非等间距新息GM(1,1)的逐步优化模型及其应用

Non-equidistant step by step optimum new information GM(1,1) and its application

应用灰色系统建模方法及新信息原理,在GM(1,1)建模思想的基础上提出了一种基于直接建模的逐步优化的新息非等间距GM(1,1)模型,该模型采用原始数据的第n个分量作为灰色微分方程的初始条件,通过优化背景值与差商调节系数来估计模型参数.该模型不仅适合于等间距建模,也适合于非等间距建模,且突破了发展系数的绝对值较大时,不能用GM(1,1)模型的禁区,提高了建模的精度.实例表明所建模型的实用性与可靠性.

Applying modeling method of grey system and new information principle, in the basis of the grey modeling thought, non-equidistant step by step optimum new information GM（1,1） model was put forward, which was directly modeled according to original data, whose parameters were estimated by optimizing derivative＇s adjusting coefficients whiting values ＆ background values coefficient and the nth component was taken as the initialization. The model breaks the restricted zone of using GM（1,1） when the absolute value of the development coefficient is quite big, which can be used in non-equal interval ＆ equal intervM time series and improve the modeling precision. Examples validate the practicability and reliability of the proposed model.