时变参数灰色模型背景值重构及实现  

Reconstruction and computation of background value in PGM(1,1)model

作　　者：周万春[1] 周强波 黄九松 刘鸿剑 

机构地区：[1]重庆市合川区国土资源和房屋勘测队,重庆401520 [2]核工业二三〇研究所,长沙410007 [3]重庆两江新区开发投资集团有限公司,重庆401120 [4]中国能源建设集团甘肃省电力设计院有限公司,兰州730050

出　　处：《测绘科学》2016年第6期173-178,共6页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(40571120;41374007);江西省数字国土重点实验室开放基金项目(DLLJ201411);放射性地质与勘探技术国防重点学科实验室开放基金项目(2010RGET13);浙江省自然科学基金项目(Y1090671)

摘　　要：针对时变参数灰色模型PGM(1,1)的背景值重构收敛速度及稳定性问题,该文运用积分的方法综合序列在Δt内不同变化趋势,导出背景值模型的准确表达式。实现了反映序列对新老信息偏爱程度的最优权值介于(0,1)内,且非不能越过某一阈值;给出了背景值重构模型最优解准确求取的具体算法步骤。基于MATLAB语言的实验结果表明:改进模型预测精度高,易于实现;所研究的带权灰色模型GM(1,n)背景值模型的重构及计算方法验证了PGM(1,1)模型重构及计算实现方法的有效性和实用性。This paper tried to reconstruct and compute the background value in PGM（1,1）Model.In this paper,the limitation of many traditional methods were analyzed and the varied step iterative algorithm was adopted,which was proved to have better prediction effect.According to the integral method,the change trends of time series atΔt were considered.The accurate expression of background value model was also established.The optimal solution of background value model was between 0and 1,and also could beyond a certain threshold.The p-weigh reflected the preferences of time series on information＇s between old and new.The specific algorithmic model of this reconstrucion model was proposed.The algorithmic model verified by MATLAB simulation experiment showed that it had better prediction effect and realization.The research results had reference value for the reconstruction and computation of PGM（1,n）model,and further showed that this method was valid and practicable.

关 键 词：灰色模型GM(1 1) 时变参数灰色模型PGM(1 1) 背景值重构 

分 类 号：P208[天文地球—地图制图学与地理信息工程]