岩土力学参数概率分布的切比雪夫多项式推断

Assessment of probability distribution of mechanical parameters of rock & soil by using Chebyshev orthogonal polynomials

提出了较大样本岩土力学参数概率分布的切比雪夫多项式逼近法。基于数值逼近原理,直接根据试验样本矩,运用切比雪夫多项式推断岩土力学参数的概率密度函数,并用精度较高的K-S检验法,从理论上证明所求密度函数的正确性和实用性。该方法直接根据试验样本信息和统计方法推断,而不是事先假定成经典的理论概率分布,因此数学和物理意义更加充分。通过对各种经典分布曲线(正态分布、指数分布、对数正态分布等)数值检验,结果表明所得到的逼近表达式有很好的拟合性能。根据样本数据得出的某岩石抗压强度概率密度函数,与实际统计所得分布频率非常接近,可以满足岩土工程可靠性分析的要求。

Chebyshev orthogonal polynomial approximation （CPA） method is presented to define the probabilistic density functions of the rock ＆ soil mechanical parameters in this paper. Based on numerical approximation theory, Chebyshev polynomial is introduced to match the probabilistic density function of the rock ＆ soil random parameters from the larger sample data. Kolmogorov-Smirnov test is used to verify the availability of this method. Six classical distributions, the normal distribution,the exponential distribution, the log-normal distribution, the gamma distribution, the extreme Ⅰ distribution and the Weibull distribution, are compared with the corresponding CPA density functions generated from the moments. Little differences are found out between classical distribution and its corresponding CPA density function. The CPA density function of a rock uni-axial compressive strength is generated using the moments about the origin. The results of the case study show that the CPA density function is accurate and can be used in stochastic reliability analysis of rock and soil engineering.