测量不确定度信息约束下的最大熵分布研究  

Research on Maximum Entropy Distribution Under Measurement Uncertainty Constraints

作　　者：方兴华 宋明顺 鲁伟 

机构地区：[1]中国计量大学经济与管理学院,杭州310018

出　　处：《系统科学与数学》2017年第12期2337-2346,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(71071147);浙江省自然科学基金(LQ18G020005);浙江省标准化与知识产权管理人文社会科学重点研究基地(SIPM3207)资助课题

摘　　要：不确定度报告广泛存在于计量工作中,在不确定度报告的有效周期内,如何利用已有的不确定度信息为后续的测量不确定度评定服务是一个重要的问题.文章以被测量已有的不确定度信息为约束条件,提出了一种结合最大信息熵原理和Heaviside阶梯函数的最大熵分布确定方法,实现被测量分布的推导.同时给出遗传算法计算拉格朗日乘子.通过实例分析发现,当被测量为对称性分布时,基于不确定度信息的最大熵分布与理论分布拟合地较好,而当被测量为非对称性分布时,拟合存在一定的偏差.但在仅有测量不确定度信息的情况下,最大熵分布是对被测量真实分布较好的近似,因而可将此分布用于后续的不确定度评定.Measurement uncertainty reports are widely used in metrology. It is very important to utilize uncertainty information effectively which is within the term of validity to the future uncertainty measurement. It proposes a methodology which combining the principle of maximum entropy and the Heaviside step function to determine the distribution of measurand with the constraints of prior uncertainty information. The genetic algorithm is given to optimize the computation of Lagrange multiplier at the same time. It has been proven that the maximum entropy distribution based on the uncertainty information and the theoretical distribution are almost overlapped in the case of symmetric distribution, but there is a certain deviation between the two distributions for the situation of asymmetric distribution. However, the maximum entropy distribution is an appropriate approximation to the measurand true distribu- tion if only the prior measurement uncertainty information is known, and it can be useful when the measurand is participated in the further measurement uncertainty evaluation.

关 键 词：最大信息熵 Heaviside阶梯函数 测量不确定度 遗传算法 

分 类 号：O21[理学—概率论与数理统计]