全最小一乘的灰色模型在变形监测中的应用

Application of the Total Least Absolute Gray Model Deviation in Deformation Monitoring

简述了全最小一乘准则下的参数估计理论和灰色GM(1,1)模型建模原理,介绍了全最小一乘准则下的灰色GM(1,1)模型参数估计和利用线性规划模型进行参数计算的方法。通过实例与最小二乘准则下灰色GM(1,1)模型计算出的各项指标进行对比,结果显示,利用全最小一乘准则下的灰色GM(1,1)模型进行变形预测,不论有无异常值存在,其预测值均有较强的稳健性。因此,该模型对工程变形监测的预报具有重要的意义。

This paper briefly described the parameter estimation theory and gray GM (1, 1) modeling principle by use of the total least absolute deviation. It introduced the gray GM (1, 1) parameter estimation method and parameter calculation method of the linear programming model. Compared with calculating indicators using least square gray GM (1,1) model, the predictive data predicted by gray GM (1,1) model of total least absolute deviation were robust, whether the deformation monitoring data contain the abnormal data or not. It had important implications for forecasting of engineering deformation monitoring.