基于整体最小二乘的灰色模型在大坝变形分析中的应用

A TLS-GM model based on total least squares and its application in dam deformation monitoring

在对大坝进行变形分析时,传统的灰色模型在求解灰色参数的过程中,只认为观测向量存在误差,可直接应用最小二乘法。而实际上由于多方面原因,系数矩阵可能存在误差,故本文考虑到系数矩阵的误差,提出基于整体最小二乘的TLS-GM模型,并将该模型用于某大坝变形监测观测资料中,与传统的GM(1,1)模型的预测结果进行了比较分析,认为TLS-GM模型的预测精度要高于GM(1,1)模型。

In the dam deformation monitoring analysis,the traditional grey mode solves grey parameter directly by the least squares method that only considers errors of observation vectors. In fact,because of many reasons,coefficient matrix may exist errors. Therefore,considering errors in the coefficient matrix,a TLS-GM model that based on total least squares method is proposed and applied to the dam deformation monitoring data analysis. The result shows that the prediction accuracy of the TLS-GM model is higher than the traditional GM（ 1,1） model.