GM(1,1)灰色预测模型的改进与应用  

Application of improved GM(1,1)grey prediction model

作　　者：杨国华 颜艳[1,2,3] 杨慧中 Yang Guohua;Yan Yan;Yang Huizhong(Jiangsu Province Business Intelligence Technology Application Engineering Technology Researchand Development Center,Wuxi 214153,China;Jiangsu Province Wireless Sensor SystemApplication Engineering Technology Research and Development Center,Wuxi 214153,China;School of Internet of Things,Wuxi Vocational Institute of Commerce,Wuxi 214153,China;School of Internet of Things,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江苏省商业智能技术应用工程技术研究开发中心,江苏无锡214153 [2]江苏省无线传感系统应用工程技术研究开发中心,江苏无锡214153 [3]无锡商业职业技术学院物联网技术学院,江苏无锡214153 [4]江南大学物联网工程学院,江苏无锡214122

出　　处：《南京理工大学学报》2020年第5期575-582,共8页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(61403166;61773181);江苏省自然科学基金(BK20140164);中央高校基本科研业务费专项资金(JUSRP51733B)。

摘　　要：针对传统GM(1,1)模型预测精度低的问题,采用变权构造背景值,并将模拟拟合的残差构建多项式作为修正值引入模型中,建立改进的GM(1,1)模型。利用该模型对2个实例进行了模拟和预测。结果表明,针对非指数函数特征的数据序列,通过该文改进的GM(1,1)模型预测,在保持模型精度相对稳定的情况下,拟合平均相对误差、残差均方差和预测平均相对误差值都更小。Aiming at the problem of low prediction accuracy of traditional GM(1,1)model,variable weight is used to construct background value,and the polynomial constructed by simulation fitting residual error is introduced into the model as the modified value to establish an improved GM(1,1)model.The model is used to simulate and predict two examples.The results show that,for the data series with non exponential function characteristics,the fitting average relative error,residual mean square error and prediction average relative error are smaller under the condition of keeping the model accuracy relatively stable.

关 键 词：灰色预测模型 残差 多项式 非指数函数特征 数据序列 平均相对误差 残差均方差 预测平均相对误差 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]