be collected for geotechnical parameters as possible in order to obtain high accuracy in the identified margins and copulas.

     

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