Skip to main content

Advertisement

SpringerLink
Log in

Developing a fuzzy neural network-based support vector regression (FNN-SVR) for regionalizing nitrate concentration in groundwater

  • Published:
Environmental Monitoring and Assessment Aims and scope Submit manuscript

Abstract

The aim of this study is to develop a fuzzy neural network-based support vector regression model (FNN-SVR) for mapping crisp-input and fuzzy-output variables. In this model, an artificial neural network (ANN) estimator based on multilayer perceptron (MLP) is considered as the kernel function of the SVR, whereas asymmetric triangular fuzzy H-level sets are assumed for model parameters including weight and biases of the ANN model. A genetic algorithm (GA) with real coding is implemented to optimize the model parameters during the training phase. To evaluate the efficiency and applicability of the proposed model, it is applied for simulating and regionalizing nitrate concentration in Karaj Aquifer in Iran. The goodness-of-fit criteria indicate a better performance of the FNN-SVR compared to some benchmark models such as geostatistic techniques as well as traditional SVR models with linear, quadratic, polynomial, and Gaussian kernel functions for modeling nitrate concentrations in groundwater.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Alvisi, S., & Franchini, M. (2011). Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environmental Modelling & Software, 26, 523–537.

    Article  Google Scholar 

  • Aqil, M., Kita, I., Yano, A., & Nishiyama, S. (2007). A comparative study of artificial neural networks and neuro-fuzzy in continuous modeling of the daily and hourly behaviour of runoff. Journal of Hydrology, 337, 22–34.

    Article  Google Scholar 

  • Asefa, T., & Kemblowski, M.W. (2002). Support vector machines approximation of flow and transport models in initial groundwater contamination network design. EOS. Transactions of the American Geophysical Union, Fall Meeting 2002, abstract #H72D-0882.

  • Asefa, T., Kemblowski, M. W., Urroz, G., McKee, M., & Khalil, A. (2004). Support vectors-based groundwater head observation networks design. Water Resources Research. doi:10.1029/ 2004WR003304.

    Google Scholar 

  • Asefa, T., Kemblowski, M. W., Lall, U., & Urroz, G. (2005). Support vector machines for nonlinear state space reconstruction: application to the Great Salt Lake time series. Water Resources Research. doi:10.1029/2004WR003785.

    Google Scholar 

  • Asefa, T., Kemblowski, M., McKee, M., & Khalil, A. (2006). Multi-time scale stream flow predictions: the support vector machines approach. Journal of Hydrology, 318, 7–16.

    Article  Google Scholar 

  • Babovic, V., Keijzer, M., & Bundzel, M. (2000). From global to local modelling: a case study in error correction of deterministic models, hydroinformatics. USA: Iowa Institute of Hydraulic Research, Iowa.

    Google Scholar 

  • Behzad, M., Asghari, K., & Coppola, E. A. (2010). Comparative study of SVMs and ANNs in aquifer water level prediction. Journal of Computing in Civil Engineering ASCE, 24, 408–413.

    Article  Google Scholar 

  • Cawley, G. C., & Talbot, N. L. C. (2004). Fast exact leave-one-out cross-validation of sparse least-squares support vector machines. Neural Networks, 17(10), 1467–1475.

    Article  Google Scholar 

  • Chang, F. J., & Chen, L. (2004). Real-coded genetic algorithm for rule-based flood control reservoir management. Water Resources Management, 12(3), 185–198.

    Article  Google Scholar 

  • Cherkassky, V., & Yunqian, M. Y. (2002). Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks, 17, 113–126. doi:10.1016/S0893-6080(03)00169-2.

  • Chuang, C. C. (2008). Extended support vector interval regression networks for interval input–output data. Information Sciences, 178, 871–891.

    Article  Google Scholar 

  • Dahiy, S., Singh, B., Gaur, S., Garg, V. K., & Kushwaha, H. S. (2007). Analysis of groundwater quality using fuzzy synthetic evaluation. Journal of Hazardous Materials, 147, 938–946.

    Article  Google Scholar 

  • Dibike, Y. B. (2000). Machine learning paradigms for rainfall-runoff modeling, hydroinformatics. USA: Iowa Institute of Hydraulic Research, Iowa.

    Google Scholar 

  • Dibike, Y. B., Velickov, S., Solomatine, D., & Abbott, M. B. (2001). Model induction with support vector machines: introduction and applications. Journal of Computing in Civil Engineering, 15(3), 208–216.

    Article  Google Scholar 

  • Gill, M. K., Asefa, T., Kemblowski, M. W., & McKee, M. (2006). Soil moisture prediction using support vector machines. Journal of the American Water Resources Association, 42(4), 1033–1046.

