Landslide Groundwater Level Time Series Prediction Based on Phase Space Reconstruction and Wavelet Analysis-Support Vector Machine Optimized by PSO Algorithm
-
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.
-
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) 
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
-
An, X., Jiang, D., Liu, C., et al., 2011. Wind Farm Power Prediction Based on Wavelet Decomposition and Chaotic Time Series. Expert Systems with Applications, 38(9): 11280-11285. doi: 10.1016/j.eswa.2011.02.176 Cui, W.Z., Zhu, C.C., Bao, W.X., et al., 2004. Prediction of the Chaotic Time Series Using Support Vector Machines. Acta Physica Sinica, 53(10): 3303-3310 (in Chinese with English abstract). doi: 10.7498/aps.53.3303 Gu, W.C., Chai, B.R., Teng, Y.P., 2014. Research on Support Vector Machine Based on Particle Swarm Optimization. Transactions of Beijing Institute of Technology, 34(7): 705-709(in Chinese with English abstract). http://www.researchgate.net/publication/292867417_Research_on_support_vector_machine_based_on_particle_swarm_optimization Han, M., 2007. Prediction Theory and Method of Chaotic Time Series. China Water Power Press, Beijing, 28-30 (in Chinese). Huang, F.M., Tian, Y.G., 2014. WA-VOLTERRA Coupling Model Based on Chaos Theory for Monthly Precipitation Forecasting. Earth Science—Journal of China University of Geosciences, 39(3): 368-374(in Chinese with English abstract). doi: 10.3799/dqkx.2014.035 Kennedy, J., Eberhart, R., 1995. Particle Swarm Optimization. In: Proceedings of the 4th IEEE International Conference on Neural Networks. IEEE Service Center, Piscataway, 1942 -1948. Li, C.D., Tang, H.M., Hu, B., et al., 2008. Research on Application of Wavelet Analysis and RBF Neural Network to Prediction of Foundation Settlement. Rock and Soil Mechanics, 29(7): 1917-1922(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-YTLX200807040.htm Li, C.D., Tang, H.M., Hu, X.L., et al., 2009. Landslide Prediction Based on Wavelet Analysis and Cusp Catastrophe. Journal of Earth Science, 20(6): 971-977. doi: 10.1007/s12583-009-0082-4 Liu, H., Tian, H.Q., Chen, C., et al., 2011. Short-Term Forecasting Optimization Algorithm for Unsteady Wind Speed Signal Based on Wavelet Analysis Method and Neutral Networks Method. Journal of Central South University (Science and Technology), 42(9): 2704-2711(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZNGD201109029.htm Liu, X.X., Xia, Y.Y., Zhang, X.S., et al., 2005. Effects of Drawdown of Reservoir Water Level on Landslide Stability. Chinese Journal of Rock Mechanics and Engineering, 24(8): 1439-1444(in Chinese with English abstract). http://www.cnki.com.cn/Article/CJFDTotal-YSLX200508034.htm Luo, H.M., Tang, H.M., Zhang, G.C., et al., 2008. The Influence of Water Level Fluctuation on the Bank Landslide Stability. Earth Science—Journal of China University of Geosciences, 33(5): 687-692(in Chinese with English abstract). doi: 10.3799/dqkx.2008.084 Maiti, S., Tiwari, R.K., 2014. A Comparative Study of Artificial Neural Networks, Bayesian Neural Networks and Adaptive Neuro-Fuzzy Inference System in Groundwater Level Prediction. Environmental Earth Sciences, 71(7): 3147-3160. doi: 10.1007/s12665-013-2702-7 Peng, L., Niu, R.Q., Wu, T., 2013. Time Series Analysis and Support Vector Machine for Landslide Displacement Prediction. Journal of Zhejiang University(Engineering Science), 47(9): 1672-1679(in Chinese with English abstract). Peng, L., Niu, R.Q., Ye, R.Q., et al., 2012. Prediction of Ground Water Level in Landslides Based on Genetic-Support Vector Machine. Journal of Central South University (Science and Technology), 43(12): 4788-4795 (in Chinese with English abstract). http://www.cqvip.com/QK/90745B/201212/44479949.html Qiu, J.P., Xing, J., Jiang, A.N., et al., 2012. Supersonic Forecast of the Strength of Ore and Rock Based on Particle Swarm Support Vector Machine. Journal of Northeastern University(Natural Science), 33(5): 731-734(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DBDX201205031.htm Ren, J., Huang, D.D., Li, Z.N., 2005. Character Recognition Based on Support Vector Machines and Wavelet. Journal of Zhejiang University(Engineering