基于Bootstrap法的小样本岩土参数标准值计算

发布时间：2018-02-09 06:31

本文关键词： 岩土参数标准值 Bootstrap法小样本区间估计　出处：《华中科技大学学报(自然科学版)》2017年08期 　论文类型：期刊论文

【摘要】：针对小样本条件下岩土参数均值的t分布估计区间较宽、所得工程设计参数标准值偏离真值较大的问题,进行了岩土参数总体分布明确条件下的小样本勘察取样计算机随机模拟,利用充足批次重复抽样构建标准值空间,对比了非参数Bootstrap法与传统t分布法的区间估计差异,讨论了Bootstrap法岩土参数标准值随样本统计量及容量的变化规律.研究表明:同一置信水平下,Bootstrap法能充分利用小样本经验分布信息,有效收窄岩土参数的均值估计区间,所得标准值较t分布法更接近于真值;Bootstrap法的岩土参数均值置信区间宽度随样本容量增大而逐渐减小,其标准值与样本容量呈现良好的负幂函数关系,据此提出了以样本平均值为基准、样本容量和标准差为影响参数的标准值计算式;当样本容量n20时,Bootstrap法更能体现出减少标准值偏离真值误差的明显效果.
[Abstract]:In view of the problem that the estimation interval of t distribution of the mean value of geotechnical parameters is wide under the condition of small sample, the standard values of engineering design parameters deviate greatly from the true values. The computer random simulation of small sample survey sampling under the condition of definite total distribution of geotechnical parameters is carried out. The standard value space is constructed by sufficient batch repeated sampling, and the difference of interval estimation between the nonparametric Bootstrap method and the traditional t distribution method is compared. The variation of standard values of geotechnical parameters with sample statistics and capacity by Bootstrap method is discussed. The results show that the bootstrap method can make full use of the empirical distribution information of small samples and effectively narrow the mean estimation interval of geotechnical parameters at the same confidence level. The obtained standard value is closer to the true value than the t-distribution method. The width of the confidence interval of the mean value of the geotechnical parameters decreases with the increase of the sample size, and the standard value and the sample size show a good negative power function relationship. Based on this, a standard value calculation formula with sample average value as reference and sample size and standard deviation as influence parameters is put forward, and the bootstrap method can better reflect the obvious effect of reducing the deviation error of standard value when the sample size is n20.
【作者单位】：西南交通大学土木工程学院;西南交通大学高速铁路线路工程教育部重点实验室;
【基金】：国家重点基础研究发展计划资助项目(2013CB036204)
【分类号】：TU43

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