二次时变参数离散灰色模型  

Quadratic time-varying parameters discrete grey model

作　　者：邬丽云[1] 吴正朋[1] 李梅[1] 

机构地区：[1]中国传媒大学理学院,北京100024

出　　处：《系统工程理论与实践》2013年第11期2887-2893,共7页Systems Engineering-Theory & Practice

摘　　要：本文基于离散灰色模型模拟值增长率恒定的原因,通过引入二次时间项来构造了二次时变参数离散灰色模型(quadratic time-varying parameters discrete grey model,简称为QDGM(1,1)模型).并且研究了该模型的性质.结果说明,QDGM(1,1)模型具有白指数规律重合性,线性规律重合性,二次规律重合性,伸缩变换一致性.应用最优化方法研究QDGM(1,1)模型迭代基值问题,建立优化模型并提出求解算法.最后叙述了应用QDGM(1,1)模型建模和预测的步骤,并通过实例比较了QDGM(1,1)模型与原离散灰色模型及其非齐次离散模型和线性时变参数离散灰色模型的预测能力,最终结果表明本文提出的QDGM(1,1)模型具有更高的模拟和预测精度.Based on the reason that the growth of discrete grey model is constant, the paper structured quadratic time-varying parameters discrete grey model （referred to as QDGM（1,1）） by introducing quadratic time-varying terms. And then the paper researched properties of the new model, and reached the conclusion that QDGM（1,1） possessed white exponential law coincidence, linear law coincidence, quadratic law coincidence and consistency of stretching transformation. What＇s more, the paper applied optimiza- tion method to optimizing the iterative starting value of the new model, and introduced the steps of using QDGM（1,1） to predict. Finally, the new model was compared with another three discrete grey models through an instance. It was proved that the new model greatly improves the simulation and prediction precision.

关 键 词：灰色系统 离散模型 模拟预测 二次时变参数 

分 类 号：N941[自然科学总论—系统科学]