Prediction of groundwater levels using evidence of chaos and support vector machine

Many nonlinear models have been proposed to forecast groundwater level. However, the evidence of chaos in groundwater levels in landslide has not been explored. In addition, linear correlation analyses are used to determine the input and output variables for the nonlinear models. Linear correlation analyses are unable to capture the nonlinear relationships between the input and output variables. This paper proposes to use chaos theory to select the input and output variables for nonlinear models. The nonlinear model is constructed based on support vector machine (SVM). The parameters of SVM are obtained by particle swarm optimization (PSO). The proposed PSO-SVM model based on chaos theory (chaotic PSO-SVM) is applied to predict the daily groundwater levels in Huayuan landslide and the weekly, monthly groundwater levels in Baijiabao landslide in the Three Gorges Reservoir Area in China. The results show that there are chaos characteristics in the groundwater levels. The linear correlation analysis based PSO-SVM (linear PSO-SVM) and chaos theory-based back-propagation neural network (chaotic BPNN) are also applied for the purpose of comparison. The results show that the chaotic PSO-SVM model has higher prediction accuracy than the linear PSO-SVM and chaotic BPNN models for the test data considered.

[1]  Thom Bogaard,et al.  The effect of groundwater fluctuations on the velocity pattern of slow-moving landslides , 2009 .

[2]  Yao Yevenyo Ziggah,et al.  GPS Monitoring Landslide Deformation Signal Processing using Time-series Model , 2016 .

[3]  Vahid Nourani,et al.  An ANN‐based model for spatiotemporal groundwater level forecasting , 2008 .

[4]  Shakeel Ahmed,et al.  Comparison of FFNN and ANFIS models for estimating groundwater level , 2011 .

[5]  Kaz Adamowski,et al.  Application of nonparametric regression to groundwater level prediction , 1991 .

[6]  Vahid Nourani,et al.  A geomorphology-based ANFIS model for multi-station modeling of rainfall–runoff process , 2013 .

[7]  Lu-Hsien Chen,et al.  Application of Integrated Back-Propagation Network and Self-Organizing Map for Groundwater Level Forecasting , 2011 .

[8]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[9]  Shih-Wei Lin,et al.  Particle swarm optimization for parameter determination and feature selection of support vector machines , 2008, Expert Syst. Appl..

[10]  Shou-yu Chen,et al.  Improved annual rainfall-runoff forecasting using PSO-SVM model based on EEMD , 2013 .

[11]  Heng Tao Shen,et al.  Principal Component Analysis , 2009, Encyclopedia of Biometrics.

[12]  Chi Dung Doan,et al.  Efficient implementation of inverse approach for forecasting hydrological time series using micro GA , 2005 .

[13]  Saumen Maiti,et al.  A comparative study of artificial neural networks, Bayesian neural networks and adaptive neuro-fuzzy inference system in groundwater level prediction , 2014, Environmental Earth Sciences.

[14]  G. P. King,et al.  Phase space reconstruction for symmetric dynamical systems , 1992 .

[15]  Rathinasamy Maheswaran,et al.  Long term forecasting of groundwater levels with evidence of non-stationary and nonlinear characteristics , 2013, Comput. Geosci..

[16]  Ronny Berndtsson,et al.  Evidence of chaos in the rainfall-runoff process , 2001 .

[17]  Desheng Dash Wu,et al.  Power load forecasting using support vector machine and ant colony optimization , 2010, Expert Syst. Appl..

[18]  H. Hentschel,et al.  On the characterization of chaotic motions , 1983 .

[19]  Vahid Nourani,et al.  Liquid Analog Model for Laboratory Simulation of Rainfall–Runoff Process , 2007 .

[20]  Chao Liu,et al.  Wind farm power prediction based on wavelet decomposition and chaotic time series , 2011, Expert Syst. Appl..

[21]  I A Basheer,et al.  Artificial neural networks: fundamentals, computing, design, and application. , 2000, Journal of microbiological methods.

