Landslide Displacement Prediction Based on Varying Coefficient Regression Model in Three Gorges Reservoir Area
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摘要: 降雨-库水联合作用影响着三峡库区滑坡，而降雨、库水分别对滑坡演化的贡献及作用规律迄今尚不明确.以库区树坪滑坡和八字门滑坡为例，通过分析降雨和库水位资料，采用变系数回归模型，对滑坡位移进行预测.实验结果表明：经过改进的变系数回归模型方法不仅比传统的线性回归模型、自回归积分滑动平均模型、支持向量机模型方法具有更高的预测精度，而且能定量地给出各影响因素对滑坡位移的贡献.Abstract: Landslides in Three Gorges reservoir area are affected by both the rainfall and the reservoir water, but their respective contribution and the laws of the landslide evolution remain unclear. In this paper, we analyzed the rainfall and water level data, and applied a varying coefficient regression model for landslide displacement prediction taking Shuping landslide and Bazimen landslide in the reservoir area as the study area. The results of experiments show that the improved varying coefficient regression model is not only more accurate than traditional linear regression model, auto-regressive Integrated moving average model and support vector mchine model, but also it can give quantitative contribution of each factor on the landslide displacement.
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图 1 树坪滑坡GPS监测点布置平面图(a)和工程地质剖面(b)
来源于三峡库区地质灾害防治工作指挥部，经过适当修改整饰
Fig. 1. Layout of GPS monitoring points (a) and geological profile (b) of Shuping landslide
图 2 八字门滑坡GPS监测点布置平面(a)和工程地质剖面(b)
来源于三峡库区地质灾害防治工作指挥部，经过适当修改整饰
Fig. 2. Layout of GPS monitoring points (a) and geological profile (b) of Bazimen landslide
图 3 监测点累计位移与相对位移
Fig. 3. Cumulative displacement and relative displacement of monitoring points
图 4 降雨与监测点相对位移的关系
Fig. 4. The relationship between rainfall and relative displacement of monitoring points
图 5 库水位差与监测点相对位移的关系
Fig. 5. The relationship between water level difference and relative displacement of monitoring points
图 6 监测点累计位移真实值与拟合/预测值对比
Fig. 6. The comparison of true values and fitting/predicted values of monitoring points
图 8 各自变量因素系数变化及预测值
Fig. 8. Predicted value and coefficient changes of each independent variable factor
表 1 变系数回归模型和改进的变系数回归模型预测结果
Table 1. Prediction results from varying coefficient regression and improved varying coefficient regression
日期 变系数回归 改进的变系数回归 原始值(mm) 预测值(mm) 误差(%) 原始值(mm) 预测值(mm) 误差(%) ZG85 2010-11-12 2 330.8 2 316.532 -0.612 16 2 330.8 2 325.660 762 -0.220 490 2010-12-11 2 339.3 2 321.932 -0.742 43 2 339.3 2 344.587 696 0.226 038 2011-01-14 2 349.9 2 316.524 -1.420 30 2 349.9 2 355.631 293 0.243 895 2011-02-21 2 369.6 2 330.334 -1.657 08 2 369.6 2 389.211 497 0.827 629 2011-03-13 2 390.5 2 337.750 -2.206 66 2 390.5 2 419.628 201 1.218 498 2011-04-09 2 420.1 2 344.962 -3.104 77 2 420.1 2 451.231 368 1.286 367 2011-05-12 2 493.8 2 389.472 -4.183 51 2 493.8 2 519.672 382 1.037 468 2011-06-12 2 653.8 2 435.680 -8.219 18 2 653.8 2 596.337 785 -2.165 280 ZG111 2008-01-11 662.4 672.041 2 1.455 49 662.4 672.410 5 1.511 24 2008-02-16 668.0 666.478 6 -0.227 76 668.0 666.906 2 -0.163 74 2008-03-11 672.2 660.134 2 -1.794 98 672.2 660.290 9 -1.771 66 2008-04-10 671.8 660.483 5 -1.684 50 671.8 660.183 1 -1.729 22 2008-05-12 683.8 681.754 7 -0.299 11 683.8 680.924 2 -0.420 56 2008-06-18 691.6 691.406 7 -0.027 96 691.6 690.482 8 -0.161 54 2008-07-13 706.0 709.959 6 0.560 86 706.0 709.399 2 0.481 47 2008-08-15 719.9 743.671 2 3.302 01 719.9 744.446 6 3.409 72 2008-09-17 816.9 789.395 1 -3.366 99 816.9 792.501 8 -2.986 68 2008-10-20 826.2 816.195 9 -1.210 86 826.2 822.810 1 -0.410 30 2008-11-21 823.7 827.996 7 0.521 63 823.7 838.704 7 1.821 62 2008-12-21 828.4 826.307 4 -0.252 61 828.4 838.750 1 1.249 41 2009-01-08 831.2 821.230 5 -1.199 41 831.8 831.200 0 -0.081 76 
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表 2 监测点5种模型的预测对比
Table 2. Prediction and comparison of five models
模型 ZG85 ZG111 最大误差 最小误差 平均绝对误差 均方根误差 最大误差 最小误差 平均绝对误差 均方根误差 ARIMA 4.09 0.88 2.29 61.74 7.51 0.210 4.60 36.43 SVR 6.80 0.38 1.70 68.04 6.80 0.380 1.70 68.04 线性回归 3.24 0.25 1.25 37.21 7.90 0.260 1.36 19.07 变系数回归 8.21 0.61 2.76 93.57 3.36 0.027 1.22 12.19 改进的变系数回归 1.28 0.22 0.63 19.23 3.40 0.080 1.24 12.22
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