概率信息不完全系统的统计矩估计方法

POINT ESIMATE FOR STATISTICAL MOMENTS OF SYSTEMS WITH INCOMPLETE PROBABILITY INFORMATION

根据已知变量概率信息的不同,概率信息不完全系统可分为子类I、子类II和子类III。现有的统计矩点估计法可以方便地用于概率信息完全系统和概率信息不完全系统子类I,但是对可能出现的概率信息不完全系统子类II和子类III无能为力。为此,该文在重点研究子类III的等效相关系数求解方法的同时给出了子类II等效相关系数的简化方法,并发展了适用于一般概率信息不完全系统的广义Nataf变换;在此基础上,结合多变量函数的单变量降维近似模型,提出了概率信息不完全系统的统计矩估计方法,并讨论了参考点选择、变量排序等对计算效率的影响;最后,通过算例对建议方法进行了系统的验证。算例结果表明:该文建议的等效相关系数求解方法准确有效、变量排序策略切实可行,统计矩估计法具有广泛适用性且对于低阶矩具有较理想的精度。

According to the known probability information, random system with incomplete probability information can be classified into three classes, namely sub-class Ⅰ, sub-class Ⅱ and sub-class Ⅲ. The existing point estimate methods （PEM） for statistical moments are only suitable for systems with complete information and sub-class Ⅰ, but not for sub-class Ⅱ and sub-class Ⅲ. In this paper, equivalent correlation coefficients （ECC） of variables in the sub-class Ⅲ are studied, together with the simplified approach for the ECCs of variables in sub-class Ⅱ. By combining with the univariate dimension reduction model of a multivariable function, the point estimate for moments of system with incomplete information is proposed. The influence of both the reference point and the order of variables on the efficiency of this PEM are discussed in details. Finally, several examples are illustrated to verify the proposed PEM. The results show that 1） the approaches for the ECCs are of high precision, 2） the technology for reordering the variables is effective for improving the efficiency of the PEM, and 3） the proposed PEM are suitable for all systems with incomplete information and accurate for the first lower moments of system.