测量数据的信息熵与测量误差熵研究

以Shannon信息论为基础,详细分析了测量过程的物理机制和被测量与测量结果的映射关系,建立被测量、测量误差和测量结果的信息论数学模型。研究了用信息集合和信息熵模型表征测量数据不确定度、被测量值和测量结果的方法,以及被测量信息熵、测量误差熵和测量结果信息熵的内涵、相互关系和求解方法。并推导了典型分布下传统的不确定度理论中的不确定度、置信系数与测量信息论中信息熵的数学关系,为从传统不确定度理论到测量信息论的数据处理方法过渡做了一些前期预研。

Information Entropy and Error Entropy of Measurement Data

The paper introduces the model of the measured quantity, error and measuring data on the base of Shannon information theory after analysing the physical mean of the measurement and the relationship between the measured quantity and the measuring results. The measuring uncertainty, the measured quantity and the measuring results are presented by the model of the information entropy. The measuring information entropy and the error entropy are defined and their relationship is gived. And the mathematic relation of the information entropy and uncertainty of same special distributions is deduced.