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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“3?”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。
In order to get the best method to infer the probability distribution of geotechnical parameters, the method of determining the integral interval based on “3? ” Criterion and adjusting the sample data skewness is first considered considering the characteristics that geotechnical parameters are all non-negative. Based on the five sets of typical geotechnical parameters as the basic information, the probability distribution function was inferred by classical distribution fitting method, maximum entropy method, general polynomial approximation method, orthogonal polynomial approximation method and normal information diffusion method. KS test to test. Through the comparison of the test value, the cumulative probability value and the function curve of the obtained probability distribution, the advantages and disadvantages of the above methods are studied. The results show that compared with the classical distribution fitting method, the other four methods are generally lower in test value, which overcome the shortcoming of stochastic volatility that the classical distribution can not react, and satisfy the requirement that the cumulative probability is equal to one. However, the test value of the maximum entropy method is larger than the test value of the classical distribution. The probability density function of the general polynomial and the orthogonal polynomial method has a negative value in the local distribution of the sample data. The normal information diffusion method does not have the above defects, and the test results obtained by this method is the smallest, the cumulative probability is always 1, and it can be a multi-peak state with the sample fluctuation and the fitting precision is the highest Good reasoning method. Finally, the criterion for determining the optimal probability distribution of geotechnical parameters is given.