信息熵在曲线拟合辨识中的应用

在对测量数据进行曲线拟合辨识时,常用的误差指标,如均方根误差和误差平方和,没有考虑样本数据的概率统计特性.基于信息熵原理介绍了一种新的曲线拟合辨识方法.将曲线拟合过程看作加性信道,建立了曲线拟合模型.首先将样本数据进行多种曲线拟合,采用最大熵方法根据样本值估计出自变量的概率密度函数和信息熵;再根据拟合曲线计算拟合结果熵和误差熵,最后计算出拟合模型的互信息,选取互信息最大的曲线作为样本的最佳拟合曲线,并给出了应用实例.由于该方法充分考虑了样本数据的概率统计规律,因此能提高测量精度,具有更大的适用范围,对于测量信息论的研究有一定的参考价值.

Application of information entropy in curve fitting recognition

In the recognition of curve fitting for measurement data, common error indexes, such as RMS error and error square sum, don＇t consider sample＇s probability statistics properties. A curve fitting recognition method was introduced based on information entropy. A curve fitting model was established through taking a curve fitting course as an additive channel. First, variety curves were selected to fit sample. The Maximum Entropy Method was used to estimate the independent variable＇s probability density function and information entropy according to sample. Then, the fitting result entropy and the error entropy were calculated according to fitting curve. Finally, the fitting model＇s mutual information was calculated. The curve with maximum mutual information was selected as sample＇s optimal fitting curve. An application example was provided in the end. Since the method fully considers sample＇s probability statistics properties, the method can improve measurement＇s precision, has more extensive adaptability and some reference value to research on measurement information theory.