摘要
针对灰色预测模型拟合非齐次指数序列时的误差,对白化微分方程和参数无偏估计方法展开研究.首先梳理现有非齐次灰色预测模型,建立NGM(1,1,k)的基本形式;然后从灰导数和背景值两个角度分别优化,提出NGM(1,1,k)的两类无偏基本形式,通过验证两者的统一性得到无偏NGM(1,1,k)的直接建模方法,并且证明该建模方法具有白指数重合性;最后利用6类数据拟合和南京城市天然气供气量两个算例验证了所提出模型的有效性和实用性.
According to the error problem of grey prediction models calculating non-homogenous index sequences, the whitenization differential equation and the parameter unbiased estimation method are discussed. Firstly, the different forms of the existed non-homogeneous grey prediction model are proved, and the basic form of NGM（1, 1, k） is built. Then two kinds of unbiased basic form of NGM （1, 1, k） are proposed from two aspects which are grey derivative optimization and background value optimization. The direct modeling method of unbiased NGM（1, 1, k） is constructed by verifying the unity of the two models, and the whitenization index repeatability of this method is proved. Finally, the rationality and effectiveness of the model are verified by two examples which are the fitting of six types of data and the total amount simulation of natural gas supply in Nanjing.
出处
《控制与决策》
EI
CSCD
北大核心
2017年第5期823-828,共6页
Control and Decision
基金
国家自然科学基金项目(71071077
71371098)
江苏高校哲学社会科学重点研究基地项目(2012JDXM005)
江苏省研究生培养创新工程项目(KYZZ_0106)
中央高校基本科研业务费专项资金项目(NC2012001
NR2013033)
