基于虚拟变量控制的GM(1,N)模型构建及其应用

Construction and application of GM(1,N ) based on control of dummy variables

现实中系统行为特征序列常受到虚拟变量的影响,而此时传统GM(1,N)模型不能准确地描述系统特征的变化规律.将虚拟变量引入传统GM(1,N)模型的灰作用量,构建虚拟变量控制的GM(1,N)模型,讨论新模型的参数求解方法;鉴于背景值对模型精度有着重要影响,利用粒子群优化算法对含有插值系数的背景值进行优化求解;从两个角度提出虚拟变量有效性检验方法.最后,通过河南省农民人均收入预测案例表明,新模型能够准确描述虚拟变量影响下系统特征序列的未来变化趋势.

To solve the problems that the traditional GM（1,N） model can not describe precisely the changing patterns of the system behavior characteristic variables influenced by the dummy variables in the real life, the dummy variables are introduced into the grey acting term of the conventional GM（1,N） model, and the novel GM（1,N） model is built with discussing the estimating methods of the parameters. Due to the great effect of the background value on the precision of modeling, the interpolated coefficient of the background value is optimized by using the PSO algorithm. The test methods of validity are proposed from two perspectives. Finally, the per capital income of farmers in Henan province is simulated and predicted, which shows that the proposed model can effectively describes the future trend of system change influenced by dummy variables.