Landslide Groundwater Level Time Series Prediction Based on Phase Space Reconstruction and Wavelet Analysis-Support Vector Machine Optimized by PSO Algorithm
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摘要: 预测滑坡地下水位的动态演变过程对滑坡稳定性分析具有重要意义, 三峡库区库岸滑坡地下水位时间序列受多种因素影响, 呈现出高度非线性非平稳的特征.为对其进行预测, 提出一种基于相空间重构的小波分析-粒子群优化支持向量机(wavelet analysis-support vector machine, 简称WA-PSVM)模型.该模型引入小波变换法对地下水位序列进行时频分解, 将非平稳的地下水位序列转变为多个不同分辨率尺度下的较平稳的地下水位子序列; 然后重构各子序列的相空间, 再利用PSVM(全称support vector machine)模型对地下水位各子序列进行预测, 最后将各子序列预测值相加得到最终预测结果.以三峡库区三舟溪滑坡前缘STK-1水文孔日平均地下水位序列为例, 首先分析滑坡前缘地下水位变化的影响因素, 再将WA-PSVM模型应用于地下水位预测, 并与单独PSVM模型和小波分析-BP网络模型(wavelet analysis-back propagation, 简称WA-BP)作对比.结果表明: 滑坡前缘地下水位受降雨和库水位影响较大, 利用WA-PSVM模型对STK-1水文孔地下水位进行预测的均方根误差为0.073m、拟合优度为0.966, WA-PSVM模型预测精度高于单独PSVM模型和WA-BP模型.WA-PSVM模型解决了地下水位序列非线性非平稳的问题, 在不考虑影响因素的情况下能获得满意的预测效果, 具有较高的建模效率和较强的实用性.Abstract: It is of great significance to predict the dynamic evolution process of landslide underground water level for landslide stability analysis. For the problem that the evolution process of groundwater level in reservoir landslide is a highly non-linear and non-stationary time series affected by many factors, to predict landslide groundwater level time series, a coupling model based on phase space reconstruction and wavelet analysis-support vector machine (WA-PSVM) optimized by particle swarm optimization is proposed. Firstly, the groundwater level time series was decomposed into several different frequency components to transform the non-stationary groundwater level time series into stationary time series. Secondly, the PSVM model was established for each component prediction based on the phase-space reconstruction. At last, the final prediction result was obtained by adding the predicted values of all frequency components. Taking daily average groundwater level time series of STK-1 hydrology hole on Sanzhouxi Landslide in the Three Gorges Reservoir Area for example, the influencing factors of landslide groundwater level fluctuation were analyzed and WA-PSVM model was used to predict the STK-1 groundwater level values. Meanwhile, the single PSVM model and wavelet analysis-back propagation neural network (WA-BP) model were also used for groundwater level prediction. The results show that reservoir water level fluctuation and rainfall are the main factors of groundwater level fluctuation in the reservoir landslide leading edge. We also find that the root-mean-square error (RMSE) of the proposed model for groundwater level time series prediction in STK-1 hydrology holes is 0.073m, the goodness of fit is 0.966, respectively. The prediction accuracy of WA-PSVM model is higher than the single PSVM model and WA-BP model. What is more, WA-PSVM model solves the non-linear and non-stationary problem. WA-PSVM model also has a high operating efficiency and strong applicability without considering the impacts of reservoir water level fluctuation and seasonal rainfall.
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图 1 地下水位预测WA-PSVM模型建模流程
Fig. 1. Flowchart of WA-PSVM model for groundwater level prediction
图 3 三舟溪滑坡地下水位监测点布置
Fig. 3. Locations of groundwater monitoring points of the Sanzhouxi landslide
图 5 STK-1水文孔地下水位值与降雨、库水位相关性分析
Fig. 5. Correlation analysis between STK-1 groundwater level and rainfall, reservoir water level
图 7 子序列a4和d1, d2, d3, d4预测值
Fig. 7. Predicted values of each frequency series a4 and d1, d2, d3, d4
图 8 WA-PSVM模型、WA-BP模型和单独PSVM模型滑坡STK-1地下水位一步预测结果对比
Fig. 8. Final prediction results comparison of WA-PSVM model, WA-BP model and single PSVM model
表 1 WA-PSVM模型、WA-BP模型和单独PSVM模型的输入输出变量
Table 1. Input variables and output variables for WA-PSVM, WA-BP and single PSVM model
序列 输出变量 输入变量 原始序列 (Zi) (Zi-1, Zi-2，Zi-3) a4 (a4i) (a4i-1, a4i-2，a4i-3) d1 (d1i) (d1i-1, d1i-2，d1i-3，d1i-4，d1i-5，d1i-6，d1i-7) d2 (d2i) (d2i-1, d2i-2，d2i-3，d2i-4，d2i-5，d2i-6) d3 (d3i) (d3i-1, d3i-2，d3i-3，d3i-4) d4 (d4i) (d4i-1，d4i-2，d4i-3，d4i-4) 
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表 2 SVM模型对原始序列和各个子序列进行预测时的最佳参数组合
Table 2. Parameter combinations of SVM model for original groundwater level time series and each component
序列 SVM模型参数组合 原始序列 c=1 047.85，ε=0.012，φ=0.173 a4 c=1 446.33，ε=0.011，φ=0.187 d1 c=2 477.26，ε=0.078，φ=0.092 d2 c=1 764.97，ε=0.009，φ=0.136 d3 c=869.33，ε=0.012，φ=0.045 d4 c=2 879.52，ε=0.011，φ=0.038
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表 3 STK-1地下水位不同模型预测结果对比
Table 3. Comparison of different models for one day ahead forecasting of STK-1 groundwater level series
模型 RMSE(m) R2 WA-PSVM 0.073 0.966 WA-BP 0.112 0.931 单独PSVM 0.216 0.741
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