岩土参数最优概率分布推断方法及判别准则的研究
Research on approximation method and discriminative criterion of the optimal probability distribution of geotechnical parameters
宫凤强 1黄天朗 2李夕兵1
作者信息
- 1. 中南大学资源与安全工程学院,湖南长沙410083;中南大学高等研究中心,湖南长沙410083
- 2. 中南大学资源与安全工程学院,湖南长沙410083
- 折叠
摘要
为了获得岩土参数概率分布的最佳推断方法,首先考虑岩土参数均为非负值的特性,提出以“3σ”准则为基础并考虑样本数据偏度进行调整的积分区间确定方法;以5组典型岩土参数作为基本信息,利用经典分布拟合法、最大熵法、一般多项式逼近法、正交多项式逼近法和正态信息扩散法分别对其概率分布函数进行了推断,并根据K-S检验法进行检验.通过所得概率分布的检验值、累积概率值和函数曲线的对比,研究上述方法的优劣.结果表明:与经典分布拟合法相比,其他4种方法的检验值普遍较小,均克服了经典分布无法反应样本随机波动性的缺陷,并且满足累积概率值等于1的要求.但最大熵法的检验值存在大于经典分布检验值的情况,一般多项式和正交多项式方法的概率密度函数则在样本数据局部分布区间存在负值情况.正态信息扩散法不存在上述缺陷,而且该方法得到的检验值最小,累积概率值始终为1,并可以随着样本的波动呈现多峰状态,拟合精度最高,是一种比较理想的最佳推断方法.最后给出了岩土参数最优概率分布的判别准则.
Abstract
In order to obtain the optimal probability distribution of geotechnical parameters,the non-negative characteristics of the parameter values was firstly considered and an integral distribution interval standard was determined,which was based on the "3σ" principle and adjusted according to the skewness of sample data.The probability distribution functions of five groups of typical geotechnical parameters were inferred by using the typical distribution fitting method(TDF method),the maximum entropy method(ME method),the general polynomial approximation method(GP method),the orthogonal polynomial approximation method(OP method) and the normal information diffusion method(NID method).The Kolmogorov-Smirov testing method was used to assess the availability of those methods above.The availability of the probability distribution functions obtained with five methods were compared according to the testing values,the cumulative probability and the fitting function curves.The results show that the test values of four methods are generally lower than that of TDF method.And those four methods can overcome the shortcomings of the distribution with a single peak,reflect the fluctuation of the actual data distribution and meet the conditions that the cumulative value of probability is equal to 1.However,the test value of ME method is sometimes larger than that of TDF method,and the value of PDF at local distribution interval of distribution data will be less than zero for GP and OP methods.In contrast,the test value of NID method is the lowest and the cumulative probability value is always 1,and the fitting accuracy is the highest among all those methods.Finally,the criterion for judging the optimal probability distribution of geotechnical parameters is given.
关键词
岩土力学/岩土参数/可靠度分析/概率分布/随机波动性/拟合方法/正态信息扩散法Key words
rock and soil mechanics/geotechnical parameters/reliability analysis/probability distribution function/stochastic volatility/fitting method/normal information diffusion method引用本文复制引用
基金项目
国家自然科学基金(41102170)
中央高校基本科研业务费专项资金项目(2011QNZT090)
出版年
2016
NETL
NSTL
维普
万方数据