灰色系统建模数据的一种变换方法

Method of the Original Data Transformation for Grey Systems Modeling

灰色模型的数据处理方法通常是累加生成、累减还原，由此建立起来的灰色模型，其精度往往因较差而不能满足实际要求为此，许多科技工作者从理论和应用上进行了广泛深入的研究研究成果表明，原始数据的模式及其光滑特性是影响灰色模型精度的两个主要因素，于是形成两种提高灰色模型精度的方法：对传统的ＧＭ模型修正，使之适应原始数据的模式；对原始数据进行变换，改善其光滑特性，并由此得到了一些变形的灰色模型和原始数据的变换函数在此基础上，笔者提出一种能同时兼顾原始数据的模式及其光滑特性的灰色模型原始数据变换方法———辅助曲线变换法该方法以灰色模型残差序列的标准差最小为目标，通过约束变换后数据序列的光滑特性、模型还原后的误差，建立了寻找最优辅助曲线的一般优化模型实例表明，这种方法不会改变原始数据的特征，能适应不同模式的原始数据。

Because the precision of Gray Method by means of Accumulated Generating Operation and Inverse Accumulated Generating Operation usually can not meet the requirement of actual forecasting, many researches on theory and application have been done. The results show that the pattern and smoothness of original data are the two main factors, which leads to two ways of improving model precision,the remedying model and the original discrete series. In this paper, a new way to transform the original discrete by constructing auxiliary curve is presented, which gives a general optimum method by containing the smoothness and model error to seek the best curve which minimizes the model's variance of residual error series. Practical examples show that under the circumstances of keeping the characteristic of original discrete series, the method can improve the precision of Gray Model and have a wide adaptability.