改进的含时间幂次项灰色模型及建模机理  

Improved grey forecasting model with time power and its modeling mechanism

作　　者：吴紫恒 吴仲城[1] 李芳[1] 冯东 WU Zi-heng;WU Zhong-cheng;LI Fang;FENG Dong(High Magnetic Field Laboratory,Hefei Institutes of Phsical Science,Chinese Academy of Sciences,Hefei 230000,China;Science Island Branch of Graduate School,University of Science and Technology of China,Hefei 230000,China)

机构地区：[1]中国科学院合肥物质科学研究院强磁场科学中心,合肥230000 [2]中国科学技术大学研究生院科学岛分院,合肥230000

出　　处：《控制与决策》2019年第3期637-641,共5页Control and Decision

基　　金：国家自然科学基金项目(61273323)

摘　　要：为提高灰色预测模型的预测精度,针对传统含时间幂次项灰色预测模型的局限性,根据实际应用的需要,提出一种改进的含时间幂次项灰色模型NGM(1, 1, t~γ).对该模型的建模机理、参数估计等进行研究,通过积分变换,得到与该模型白化方程相匹配的灰色微分方程,并给出模型参数的最小二乘解和时间响应式.讨论幂次项指数几种特殊取值下该模型的性质和适用范围,以误差平方和最小为目标,对NGM(1, 1, t~γ)模型的初始点进行优化,给出相应的优化公式.研究表明, GM(1, 1)和NGM(1, 1, k)模型均是NGM(1, 1, t~γ)模型的特殊形式,因此,该模型拓展了灰色预测理论的体系,扩大了灰色预测理论的应用范围.最后通过实验表明,所提出的改进含时间幂次项灰色预测模型具有更好的拟合和预测精度,从而验证了其有效性和实用性.To improve the forecasting accuracy of grey forecasting model, in view of limitation of the traditional grey forecasting model with time power, this paper proposed an improved grey forecasting model NGM(1, 1, t^γ) with time power according to the practical application need. The modeling mechanism is studied, the grey differential equation which matches the winterization equation is obtained by integral transformation, and the model parameters least-square solutions and the time response function are given. The initial point of NGM(1, 1, t^γ) is optimized with the minimum of the square sum of the error as the target. Researches show that GM(1, 1) and NGM(1, 1, k) are special forms of NGM(1, 1, t^γ) which broadens the application fields of the grey forecationg model. Finally, experiment results show that the improved model has more approximating and forecasting accuracy, which demonstrates its effectiveness and applicability.

关 键 词：灰色预测模型 时间幂次项 NGM(1 1 t^γ) 建模机理 积分变换 初始点 

分 类 号：N941.5[自然科学总论—系统科学]