GM(1,1)模型的建模条件

Modeling conditions of GM (1,1) model

GM(1,1)模型是灰色系统理论的核心预测模型,对GM(1,1)模型的建模条件进行研究是提高模拟精度的基础.采用理论证明和数值算例相结合的方法对GM(1,1)模型的建模条件进行研究,拓展了经典灰色预测模型的级比判定条件.结果表明:当原始序列的累加序列值都相等时,发展系数不存在;提高原始序列光滑度不是提高模拟精度的充分条件.

GM （ 1,1 ） model is the core prediction model in grey system. The study on the modeling conditions of grey system has been considered the base of improving the simulation accuracy. This paper adopts the method of combining theory proof and numerical example to study the modeling conditions of grey system, with the purpose to expand the class ratio judgment conditions of traditional grey prediction model. Results indicate that when the accumulate values of the raw sequence are equal, the development coefficient does not exist. The class ratio judgment intervals of the traditional modeling condition are not accurate enough, due to the still incomplete understanding of class ratio. Improving the smooth degree of the raw sequence is not the adequate condition to improve the simulation accuracy. Therefore, the modeling conditions of the traditional GM （ 1,1 ） model still need further research.