最大熵原理在测量数据处理中的应用

Measurement data processing based on maximum entropy method

针对测量数据处理中掺杂主观因素且不能准确反映客观事实的问题,采用最大熵方法,根据已有的测量数据求取被测量的概率分布,进而对此概率分布在不同矩约束条件下进行估计和评价。测量数据源自计算机产生的呈标准正态分布的测量数据样本,计算测量结果用MATLAB编程做出仿真图形,仿真结果与计算结果表明:采用最大熵方法所确定的概率分布是含有最少主观假定的分布,并随着矩约束的增加,取得的被测量的概率分布更加接近真实分布,用所测定的测量结果进行估计以及用测量不确定度进行评价,可知计算结果是可靠的。

In the analysis of measurement data with adulterated subjective factor, it is difficult to accurately reflect objective measurement result. To solve this problem, the maximum entropy method（MEM）is used to determine the probability distribuion of the given measurement data, and the probability distribution is estimated and evaluated under different moment constraints. The measurement data came from the measurement sample data with standard normal distribution. The result is validated by the MATLAB software. Simulation and calculation results prove that the probability distribution determined by the MEM is the reasonable distribution with least subjective assumption, and the probability distribution obtained would be closer to the real distribution as the moment constrains are increased, and the evaluation of measurement result and its uncertainty features high precision,which means the calculation results are reliable.