基于Bootstrap法的小样本岩土参数标准值计算  

Calculating formula for standard value of small-sample geotechnical parameters based on Boot strap method

作　　者：罗强[1,2] 骆飞[1,2] 蒋良潍[1,2] 张文生[1,2] Luo Qiang Luo Fei J iang Liangwei Zhang Wensheng(School of Civil Engineering MOE Key Laboratory of High-speed Railway Engineering, Southwest Jiaotong University,Chengdu 610031, China)

机构地区：[1]西南交通大学土木工程学院,四川成都610031 [2]西南交通大学高速铁路线路工程教育部重点实验室,四川成都610031

出　　处：《华中科技大学学报（自然科学版）》2017年第8期93-98,共6页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家重点基础研究发展计划资助项目(2013CB036204)

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n<20时,Bootstrap法更能体现出减少标准值偏离真值误差的明显效果.For the problem that the estimated interval of mean value of geotechnical parameters using t-distribution method with limited samples varied in a wide range and the standard value of design parameters deviated highly from the true value,computer stochastic simulation was carried out to model the site-investigate sampling with known distribution type of geotechnical parameters.Based on the standard value space constructed from replicates with sufficient batches,the estimated interval available from nonparametric Bootstrap method and traditional t-distribution method was compared,and the change law of standard value of geotechnical parameters by Bootstrap method versus statistics and size of sample was discussed.The results show that Bootstrap method can make full use of empirical distribution contained in insufficient information,and thus to effectively narrow the mean confidence interval of geotechnical parameter under the same confidence level,which makes the standard value be closer to the true value thant-distribution method.The width of mean confidence interval for geotechnical parameters by Bootstrap method decreases with the increase of sample size,and the standard value shows a satisfied negative power functioning relationship with the sample size.A mean-based expression of standard value considering the effect of sample size and standard deviation was proposed.The advantage of Bootstrap method to reduce deviation between the standard value and the true is more obvious when the sample size is smaller than 20.

关 键 词：岩土参数 标准值 BOOTSTRAP法 小样本 区间估计 

分 类 号：TU192[建筑科学—建筑理论]