最优多项式时变参数离散灰色模型及应用  

Optimal Polynomial Time-varying Parameters Discrete Grey Model and Its Applications

作　　者：刘晓梅[1] 周钢 邱洋青 Liu Xiaomei;Zhou Gang;Qiu Yangqing(College of Science,Shanghai Polytechnic University,Shanghai 201209,China;School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海第二工业大学理学院,上海201209 [2]上海交通大学数学科学学院,上海200240

出　　处：《统计与决策》2022年第20期31-36,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(50876066);上海第二工业大学应用数学重点学科(XXKPY1604)。

摘　　要：针对复杂的非线性小样本序列,文章在离散GM(1,1)模型基础上引入多项式时间项构造了多项式时变参数离散灰色模型(PDGM(1,1)模型),证明了该模型的白指数规律、多项式规律重合性和伸缩变换一致性,优化了该模型的迭代基值。并且通过在PDGM(1,1)模型的发展系数和灰作用量中选取多个不同的多项式时间项,构造了一系列PDGM(1,1)模型,根据MAPE最小原则建立了最优多项式时变参数离散灰色模型。实例建模的结果表明该模型具有较高的模拟和预测精度。In view of the complex nonlinear small sample sequence,this paper constructs a polynomial time-varying parameters discrete grey model(PDGM(1,1)model)by introducing polynomial time terms based on the discrete GM(1,1)model,proves white exponential law,polynomial law coincidence and consistency of stretching transformation of the model,and optimizes the iterative starting value of the proposed model.Furthermore,a series of PDGM(1,1)models are constructed by selecting several different polynomial time terms from the development coefficients and grey action of the PDGM(1,1)model,and the optimal polynomial time-varying parameter discrete grey model is established according to MAPE minimum principle.The simulation results show that the model has high simulation and prediction accuracy.

关 键 词：灰色理论 时变参数 离散模型 灰色预测 

分 类 号：N941.5[自然科学总论—系统科学]