基于TLS的非线性GM-AR高边坡变形预测模型及应用

Nonlinear GM-AR Model of High Slope Deformation Prediction Based on TLS and Its Application

为提高传统GM-AR模型预测精度,提出一种基于整体最小二乘(TLS)的非线性GM-AR变形预测模型。首先利用TLS参数估计的GM(1,1)模型提取变形序列中具有确定性的趋势项,然后再对剔除趋势项后的随机部分建立TLS参数估计的AR预测模型,最后叠加两者的预测结果作为最终的变形预测结果,并以三峡库区某高边坡的变形数据为例对模型进行验证。结果表明,相对于传统最小二乘(LS)参数估计的非线性GM-AR模型及GM(1,1)、AR两个单一模型,基于TLS的非线性GM-AR模型的预测精度更高,可在变形预测中应用。

In order to improve the prediction accuracy of traditional GM-AR model,nonlinear GM-AR deformation prediction model based total least squares was proposed.First,the GM（1,1）model based total least squares parameter estimation was used to extract the deterministic trend items from the deformation series.Then the AR prediction model based total least squares parameter estimation was established to handle the random part after removing the trend item.Finally,the prediction results of the two were superimposed as the final deformation predictions.The deformation data of a high slope in the Three Gorges reservoir area was selected to verify the model.The results show that the proposed model has higher prediction accuracy than the traditional nonlinear GM-AR model and two single models based least squares parameter estimation,and it is suitable for application in deformation prediction.