岩石力学参数概率分布的信息熵推断

基于信息论的最大熵原理，直接用牛顿迭代法，由样本矩来推断岩石力学参数的概率密度函数，并且用精度较高的K-S检验法，从理论上证明所求的密度函数的正确性。算例表明，该方法避免了复杂的数值计算，可以满足岩石工程随机可靠性分析的要求。直接根据试验样本信息和统计方法推断，而不是先假定成经典的理论概率分布，具有更充分的数学和物理意义。由于概率分布采用指数形式而不是幂函数系多项式，避免了计算中的震荡等不稳定现象。

PROBABILITY DISTRIBUTION OF ROCK MECHANICS PARAMETERS BY USING MAXIMUM ENTROPY METHOD

Maximum entropy (ME) method is used to generate probability density functions of rock mechanics parameters from sample data. The Lagrangian function is introduced to infer the analytical form of the ME density function. The Newton iteration method is combined with Kolmogorov-Smirnov test in order to determine the parameters of the ME density function and assess the availability of ME density function. A few examples are used to illustrate the applicability of proposed method. Two classical distributions,the normal distribution and the exponential distribution,are compared with the corresponding ME density functions generated from the moments. Little differences are found out between classical distribution and its corresponding ME density function. The ME density function of a rock uniaxial compressive strength is generated using the moments about the origin. Kolmogorov-Smirnov test is used to verify the ME function. The results of the case study show that the ME function is accurate enough and can be used in stochastic reliability analysis of rock engineering.