Science), 39(12): 2016-2020(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-ZDZC200512037.htm Ren, L., Xiang, X.Y., Ni, J.J., 2011. Forecast Modeling of Monthly Runoff with Adaptive Neural Fuzzy Inference System and Wavelet Analysis. Journal of Hydrologic Engineering, 18(9): 1133-1139. http://www.researchgate.net/publication/273748128_Forecast_Modeling_of_Monthly_Runoff_with_Adaptive_Neural_Fuzzy_Inference_System_and_Wavelet_Analysis Siek, M., Solomatine, D.P., 2010. Nonlinear Chaotic Model for Predicting Storm Surges. Nonlinear Processes in Geophysics, 17(5): 405-420. doi: 10.5194/npg-17-405-2010 Tang, M., Ma, G.W., Xu, G., 2007. Analysis and Forecasting SMP Using Wavelet Transform. Journal of Sichuan University(Engineering Science Edition), 39(4): 12-15 (in Chinese with English abstract). Wang, Z.L., Sun, H.Y., Liu, Y.L., et al., 2011. Time Series Analysis about Groundwater Level in Slope and Rainfall. Journal of Zhejiang University(Engineering Science), 45(7): 1031-1037(in Chinese with English abstract). doi: 10.3785/j.issn.1008-973X.2011.07.027 Wolf, A., Swift, J.B., Swinney, H.L., 1986. Determining Lyapunov Exponents from Time Series. Physica D, 16(2): 285-371. Yang, Z.P., Lu, W.X., Li, P., 2005. Application of Time Series Model to Predict Groundwater Regime. Journal of Hydraulic Engineerinmg, 32(12): 1475-1479 (in Chinese with English abstract). doi: 10.3321/j.issn:0559-9350.2005.12.013 Zhang, S.Q., Jia, J., Gao, M., 2010. Study on the Parameters Determination for Reconstructing Phase-Space in Chaos Time Series. Acta Physica Sinica, 59(3): 1576-1582 (in Chinese with English abstract). doi: 10.7498/aps.59.1576 Zhou, C.Y., Zhang, L., Huang, X.Y., 2005. Classification of Rocks Surrounding Tunnel Based on Improved BP Network Algorithm. Earth Science—Journal of China University of Geosciences, 30(4): 480-486(in Chinese with English abstract). http://www.researchgate.net/publication/289965821_Classification_of_rocks_surrounding_tunnel_based_on_improved_BP_network_algorithm 崔万照, 朱长纯, 保文星, 等, 2004. 混沌时间序列的支持向量机预测. 物理学报, 53(10): 3303-3310. https://www.cnki.com.cn/Article/CJFDTOTAL-WLXB200410011.htm 谷文成, 柴宝仁, 滕艳平, 2014. 基于粒子群优化算法的支持向量机研究. 北京理工大学学报, 34(7): 705-709. https://www.cnki.com.cn/Article/CJFDTOTAL-BJLG201407010.htm 韩敏, 2007. 混沌时间序列预测理论与方法. 北京: 中国水利水电出版社, 28-30. 黄发明, 田玉刚, 2014. 混沌序列WA-VOLTERRA耦合模型在月降水量预测中的应用. 地球科学——中国地质大学学报, 39(3): 368-374. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201403014.htm 李长冬, 唐辉明, 胡斌, 等, 2008. 小波分析和RBF神经网络在地基沉降预测中的应用研究. 岩土力学, 29(7): 1917-1922. doi: 10.3969/j.issn.1000-7598.2008.07.035 刘辉, 田红旗, 陈超, 等, 2011. 基于小波分析法与神经网络法的非平稳风速信号短期预测优化算法. 中南大学学报(自然科学版), 42(9): 2704-2711. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201109029.htm 刘新喜, 夏元友, 张显书, 等, 2005. 库水位下降对滑坡稳定性的影响. 岩石力学与工程学报, 24(8): 1439-1444. doi: 10.3321/j.issn:1000-6915.2005.08.027 罗红明, 唐辉明, 章广成, 等, 2008. 库水位涨落对库岸滑坡稳定性的影响. 地球科学——中国地质大学学报, 33(5): 687-692. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200805015.htm 彭令, 牛瑞卿, 吴婷, 2013. 时间序列分析与支持向量机的滑坡位移预测. 浙江大学学报(工学版), 47(9): 1672-1679. doi: 10.3785/j.issn.1008-973X.2013.09.024 彭令, 牛瑞卿, 叶润清, 等, 2012. 基于进化支持向量机的滑坡地下水位动态预测. 中南大学学报(自然科学版), 43(12): 4788-4795. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201212031.htm 邱景平, 邢军, 姜谙男, 等, 2012. 基于粒子群支持向量机的矿岩强度指标的超声预测. 东北大学学报(自然科学版), 33(5): 731-734. https://www.cnki.com.cn/Article/CJFDTOTAL-DBDX201205031.htm 任俊, 黄丹丹, 李志能, 2005. 基于支撑向量机和小波的字符识别. 浙江大学学报(工学版), 39(12): 2016-2020. doi: 10.3785/j.issn.1008-973X.2005.12.038 唐明, 马光文, 徐刚, 2007. 基于小波变换的系统边际电价分析与预测. 四川大学学报(工程科学版), 39(4): 12-15. doi: 10.3969/j.issn.1009-3087.2007.04.003 王智磊, 孙红月, 刘永莉, 等, 2011. 降雨与边坡地下水位关系的时间序列分析. 浙江大学学报(工学版), 45(7): 1031-1037. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDZC201107028.htm 杨忠平, 卢文喜, 李平, 2005. 时间序列模型在吉林西部地下水动态变化预测中的应用. 水利学报, 32(12): 1475-1479. doi: 10.3321/j.issn:0559-9350.2005.12.013 张淑清, 贾健, 高敏, 2010. 混沌时间序列重构相空间参数选取研究. 物理学报, 59(3): 1576-1582. https://www.cnki.com.cn/Article/CJFDTOTAL-WLXB201003025.htm 周翠英, 张亮, 黄显艺, 2005. 基于改进BP网络算法的隧洞围岩分类. 地球科学——中国地质大学学报, 30(4): 480-486. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200504014.htm -
点击查看大图
图(8) / 表(3)
计量
- 文章访问数: 4224
- HTML全文浏览量: 471
- PDF下载量: 489
- 被引次数: 0
