基于数值积分公式的GM（1,1）模型优化研究  

Research and Its Optimization of GM(1, 1)Model Based on Numerical Integration Formula

作　　者：沈艳[1] 尹金姗 韩帅 韩煜 SHEN Yan;YIN Jinshan;HAN Shuai;HAN Yu(College of Science,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学理学院

出　　处：《计算机工程与应用》2019年第24期41-45,共5页Computer Engineering and Applications

摘　　要：GM(1,1)模型采用最小二乘法求解参数,当数据中存在异常点时这种方法就会加大模型预测误差。从优化参数视角出发,利用基于Simpson积分公式的四阶Runge-Kutta法修正GM(1,1)模型参数辨识,提出一种新的改进GM(1,1)模型以降低模型的预测误差。同时从不同发展系数取值和预测步数两种情形进一步分析改进模型的适用范围。通过实例验证了改进模型的有效性。The least square method is used to solve the parameters in GM(1,1)model.When there are outliers in the data,this method will increase the prediction error of the model.From the viewpoint of optimizing parameters,the fourth-order Runge-Kutta method based on Simpson integral formula is used to modify the parameter identification of GM(1,1)model,and a new improved GM(1,1)model is proposed to reduce the prediction error of the model.At the same time,the scope of application of the improved model is further analyzed from two cases of different values of development coefficient and different prediction steps.Finally,an example is given to verify the effectiveness of the improved model.

关 键 词：GM(1 1)模型 发展系数 参数辨识 改进模型 

分 类 号：O29[理学—应用数学]