无偏灰色GM(1,1)模型的直接建模法

A Direct Modeling Method of the Unbiased GM(1,1)

针对灰色GM(1,1)模型的建模方法存在偏差,模型不满足协调性条件,不具有线性变换一致性,且通过累加生成建模时,原始序列第一点信息没有起作用等问题,提出了GM(1,1)的3种无偏灰微分方程形式,给出了无偏GM(1,1)的直接建模法,证明了新方法不仅具有白指数律重合性,而且具有线性变换一致性。实例分析表明,新方法提高了建模的精度,扩大了模型的适用范围,充分利用了原始序列的第一点信息。

There are some problems in GM( 1,1) modeling, such as, modeling method biased, compatibility condition not satisfied , linear transformation inconsistent and the first number of the initial sequence not functioning in modeling after an accumulated generating operation. In this paper, three grey differential equations are presented and a direct modeling method of the unbiased CM (1,1) is proposed.It is proved that the new method possesses not only white exponential law coincidence property but also linear transformation consistency. The analysis of practical examples show that it improves the modeling precision, enlarges the application scope of the model and makes full use of the first number of the initial sequence.