马尔科夫理论的优化灰色模型预测建模  

An optimized gray model deformation forecasting modeling based on Markov theory

作　　者：李克昭[1,2] 李志伟[1] 赵磊杰 

机构地区：[1]河南理工大学测绘与国土信息工程学院,河南焦作454000 [2]北斗导航应用技术协同创新中心,郑州450052

出　　处：《测绘科学》2016年第8期1-5,共5页Science of Surveying and Mapping

基　　金：国家自然科学基金项目(41202245;41272373);河南理工大学骨干教师资助项目(72105/090)

摘　　要：针对GM(1,1)模型易受建模数据随机扰动影响,且模型稳定性较差的问题,该文提出了基于马尔科夫(Markov)理论的GM(1,1)预测优化模型。首先,通过最小二乘原理选取GM(1,1)模型的最优初值,利用指数函数法构造新的背景值,同时利用正化残差序列法进一步修正残差。然后,将优化的GM(1,1)模型和马尔科夫理论有机结合,进一步对优化的GM(1,1)模型进行改进,构建了优化的灰色马尔科夫预测模型。最后,以某建筑物的变形实测数据为基础,进行了传统GM(1,1)预测模型、优化的GM(1,1)预测模型和优化的灰色马尔科夫预测模型的实例计算比较,结果表明:优化的灰色马尔科夫预测模型的拟合精度和预测精度优于传统GM(1,1)预测模型和优化的GM(1,1)预测模型,且适用性更强,稳定性更好。The original values,conformation of background values and correction of residual errors perform important factors to the precision and stability of gray GM（1,1）model.In this paper,the optimal initial values were selected by the least square principle,and new background values were created by exponential function and the residual sequence was corrected by normalized residual sequence method.Although the forecasting precision of optimized GM（1,1）mode was improved,it was still affected by random fluctuation of data easily,and the stability of it was still unsatisfactory.Markov model can reduce the fluctuation of data forecasting and improve the stability of forecasting the model.Based on above,combing the optimized GM（1,1）model and Markov theory,the optimized gray Markov forecasting model was proposed.At last,the effectivity of traditional GM（1,1）model,optimized GM（1,1）model and optimized gray Markov model were compared based on practical data of some buildings.The result showed that the fitting and forecasting accuracy of the optimized gray Markov model was better than that of traditional GM（1,1）model and optimized GM（1,1）model,which improved the applicability and stability.

关 键 词：GM(1 1)模型 马尔科夫模型 MARKOV 灰色马尔科夫模型 变形监测 

分 类 号：P208[天文地球—地图制图学与地理信息工程]