GM(1,N)模型的离散化结构解  

Dispersed structure solve of model GM(1,N)

作　　者：仇伟杰[1] 刘思峰[1] 

机构地区：[1]南京航空航天大学经济与管理学院

出　　处：《系统工程与电子技术》2006年第11期1679-1681,1699,共4页Systems Engineering and Electronics

基　　金：国家自然科学基金(70473037);江苏省自然科学基金重点项目(BK2003211)资助课题

摘　　要：针对灰色系统GM(1,N)模型是以差分方程为基础进行参数估计的,而其时间响应函数却是由微分方程的解得到的。从差分方程到微分方程的跨越,缺乏充分的科学基础和理论依据。通过对灰色系统模型建模机理进行深入剖析,利用采样定理和状态转移矩阵在差分方程和微分方程之间架起一座桥梁,通过算例仿真实验证明了该算法的有效性。Parameters of grey model GM （ 1, N） are often estimated based on related difference equation, but time response function is acquired by the solution of differential equation. No reasonable scientific or theoretical basis is given to explain the jump from difference equation to differential equation till now. The relation between difference equation and differential equation is studied by analyzing the mechanism in building grey models, and a ＂bridge＂ is set up between difference equation and differential equation by sampling theorem and state transition matrix. It proves this method has validity by analysis of simulation result.

关 键 词：GM(1 N)模型 微分方程 差分方程 采样定理 状态转移矩阵 

分 类 号：O21[理学—概率论与数理统计]