[22]  Ioannis K. Nikolos,et al.  Optimal selection of artificial neural network parameters for the prediction of a karstic aquifer's response , 2009 .

[23]  J. Adamowski,et al.  A wavelet neural network conjunction model for groundwater level forecasting , 2011 .

[24]  Y. Lai,et al.  Effective scaling regime for compution the correlating dimension from chaotic time series , 1998 .

[25]  A. Baas.  Chaos, fractals and self-organization in coastal geomorphology: simulating dune landscapes in vegetated environments , 2002 .

[26]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[27]  Dietmar Saupe,et al.  Chaos and fractals - new frontiers of science , 1992 .

[28]  Chunfeng Li,et al.  Application of BPANN for prediction of backward ball spinning of thin-walled tubular part with longitudinal inner ribs , 2008 .

[29]  Hossein Sedghi,et al.  Monthly groundwater level prediction using ANN and neuro-fuzzy models: a case study on Kerman plain, Iran , 2011 .

[30]  Mingjun Wang,et al.  Particle swarm optimization-based support vector machine for forecasting dissolved gases content in power transformer oil , 2009 .

[31]  Henry D I Abarbanel,et al.  False neighbors and false strands: a reliable minimum embedding dimension algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[33]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[34]  Chuntian Cheng,et al.  Calibration of Xinanjiang model parameters using hybrid genetic algorithm based fuzzy optimal model , 2012 .

[35]  Narayan Sahoo,et al.  Hybrid neural modeling for groundwater level prediction , 2010, Neural Computing and Applications.

[36]  Jaya Kandasamy,et al.  Prediction of hydrological time-series using extreme learning machine , 2016 .

[37]  P. C. Nayak,et al.  Groundwater Level Forecasting in a Shallow Aquifer Using Artificial Neural Network Approach , 2006 .

[38]  Wei Wang,et al.  Construct support vector machine ensemble to detect traffic incident , 2009, Expert Syst. Appl..

[39]  Hongbo Zhao,et al.  Modeling non-linear displacement time series of geo-materials using evolutionary support vector machines , 2004 .

[40]  Bellie Sivakumar,et al.  River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches , 2002 .

[41]  Kunlong Yin,et al.  Landslide Displacement Prediction of WA-SVM Coupling Model Based on Chaotic Sequence , 2014 .

[42]  Jin Wang,et al.  Short-term traffic speed forecasting hybrid model based on Chaos–Wavelet Analysis-Support Vector Machine theory , 2013 .

[43]  A. Jayawardena,et al.  Analysis and prediction of chaos in rainfall and stream flow time series , 1994 .

[44]  Juan Chang,et al.  Simulation and prediction of suprapermafrost groundwater level variation in response to climate change using a neural network model , 2015 .

[45]  Paulin Coulibaly,et al.  Improving groundwater level forecasting with a feedforward neural network and linearly regressed projected precipitation , 2008 .

[46]  L. Tham,et al.  Landslide susceptibility mapping based on Support Vector Machine: A case study on natural slopes of Hong Kong, China , 2008 .

[47]  Heung Wong,et al.  Non-parametric time series models for hydrological forecasting , 2007 .

[48]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[49]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[50]  K. P. Sudheer,et al.  Using Artificial Neural Network Approach for Simultaneous Forecasting of Weekly Groundwater Levels at Multiple Sites , 2015, Water Resources Management.

[51]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[52]  Eungyu Park,et al.  A simple model for water table fluctuations in response to precipitation , 2008 .

[53]  R. Dikau,et al.  Modeling historical climate variability and slope stability , 2004 .

[54]  Huan Wang,et al.  A Comparative Study of Artificial Neural Networks, Support Vector Machines and Adaptive Neuro Fuzzy Inference System for Forecasting Groundwater Levels near Lake Okeechobee, Florida , 2015, Water Resources Management.

[55]  Paulin Coulibaly,et al.  Groundwater level forecasting using artificial neural networks , 2005 .

[56]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[57]  Yudong Zhang,et al.  Stock market prediction of S&P 500 via combination of improved BCO approach and BP neural network , 2009, Expert Syst. Appl..

