一种优化GM(1,1)模型及其应用

An Optimized Grey GM(1,1) Model and Its Application

在优化背景值的基础上,针对传统灰色GM(1,1)模型参数估计的最小二乘算法稳健性较差的情况,提出基于全最小一乘准则的灰色GM(1,1)模型参数估计算法,同时将初始条件进行优化,从而得到了一个背景值、初始条件和模型参数同时优化的灰色GM(1,1)模型.最后,应用实例说明了优化灰色GM(1,1)模型的可行性与有效性.

Based on the premise of optimized background value,according to bad robustness of estimating parameters of traditional grey GM（1,1） model based on least square method,this paper presents a new algorithm of total least absolute deviation for estimating parameters of grey GM（1,1） model with optimization of initial value,and an optimized grey GM（1,1） model is put forward based on simultaneous optimization of background value,initial condition and model parameters.Lastly,a calculation example illustrates the feasibility and validity of the optimized grey GM（1,1） model.