小样本岩土参数概率分布的正交多项式推断方法

发布时间：2018-06-25 08:28

本文选题：小样本 + 岩土参数　；参考：《工程力学》2017年08期

【摘要】：实际工程中的岩土参数往往是小样本情况,利用经典概率分布(如正态分布、对数正态分布、贝塔分布、威布尔分布等)推断其最优概率类型时,存在样本分布区间不匹配、限定范围选择和单峰值概率分布函数无法反映参数随机波动性等三个未解决的基本问题。为此,选取了五种不同取值区间,利用10组小样本岩土参数的实测样本,以勒让德多项式和第二类切比雪夫多项式对岩土参数的概率分布函数进行推断,利用K-S检验法对所得的概率分布函数进行检验。通过区间取值匹配、拟合检验值和累积概率值的比较,提出了以3?原则为基础,同时考虑偏度进行调整的积分区间确定标准。研究结果表明:以有限比较法原理确定最优概率分布的阶数,所得最优概率分布能够反映小样本数据的随机波动;而且正交多项式推断方法所得概率分布函数的检验值均小于传统分布的检验值,说明所得分布更加符合岩土参数的实际情况。
[Abstract]:The geotechnical parameters in practical engineering are usually small samples. When the classical probability distribution (such as normal distribution, logarithmic normal distribution, Beta distribution, Weibull distribution, etc.) is used to infer the optimal probability type, the sample distribution interval does not match. The limited range selection and the single peak probability distribution function can not reflect the random volatility of parameters. For this reason, five different value ranges are selected, and the probability distribution function of geotechnical parameters is inferred by using Legendre polynomial and Chebyshev polynomial of the second kind, using 10 groups of measured samples of small sample geotechnical parameters. The probability distribution function was tested by K-S test method. By matching the interval values, fitting the test values and comparing the cumulative probabilistic values, the paper puts forward the method of 3? On the basis of the principle, the criterion of determining the integral interval is taken into account. The results show that the order of the optimal probability distribution is determined by the finite comparison method, and the optimal probability distribution can reflect the random fluctuation of the small sample data. Moreover, the test value of probability distribution function obtained by orthogonal polynomial inference is smaller than that of traditional distribution, which shows that the distribution is more in line with the actual conditions of geotechnical parameters.
【作者单位】：中南大学资源与安全工程学院;中南大学高等研究中心;浙江大学滨海和城市岩土工程研究中心;
【基金】：国家自然科学基金项目(41102170) 中央高校基本科研业务费专项资金项目(2011QNZT090)
【分类号】：TU43

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