稳健动态GM(1,1)模型及其在变形预报中的应用  

Robust dynamic GM(1,1) model and its application in deformation forecasting

作　　者：佘娣[1,2] 谢劭峰[1,2] 彭家頔[1,2] 刘燕芳[1,2] 

机构地区：[1]桂林理工大学测绘地理信息学院,广西桂林541004 [2]广西空间信息与测绘重点实验室,广西桂林541004

出　　处：《工程勘察》2012年第9期51-53,61,共4页Geotechnical Investigation & Surveying

基　　金：国家自然科学基金项目(No.41071294;No.41064001);广西科学基金资助项目(编号:桂科基0991023;No.0728097)

摘　　要：常规GM(1,1)模型基于最小二乘原理,当建模数据中含有粗差时,将对整个模型的估值产生较大影响。为此,将稳健估计引入灰色模型建模,提出了稳健动态GM(1,1)模型的建模方法。通过对静态GM、动态GM及稳健动态GM进行建模,利用MATLAB编程对实测数据进行了验证计算分析。结果表明,当监测序列含有粗差时,稳健动态GM(1,1)模型相对其他模型能有效抵抗粗差的影响,预报精度也有较明显的提高。The conventional GM （1, 1 ） model is based on the least squares principle. When gross error exists in the data, great effects will be made in the estimation of the model parameters. In this paper, the robust estimation is introduced into the grey model, and a robust dynamic GM （1, 1 ） model is put forward. Modeling of the static GM, dynamic GM and robust dynamic GM model is formulated, and is calculated, validated and analyzed with MATLAB using the measured data. Results indicate that when the monitoring data contains a gross error, the robust dynamic model can effectively resist the effects of gross errors than other GM models, and significantly improve forecast accuracy.

关 键 词：稳健估计 灰色模型 动态GM(1 1) 

分 类 号：O141.4[理学—数学]