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LANDSLIDE DISPLACEMENT PREDICTION MODEL BASED ON TIME SERIES AND MIXED KERNEL FUNCTION SA-SVR
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摘要: 本文针对阶跃型滑坡变形定量预测困难，提出一种基于时间序列分解与混合核函数SA-SVR的滑坡位移预测模型。首先基于时间序列分解原理，反复使用指数平滑法将滑坡累积位移分解为趋势项位移和周期项位移，使分解后的趋势项位移较平滑且能保证周期项位移的预测精度。同时针对多项式预测容易过拟合造成预测值偏离真实值的问题，采用K-flod交叉验证的3次多项式对趋势项位移进行预测；通过SVR核函数性质，构造泛化能力和学习能力都较强的混合核函数作为SVR模型的核方法，以滑坡诱发因子作为SVR模型输入向量，以模拟退火算法(SA)对使用混合核函数的SVR模型进行参数寻优，从而建立混合核函数的SA-SVR模型预测周期项位移；最后合并趋势项位移和周期项位移得到总位移预测值。以三峡库区白家包滑坡为例，选取ZG325监测点2012年1月~2020年9月数据进行研究，并以ZG324监测点作为辅助验证。结果表明，相较于传统SVR预测模型，模拟退火算法(SA)在参数寻优方面表现良好，混合核函数对SVR模型更加敏感，能较大幅度提高预测精度，具有较高的应用和推广价值。Abstract: This paper puts forward a landslide displacement prediction model. The model is based on time series decomposition and hybrid kernel function SA-SVR. It makes progresses on solving problems of being difficult to quantitatively predict step-type landslide deformation. Firstly,based on the principle of time series decomposition,exponential smoothing is used repeatedly to decompose the cumulative displacement of the landslide into trend displacement and periodic displacement to make the decomposed trend displacement smoother and keep the accuracy of periodic displacement forecast. At the same time,the third-order polynomial of K-flod cross-validation is used to predict the trend displacement avoiding the problems in polynomial prediction. The prediction is easy to overfit and the predicted value deviates from the true value. Based on the properties of SVR kernel function,the mixed kernel function with strong generalization ability and learning ability was constructed as the kernel method of SVR model. The landslide inducing factor is taken as the input vector of SVR model. The simulated annealing(SA)is used to optimize the parameters of SVR model using the mixed kernel function. Thus the SA-SVR model with mixed kernel function is established to predict the periodic displacement. Finally,the trend displacement and periodic displacement are combined to get the predicted total displacement. The paper takes the Baijiabao landslide in the Three Gorges reservoir area as an example,selects the data of ZG325 monitoring point from January 2012 to September 2020,and uses the ZG324 monitoring point as auxiliary verification. The results show that compared with the conventional SVR prediction model,the simulated annealing(SA)performs well in parameter optimization,and the hybrid kernel function is more sensitive to the SVR model,which can greatly improve the prediction accuracy and has high application and promotion value.
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Key words:
- Baijiabao Landslide /
- Displacement prediction /
- Time series /
- Mixed kernel function /
- SA-SVR model
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图 1 混合核函数SA-SVR位移预测技术路线
Figure 1. Displacement prediction flow chart based on hybrid kernel function SA-SVR
图 4 ZG325累积位移-降雨量-库水位监测曲线
Figure 4. Monitoring curves for cumulative displacement reservoir water level and rainfall
图 7 趋势项位移预测结果
a. 第2阶段①参数预测结果; b. 第2阶段②参数预测结果
Figure 7. Trend displacement prediction results
图 9 周期项位移与影响因子关系
a. 周期项位移和库水位关系; b. 周期项位移与库水位滞后关系; c. 周期项位移与降雨量和位移增量关系
Figure 9. Relationships between periodic displacement and influence factors
图 10 线性核比例与预测结果RMSE曲线图
Figure 10. Linear kernel ratio and prediction result RMSE curve
图 11 ZG325监测点周期项位移预测结果
Figure 11. Predicted values of periodic displacement of ZG325 monitoring point
图 12 ZG325监测点累积位移预测结果
Figure 12. Predicted values of cumulative displacement of ZG325 monitoring point
图 13 ZG324监测点趋势项位移与周期项位移预测结果
Figure 13. Trend term displacement and periodic term displacement prediction results of ZG324 monitoring point
图 14 ZG324监测点累积位移预测结果
Figure 14. Predicted values of cumulative displacement of ZG324 monitoring point
表 1 趋势项位移多项式预测参数
Table 1. Polynomial prediction parameters of trend term displacement
时间段 a b c d R2 第1阶段 -0.0004 -0.1680 17.5704 452.0679 0.9944 第2阶段① 0.0026 -0.6899 66.8027 -934.8835 0.9973 第2阶段② 0.0023 -0.6265 62.4857 -840.4339 0.9972 
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表 2 累积位移预测精度
Table 2. Accumulated displacement prediction accuracy
时间 实际累积位移 预测累积位移 绝对误差 相对误差 2019-10 1418.830 1417.062 1.768 0.125 2019-11 1418.873 1407.443 11.430 0.806 2019-12 1416.483 1409.117 7.366 0.520 2020-01 1419.963 1412.325 7.638 0.538 2020-02 1419.102 1415.721 3.381 0.238 2020-03 1418.241 1416.542 1.699 0.120 2020-04 1422.760 1417.249 5.512 0.387 2020-05 1416.102 1430.218 14.116 0.997 2020-06 1447.811 1446.016 1.796 0.124 2020-07 1458.174 1474.004 15.830 1.086 2020-08 1461.464 1472.290 10.826 0.741 2020-09 1463.388 1468.249 4.861 0.332 统计 RMSE 8.588 R2 0.790
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