具有幂指数律重合性的GM(1,1) 幂模型

针对传统GM(1,1) 幂模型不具备幂指数律重合性的问题, 分别从灰导数和背景值两个方面改进GM(1,1) 幂 模型的灰色微分方程, 提出了两种具有幂指数律重合性的GM(1,1) 幂模型并从理论上加以证明. 通过变换将两个具 有幂指数律的灰色微分方程转化成完全一致的形式, 在此基础上进行参数估计. 数值模拟和应用实例表明, 具有幂指 数律重合性的GM(1,1) 幂模型能够有效地提高模型的模拟和预测精度.

GM(1,1) power model with power exponential law coincidence

As the traditional GM(1,1) model does not have the property of exponential law coincidence, this paper improves the grey differential equation of GM(1,1) model from grey derivative and background value respectively. Two kinds of GM(1,1) power model with power exponential law coincidence are proposed and relevant theoretical proofs are also given. Two grey differential equations with power exponential law coincidence are transformed into exactly the same form, based on which parameters can be effectively estimated. Numerical simulation and application examples show that the simulation and prediction accuracy of GM(1,1) power model is effectively enhanced by using the proposed method.