基于ARMA模型的隧道位移时间序列分析

Time series analysis of tunnel displacement based on ARMA model

在新奥法隧道施工中,隧道位移监测对于评价围岩稳定性和支护结构合理性起重要作用。目前大都采用AR模型对隧道位移进行时间序列分析,避开了非线性估计,致使拟合精度和模型实用性较差。为此,介绍了具有较高预测精度和较好适用条件的ARMA模型及其常用参数估计方法,基于其参数非线性估计带来的不便性,提出一种ARMA模型参数估计近似线性方法,把残差用Taylor级数一阶展开,将非线性估计线性化,用线性最小二乘法估计参数最终值。用该方法对重庆市大足县南环二路南山隧道位移监测数据进行时间序列建模分析,预测与实测值吻合较好,证明了该方法的实用性。

The displacement monitoring of tunnel plays an important role in assessing surrounding rock＇s stability and supporting structure＇s rationality during using new Austrian tunneling method （NATM）. In light of the fact that auto regressive （AR） model is usually adopted to analyze displacement of tunnel with time series, which avoids nonlinear estimation but leads to lower fitting accuracy and poorer model＇s practicality. The auto regressive moving average （ARMA） model which has higher accuracy and good practicability is reviewed; its common parameter estimate methods is introduced; and a parametric estimation approximate linear method of ARMA model is presented in light of the inconvenience of the nonlinear parameter estimation of ARMA model, which linearizes nonlinear estimation through expanding residues with Taylor series in first order, and then estimate final parameter with linear least square method. Using the method of time series to model and analyze the displacement monitoring data of Nanshan tunnel in Dazu county of Chongqing, the prediction is in agreement with actual measurements; it is proved that the method is basically feasible.