[58]  M. Bierkens,et al.  Accuracy of spatio-temporal RARX model predictions of water table depths , 2002 .

[59]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[60]  Inmaculada Pulido-Calvo,et al.  Improved irrigation water demand forecasting using a soft-computing hybrid model , 2009 .

[61]  Richard Balon,et al.  Decreased heart rate variability in panic disorder patients: A study of power-spectral analysis of heart rate , 1993, Psychiatry Research.

[62]  Jose D. Salas,et al.  Aggregation and sampling in deterministic chaos: implications for chaos identification in hydrological processes , 2005 .

[63]  Lu-Hsien Chen,et al.  Groundwater Level Prediction Using SOM-RBFN Multisite Model , 2010 .

[64]  M. Xiaoyun,et al.  Research on the displacement response ratio of groundwater dynamic augment and its application in evaluation of the slope stability , 2015, Environmental Earth Sciences.

[65]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[66]  You‐Kuan Zhang,et al.  Effects of variations of river stage and hydraulic conductivity on temporal scaling of groundwater levels: numerical simulations , 2010 .

[67]  Elahe Fallah-Mehdipour,et al.  Prediction and simulation of monthly groundwater levels by genetic programming , 2013 .

[68]  Ping Li,et al.  Application and comparison of two prediction models for groundwater levels: a case study in Western Jilin Province, China. , 2009 .

[69]  N. Behnia,et al.  Coupling wavelet transform with time series models to estimate groundwater level , 2015, Arabian Journal of Geosciences.

[70]  Paresh Chandra Deka,et al.  Multistep Ahead Groundwater Level Time-Series Forecasting Using Gaussian Process Regression and ANFIS , 2015, ACSS.

[71]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[72]  K. P. Sudheer,et al.  Artificial Neural Network Modeling for Groundwater Level Forecasting in a River Island of Eastern India , 2010 .

[73]  Emery Coppola,et al.  Comparative Study of SVMs and ANNs in Aquifer Water Level Prediction , 2010, J. Comput. Civ. Eng..

[74]  S. Rice,et al.  The influence of quantization on the onset of chaos in Hamiltonian systems: The Kolmogorov entropy interpretation , 1981 .

[75]  Luis A. Aguirre,et al.  A nonlinear correlation function for selecting the delay time in dynamical reconstructions , 1995 .

[76]  V. V. Srinivas,et al.  Downscaling of precipitation for climate change scenarios: A support vector machine approach , 2006 .

[77]  S. P. Garcia,et al.  Multivariate phase space reconstruction by nearest neighbor embedding with different time delays. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[78]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[79]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[80]  Marc F. P. Bierkens,et al.  Predicting water table depths in space and time using a regionalised time series model , 2001 .

[81]  Madan K. Jha,et al.  Groundwater-level prediction using multiple linear regression and artificial neural network techniques: a comparative assessment , 2013, Hydrogeology Journal.

[82]  Y. Wang,et al.  Analysis and modeling of multivariate chaotic time series based on neural network , 2009, Expert Syst. Appl..

[83]  K. M. O'Connor.  River flow forecasting , 2005 .

[84]  Andrew E. Mercer,et al.  Artificial Neural Networks and Support Vector Machines: Contrast Study for Groundwater Level Prediction. , 2015 .

[85]  Marc F. P. Bierkens,et al.  Physical basis of time series models for water table depths , 2000 .

[86]  Ioannis K. Nikolos,et al.  Artificial Neural Network (ANN) Based Modeling for Karstic Groundwater Level Simulation , 2011 .

[87]  Antonio S. Cofiño,et al.  CHAOS GAME CHARACTERIZATION OF TEMPORAL PRECIPITATION VARIABILITY: APPLICATION TO REGIONALIZATION , 2006 .

[88]  Mao-sheng Zhang,et al.  Impact of reservoir impoundment-caused groundwater level changes on regional slope stability: a case study in the Loess Plateau of Western China , 2012, Environmental Earth Sciences.