A Novel Approach for Prediction of Monthly Ground Water Level Using a Hybrid Wavelet and Non-Tuned Self-Adaptive Machine Learning Model

  • Maryam Malekzadeh
  • Saeid KardarEmail author
  • Keivan Saeb
  • Saeid Shabanlou
  • Lobat Taghavi


In recent decades, due to groundwater withdrawal in the Kabodarahang region, Iran, Hamadan, hazardous events such as sinkholes, droughts, water scarcity, etc., have occurred. This study models groundwater level (GWL) of the Kabodarahang region using two novel techniques including Self-Adaptive Extreme Learning Machine (SAELM) and Wavelet-Self-Adaptive Extreme Learning Machine (WA-SAELM). Using the stepwise selection as different lags along with different input combinations, ten different SAELM and WA-SAELM models were developed. First, the best activation function is chosen for numerical models. After that, GWL values were normalized to equalize the values and enhance speed and accuracy of modeling. Then, an optimized mother wavelet is selected in order to simulate GWLs. Next, the best model was introduced as the superior model in which values of the correlation coefficient (R), Root Mean Squared Error (RMSE) and Nash-Sutcliffe efficiency coefficient (NSC) were obtained 0.969, 0.358 and 0.939, respectively. In addition, the results of the superior model are compared with classical neural network models such as Artificial Neural Network (ANN), Wavelet-Artificial Neural Network (WA-ANN), Support Vector Machine (SVM) and Wavelet-Support Vector Machine (WA-SVM). Among all models, WA-SAELM approximated GWLs with higher accuracy. Furthermore, based on the results obtained from an uncertainty analysis, the superior model was identified as a model with an underestimated performance. Additionally, an explicit and practical matrix was proposed for computing GWLs. Finally, the matrix was validated for another piezometer.


Groundwater Self-adaptive extreme learning machine Uncertainty analysis Wavelet transform Artificial neural network Support vector machine 


Compliance with Ethical Standards

Conflict of Interest



  1. Adamowski J, Sun K (2010) Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. J Hydrol 390(1–2):85–91CrossRefGoogle Scholar
  2. Basak D, Pal S, Patranabis DC (2007) Support vector regression. Neural Inf Process 11:203–225Google Scholar
  3. Bhattacharjya RK, Datta B (2009) ANN-GA-based model for multiple objective management of coastal aquifers. J Water Resour Plan Manag 135(5):314–322CrossRefGoogle Scholar
  4. Cao J, Lin Z, Huang GB (2012) Self-adaptive evolutionary extreme learning machine. Neural Process Lett 36:285–305CrossRefGoogle Scholar
  5. Cherkassky V, Ma Y (2004) Practical selection of SVM parameters and noise estimation for SVM regression. Neural Netw 17:113–126CrossRefGoogle Scholar
  6. Ebrahimi H, Rajaee T (2017) Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine. Glob Planet Chang 148:181–191CrossRefGoogle Scholar
  7. Grossmann A, Morlet J (1984) Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15(4):723–736CrossRefGoogle Scholar
  8. Haykin S (1999) Neural networks: a Comprehensive Foundation. Prentice Hall, Upper Saddle RiverGoogle Scholar
  9. Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1):489–501CrossRefGoogle Scholar
  10. Khaki M, Yusoff I, Islami N (2015) Simulation of groundwater level through artificial intelligence system. Environ Earth Sci 73(12):8357–8367CrossRefGoogle Scholar
  11. Kisi O, Shiri J (2012) Wavelet and neuro-fuzzy conjunction model for predicting water table depth fluctuations. Hydrol Res 43(3):286–300CrossRefGoogle Scholar
  12. Mayilvaganan MK, Naidu KB (2011) Application of artificial neural network for the prediction of groundwater level in hard rock region. In Trends in Computer Science, Engineering and Information Technology (673–682). Springer, Berlin: HeidelbergGoogle Scholar
  13. Moeeni H, Bonakdari H, Ebtehaj I (2017) Integrated SARIMA with neuro-fuzzy systems and neural networks for monthly inflow prediction. Water Resour Manag 31(7):2141–2156CrossRefGoogle Scholar
  14. Moore EH (1920) On the reciprocal of the general algebraic matrix. Bull Am Math Soc 26(9):394–395CrossRefGoogle Scholar
  15. Nalarajan NA, Mohandas C (2015) Groundwater level prediction using M5 model trees. J Inst Eng (India): A 96(1):57–62Google Scholar
  16. Nayak PC, Rao YS, Sudheer KP (2006) Groundwater level forecasting in a shallow aquifer using artificial neural network approach. Water Resour Manag 20(1):77–90CrossRefGoogle Scholar
  17. Nourani V, Hosseini Baghanam A, Adamowski J, Kisi O (2014) Applications of hybrid wavelet–artificial intelligence models in hydrology: a review. J Hydrol 514:358–377CrossRefGoogle Scholar
  18. Rajesh R, Prakash JS (2011) Extreme learning machines-a review and state-of-the-art. Int J Wisdom Based Comput 1(1):35–49Google Scholar
  19. Shirmohammadi B, Vafakhah M, Moosavi V, Moghaddamnia A (2013) Appl Sev data driven tech predicting Groundw level. Water Resour Manag 27:419–432CrossRefGoogle Scholar
  20. Silhavy R, Silhavy P, Prokopova Z (2017) Analysis and selection of a regression model for the use case points method using a stepwise approach. J Syst Softw 125:1–14CrossRefGoogle Scholar
  21. Singh RM (2012) Wavelet-ANN model for flood events, Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) Springer, India. 165–175Google Scholar
  22. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359CrossRefGoogle Scholar
  23. Vapnik VN (1998) Statistical learning theory. Wiley, New YorkGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Maryam Malekzadeh
    • 1
  • Saeid Kardar
    • 2
    Email author
  • Keivan Saeb
    • 3
  • Saeid Shabanlou
    • 4
  • Lobat Taghavi
    • 1
  1. 1.Department of Environmental Science, Faculty of Natural Resources and Environment, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Architecture, Faculty of Civil, Art and Architecture, Science and Research BranchIslamic Azad UniversityTehranIran
  3. 3.Department of Environment, Tonekabon BranchIslamic Azad UniversityTonekabonIran
  4. 4.Department of Water Engineering, Kermanshah BranchIslamic Azad UniversityKermanshahIran

Personalised recommendations