基于卡尔曼滤波的GM(1,1)在变形监测中的应用研究

Application of GM(1,1)in deformation monitoring based on Kalman filter

在工程变形监测中,由于监测数据的随机不确定,利用传统的GM(1,1)模型进行变形监测预测精度低、残差大。因此,文中引入卡尔曼滤波消除随机扰动误差的影响,提出一种基于卡尔曼滤波的GM(1,1)预测模型,并将该预测模型应用大坝变形工程实例。通过模型精度检验,结果表明:基于卡尔曼滤波的GM(1,1)模型预测结果与单一传统的GM(1,1)模型相比,平均残差和残差方差均有所减小,且具备较高的精度,对了解大坝变形的发展趋势以及研究大坝变形情况具有一定的参考价值。

In engineering deformation monitoring,the traditional GM(1,1)model had low prediction accuracy and large residual because of the random uncertainty of monitoring data.Therefore,Kalman filter was introduced to eliminate the influence of random disturbance errors.A GM(1,1)prediction model was proposed and applied to the dam deformation engineering based on Kalman filter.The results showed that the average residual and residual variance of the GM(1,1)model based on Kalman filter were reduced compared with the single traditional GM(1,1)model by the model accuracy test,and it had the higher accuracy.It had a certain reference value for understanding the development trend of dam deformation and studying the dam deformation situation.