多监测点滑坡变形预测的似乎不相关模型研究

doi:10.13722/j.cnki.jrme.2015.1038

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摘要采用似乎不相关模型(SUR)，可有效地考虑滑坡多个监测点的之间的关联性，对多个监测点的累计位移数据同步处理，更精确地实现滑坡的变形预测。以白水河滑坡为例，取ZG93和zg118 两个监测点，建立2个监测点的累计位移回归方程，根据两步回归法计算得到2个方程的误差协方差矩阵。由于误差协方差矩阵为非对角矩阵，所以2个监测点的回归方程实际上是相互联系的，满足似乎不相关模型的条件，可以建立2个监测点联立的似乎不相关模型，实现对ZG93和zg118两个监测点的同步变形预测。与传统的普通最小二乘法(OLS)比较，似乎不相关的估计参数比普通最小二乘估计更接近真实值，SUR模型平均相对误差均小于OLS模型平均相对误差，显示SUR模型的预测精度要高于OLS模型。

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	罗文强
	冀雅楠
	王淳越
	宋子健

关键词 ：工程地质, 似乎不相关, 多个监测点, 普通最小二乘, 相对误差

Abstract：In the process of landslide deformation monitoring，multiple monitoring points were arranged on the same landslide usually. These data of monitoring points reflected the trend of the landslide deformation and destruction from different sides，so there was a certain correlation among data of monitoring points. However，this correlation has not been considered into research on the same landslide deformation prediction of multiple monitoring points. Seemingly unrelated regressions(sur) model established in this paper could effectively deal with the correlation among data of multiple monitoring points，and could process the cumulative displacement data of multiple monitoring points in one model，and then more accurate results of deformation prediction of landslide were obtained. As an example，two regression equations were established based on the cumulative displacement data of monitoring points ZG93 and ZG118 of baishuihe landslide，then according to two-step feasible generalized least squares(FGLS)，covariance matrix of error of two regression equations was obtained. The regression equations were actually related due to the covariance matrix of error was non-diagonal，which met the conditions of SUR model，so SUR model of the two monitoring points could be created to complete the deformation prediction of two monitoring points ZG93 and ZG118 synchronously. Finally compared with the results of ordinary least squares(OLS)，parameter estimation of SUR model was closer to the true value and the average relative error of SUR model was less than OLS model，so the prediction accuracy of SUR model is higher than OLS model.

Key words： engineering geology seemingly unrelated regressions multiple monitoring points ordinary least squares relative error

引用本文:

罗文强，冀雅楠，王淳越，宋子健. 多监测点滑坡变形预测的似乎不相关模型研究[J]. 岩石力学与工程学报, 2016, 35(S1): 3051-3056.
LUO Wenqiang，JI Yanan，WANG Chunyue，SONG Zijian. Research on seemingly unrelated regressions model of landslide displacement prediction of multiple monitoring points. , 2016, 35(S1): 3051-3056.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2015.1038 或 https://rockmech.whrsm.ac.cn/CN/Y2016/V35/IS1/3051

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