基于原始序列的灰色预测模型  

An amendatory grey prediction model based on the original data sequence

作　　者：王奉伟[1,2] 周世健[3] 周清[1] 陆培鹤 

机构地区：[1]东华理工大学测绘工程学院,南昌330013 [2]国家测绘地理信息局流域生态与地理环境监测重点实验室,南昌330013 [3]南昌航空大学,南昌330063

出　　处：《测绘科学》2016年第6期34-39,共6页Science of Surveying and Mapping

基　　金：国家自然科学基金资助项目(41374007);测绘地理信息江西省研究生创新教育基地项目

摘　　要：针对原始序列平滑处理和用直线斜率代替t=k+1/2时刻导数两方面的问题,该文在分析GM(1,1)建模过程和原理的基础上,应用中心逼近原理,提出了基于原始序列的灰色预测模型OGM(1,1)。对于严格呈指数增长趋势的原始序列,通过平滑处理使其更利于建模,再通过累减获得新的初始序列,建立OGM(1,1)模型。通过对高增长、低增长和缓慢递减3种类型实测数据序列验证分析,比较GM(1,1)、PGM(1,1)和OGM(1,1)3种模型在变形监测数据处理中的拟合和预测结果,结果表明OGM(1,1)模型拟合效果更好、预测精度更高。On the basis of analyzing the process and principle of GM（1,1）model,this paper put forward the grey forecasting model OGM（1,1）based on the original sequence and the two aspects of the original sequence smoothing process,and using the linear slope instead of the derivative at the time of t=k＋1/2.The original sequence with strictly exponential growth trend was more advantageous for modeling after smoothing,the new initial sequence was obtained by regressive calculation,then the OGM（1,1）model was established.Experimental results of three models showed that the OGM（1,1）model was better than other models,which overcame the defects of traditional GM（1,1）.So the OGM（1,1）model was suitable for being applied to the deformation analysis and the deformation object prediction.

关 键 词：灰色预测模型 原始序列 GM(1 1) PGM(1 1) OGM(1 1) 

分 类 号：P208[天文地球—地图制图学与地理信息工程]