NGM(1,1,k)模型的背景值及时间响应函数优化  

Optimization of background value and time response function in NGM(1,1,k)

作　　者：刘震[1] 党耀国[1] 魏龙[1] 

机构地区：[1]南京航空航天大学经济与管理学院,南京211106

出　　处：《控制与决策》2016年第12期2225-2231,共7页Control and Decision

基　　金：国家自然科学基金项目(71071077;71371098);中央高校基本科研业务费专项资金项目(NC2012001;NR2013033);江苏省研究生培养创新工程项目(KYZZ 0106);江苏高校哲学社会科学重点研究基地项目(2012JDXM005)

摘　　要：针对NGM(1,1,k)的基本形式与白化微分方程的跳跃性关系,尝试对NGM(1,1,k)模型进行优化.首先对白化微分方程积分,得到新的NGM(1,1,k)参数估计基本形式,通过定义其中的前置与后置背景值,分析误差产生的几何原因,进而推导背景值计算公式;然后利用误差平方和构建期望函数,求解时间响应函数中的最优常数表达式;总结优化后的NGM(1,1,k)模型的建模步骤,并证明该模型具有非齐次白指数重合性;最后,通过两个算例将优化模型与经典模型进行对比,取得了良好的效果,进而验证了所提出模型的有效性和实用性.According to the jumping relation between the basic form and the whitenization differential equation in NGM（1, 1, k）, the model is optimized. Firstly, the whitenization differential equation is integrated in the interval [k- 1, k]to obtain the new parameter estimation basic form of NGM（1, 1, k）. The front and before background value are defined and the precise calculation formulas are derived. The causes of error are also analyzed in the geometric relationship. Then the desirability function is built based on the sum of the error square, to determine the optimal constant value in the time response function. The optimized modeling steps of NGM（1, 1, k） are summarized, and it is proved that the model has a non-homogeneous white exponential superposition. Finally, the optimization model and the classical model are contrasted by two examples, the good results obtained show the effectiveness and practicality of the proposed optimization model.

关 键 词：灰色预测 NGM(1 1 k) 背景值 时间响应函数 

分 类 号：N941.5[自然科学总论—系统科学]