改进AR模型在垂直形变模拟与预测中的应用研究

Research on improved AR model and its application to simulation and prediction of vertical deformation

针对垂直形变的模拟和预测应用需要,首先分析了滑动平均(MA)模型、自回归(AR)模型及滑动平均自回归(ARMA)模型及其相互关系,指出了它们之间存在的等价性.在此基础上研究了基于模型等价性的高阶AR模型替代其他模型的方法以及该法在垂直变形模拟分析中的应用,同时针对高阶AR模型在模拟与预测应用中存在的问题,详尽探讨了用多级低阶AR模型(MAR)代替高阶AR模型的方法,使得改进后的AR模型可以满足实时在线垂直形变模拟及预测的需要.最后通过实际观测数据和应用实例验证了改进模型的可行性.

To meet the need of simulation and prediction of vertical deformation, equivalent AR model with a higher order as the replacement for ARMA or MA models is derived and employed to simulate vertical deformation sequences. Furthermore, cascaded AR model is explored to replace higher order AR model to facilitate real time simulation and prediction of vertical deformation under small number of sampled observations. Validation of proposed approach is verified using practical observations.