水文地质参数概率密度函数的Legendre正交多项式逼近研究

Approximation of the probability density function of hydrogeological parameters based on Legendre orthogonal polynomial

确定水文地质参数的概率密度函数往往需要事先假设其分布类型,并且在计算时对样本的各阶矩信息利用不够。针对这一问题,引入基于Legendre正交多项式最佳平方逼近的水文地质参数概率密度函数的确定方法。阐述了方法的原理和步骤,进行三种常用分布的数值试验和室内渗透实验数据的分析,并采用模糊区间信息量分布图分析概率密度函数可靠性的方法。研究结果表明该方法不需要进行概率密度函数类型的假设,并且可以充分利用样本矩信息,能有效地逼近概率密度函数,为水文地质参数的概率密度函数的确定提供了一种新的方法。

Since the probability density function of hydrogeological parameters is difficult to determine,the method of least square approximation based on Legendre orthogonal polynomials is introduced without assuming a distribution type. This article elaborates the principle and steps of the method,and numerical experiment of three kinds of commonly used distribution function and laboratory permeability test data analysis are conducted. The reliability analysis of probability density function is made with a fuzzy interval information distribution map. The results show that this method can effectively approximate the probability density function and make full use of sample moment information during calculating without assuming the type of probability density function. Furthermore,the application of the method can improve the reliability of the groundwater uncertainty analysis.