补偿最小二乘估计精化AR(p)的变形建模与预测

Refining for AR(p) modeling based on penalized least squares estimation in deformation prediction

以AR(p)模型为例,考虑模型误差对变形预测的影响,将模型误差看做非参数信号,采用半参数补偿最小二乘方法来处理,即利用半参数中的非参数分量表达模型误差;为更好地控制残差部分VTPV和光滑部分STRS之间的平衡,提出一种求解平滑参数α的Xu函数;最后,通过实例将精化后的AR(p)模型与灰色模型、灰神经网络模型、常规AR模型的结果进行了比较。结果表明,补偿最小二乘方法能有效地处理变形建模中存在的模型误差,具有较好的预测效果。

In this paper,taking autoregressive model as an example,considering the influence of model errors in deformation analysis,and proposed that model errors as nonparametric,a penalized least squares method is used to deal with deformation data processing.There are two key steps in resolving semi-parametric model,one is to choose the regularization matrix,and the other is to determine the smoothing parameter.This paper focuses on the determination of the smoothing parameter.A new method for determining smoothing parameter,Xu function method,is presented.Finally,a prediction problem in subsidence of building used to explain the method.The results of the semi-parametric model,grey model,grey neural network model and autoregressive model,are compared,which demonstrates that the model errors can be compensated correctly by penalized least squares method and better prediction result can be obtained.