灰色NGM(1,1,k)模型背景值优化方法  

Optimization of background value in grey NGM(1,1,k) model

作　　者：童明余[1,2] 周孝华[1] 曾波[3] 

机构地区：[1]重庆大学经济与工商管理学院,重庆400040 [2]重庆师范大学图书馆,重庆400047 [3]重庆工商大学商务策划学院,重庆400067

出　　处：《控制与决策》2017年第3期507-514,共8页Control and Decision

基　　金：国家自然科学基金项目(71271226);国家社科基金重点项目(14AJL015);中国博士后科学基金特别项目(2015T80975);重庆市教委科学技术研究项目(KJ120706);重庆市基础与前沿研究计划项目(cstc2014jcyj A00024);教育部人文社会科学研究一般项目(14YJAZH033)

摘　　要：传统灰色NGM(1,1,k)模型的参数估计误差是导致该模型精度不稳定的重要因素,研究面向背景值优化基础上的参数估计方法是提高灰色模型性能的重要手段.通过积分变换,得到与NGM(1,1,k)模型白化方程匹配的灰色微分方程,推导出背景值优化公式,从而构建背景值优化的新NGM(1,1,k)模型,并从理论上解释新模型能同时模拟严格齐次和非齐次指数增长序列的原因.进一步通过算例和实例验证了所提出的模型均能显著提高序列的模拟和预测精度.The parameter estimation error of the traditional grey NGM（1, 1, k） model is an important factor that leads to the instability of the model.It is an important method to improve the performance of the grey model by studying the parameter estimation method based on the background value optimization.Firstly, the grey differential equation,which matches with the winterization equation of the NGM（1, 1, k） model, is obtained by integral transformation, and the formula to optimize the background value of this model is deduced.Then the grey NGM（1, 1, k） model based on the optimized background value is constructed, and it is proved theoretically that the novel model can simulate the homogenous and non-homogenous exponential sequences simultaneously.Finally, the simulation and prediction accuracy of the proposed model are verified by a numerical example and an application example respectively.

关 键 词：灰色系统 灰色预测模型 近似非齐次指数增长序列 NGM(1 1 k)模型 背景值 

分 类 号：N941.5[自然科学总论—系统科学]