灰色模型背景值优化的一种新方法

A New Method for Optimizing Background Value of Grey Model

文章通过将背景值改造为原始序列连续化后的原函数形式,从而使灰色微分方程与白化微分方程更加匹配,然后基于白化微分方程的解y(t)不再是原始序列的一次累加函数这一基本事实,因此不再使用传统的累减还原方法,而是将y(t)直接求导获得模拟预测公式,经过严格理论证明了本文模型具有白化指数重合性、系数重合性以及平移常数重合性,从而较原始NGM(1,1,K)模型而言,该模型具有对高低增长指数序列都能适用的优势。

This paper transforms the background value into the original function form after the continuity of the original sequence so as to make the grey differential equation more matched with the albino differential equation.Then,based on the primary fact that the solution of the albino differential equation y(t)is no longer a cumulative function of the original sequence,the paper does not use the traditional successive subtraction method any more,but directly uses the derivative of y(t)to obtain the simulation prediction formula.It is proved by rigorous theory that the model in the paper has the overlap of albinism index,coefficient and translation constant.Therefore,compared with the original NGM(1,1,K)model,the proposed model has the advantage of being applicable to both high and low growth exponential sequences.