背景值和初始条件同时优化的GM(1,1)模型

Optimization integrated background value with original condition for GM(1,1)

GM(1,1)模型是有偏差的灰指数模型,其精度取决于背景值的构造形式和初始条件的选取。已有的研究文献均是从一个侧面单独改进GM(1,1)模型,单独采用优化背景值方法或优化初始条件方法可以在一定程度上提高模型精度,因为两种改进方法完全独立。这里提出一种同时优化背景值和初始条件的新GM(1,1)模型,通过模拟数据的比较表明,新优化GM(1,1)模型有更高的精度。

As a gray exponential model with distortions, the precision of GM（1 , 1 ） depends on the conformation of background value and the selection of original condition. Existent literatures separately optimized GM（ 1,1 ） models just from one side. Independent adoptions of optimizing background values or original conditions of GM（ 1,1 ） can only improve the precision of the model in a certain extent. Based on the idea reasoned above, a new GM（ 1,1 ） model of integrated optimizing its background value and original condition is presented. Through comparisons of simulation datum, it is found that the new GM （1,1） model has a higher simulation precision.