线性组合背景值构造在GM(1,1)模型中的优越性分析

Advantage Analysis of Linear Combination Construction of Background Value in GM(1,1) Model

在假设原始数据为齐次指数序列的前提下,基于3种GM(1,1)模型缺陷分析理论,以灰微分方程和白化方程匹配为目标得出权值完全相同的线性组合背景值构造,指出原始数据为近似齐次指数序列时需要重新确定权值.仍以灰微分方程和白化方程匹配为目标得出新的权值求解方法.实例应用结果显示线性组合背景值构造形式预测精度最高.

To assume that the original data sequence is a homogenous exponential one,and based on the purpose of the matching of whitenization equation and grey differential equation in GM（1,1） model,linear combination construction of background value with same weights based on three defect analysis methods is obtained.It is indicated that the weights need to be reconsidered for the data sequences which satisfy to the homogenous exponential rule.Still for the same purpose,a new method to work out the weights is proposed.For a case study,measurement results show that with the linear combination construction of background value,the predicted precision of GM（1,1） model is the best.