    Article  Google Scholar 

  • Gill, M. K., Asefa, T., Kaheil, Y., & McKee, M. (2007). Effect of missing data on performance of learning algorithms for hydrologic predictions: implications to an imputation technique. Water Resources Research. doi:10.1029/2006WR005298.

    Google Scholar 

  • Goldberg, D. E. (1989). A comparative analysis of selection scheme used in genetic algorithms. Foundations of genetic algorithms (pp. 69–93). San Mateo: Morgan Kaufman.

    Google Scholar 

  • Han, D., Chan, L., & Zhu, N. (2007). Flood forecasting using support vector machines. Journal of Hydroinformatics, 9(4), 267–276.

    Article  Google Scholar 

  • Hao, P. Y., & Chiang, J. H. (2007). A fuzzy model of support vector regression machine. International Journal of Fuzzy Systems, 9(1), 45–50.

    Google Scholar 

  • Hao, P. Y., & Chiang, J. H. (2008). Fuzzy regression analysis by support vector learning approach. IEEE Transactions on Fuzzy Systems, 16(2), 428–441.

    Article  Google Scholar 

  • Holland, J. H. (1992). Genetic algorithms. Scientific American, 267(1), 66–72.

    Article  Google Scholar 

  • Hong, D. H., & Hwang, C. (2003a). Support vector fuzzy regression machines. Fuzzy Sets and Systems, 138(2), 271–281.

    Article  Google Scholar 

  • Hong, D. H., & Hwang, C. (2003b). Support vector fuzzy regression machines. Fuzzy Sets and Systems, 138, 271–281.

    Article  Google Scholar 

  • Hua, Z. S., & Zhang, B. (2006). A hybrid support vector machines and logistic regression approach for forecasting intermittent demand of spare parts. Applied Mathematics and Computation, 181, 1035–1048.

    Article  Google Scholar 

  • Isaaks, E. H., & Srivastava, R. M. (1989). An introduction to applied geostatistics (p. 561). Oxford: Oxford University Press.

    Google Scholar 

  • Jang, J. S. R., Sun, C. T., & Mizutani, E. (1997). Neuro-fuzzy and soft computing, a computational approach to learning and machine intelligence. USA, NJ: Prentice Hall.

  • Jeng, J.T., & Lee, T.T. (1999). Support vector machines for the fuzzy neural networks, In: Proc. IEEE International Conference on System, Man and Cybernetics (IEEE SMC’99), 115–120.

  • Jeng, J. T., Chuang, C. C., & Su, S. F. (2003). Support vector interval regression networks for interval regression analysis. Fuzzy Sets and Systems, 138, 283–300.

    Article  Google Scholar 

  • Jiang, B. T., & Zhao, F. Y. (2013). Combination of support vector regression and artificial neural networks for prediction of critical heat flux. International Journal of Heat and Mass Transfer, 62, 481–494.

    Article  Google Scholar 

  • Journel, A. G., & Huijbregts, C. J. (1978). Mining Geostatistics. San Francisco: New York Academic Press.

    Google Scholar 

  • Juang, C. F., & Hsieh, C. D. (2009). TS-fuzzy system-based support vector regression. Fuzzy Sets and Systems, 160, 2486–2504.

    Article  Google Scholar 

  • Kacprzyk, J., & Fedrizzi, M. (1992). Fuzzy regression analysis. Heidelberg: Physics-Verlag.

    Google Scholar 

  • Kalteh, A. M. (2013). Monthly river flow forecasting using artificial neural network and support vector regression models coupled with wavelet transform. Computers & Geosciences, 54, 1–8.

    Article  Google Scholar 

  • Karatzoglou, A., Meyer, D., & Hornik, K. (2006). Support vector machine in R. Journal of Statistical Software, 15(9), 1–28.

    Google Scholar 

  • Kazemi, S. M., & Hosseini, S. M. (2011). Comparison of spatial interpolation methods for estimating heavy metals in sediments of Caspian Sea. Expert Systems with Applications, 38, 1632–1649.

    Article  Google Scholar 

  • Kecman, V. (2001). Learning and soft computing: support vector machines, neural networks and fuzzy logic models. Cambridge, MA: The MIT Press.

    Google Scholar 

  • Khan, M. S., & Coulibaly, P. (2006). Application of support vector machine in lake water level prediction. Journal of Hydrologic Engineering, 11, 199–205.

    Article  Google Scholar 

  • Kholghi, M., & Hosseini, S. M. (2009). Comparison of groundwater level estimation using neuro-fuzzy and ordinary Kriging. Environmental Modeling and Assessment. doi:10.1007/s10666-008-9174-2.

    Google Scholar 

  • Krishna, B., Satyaji, R. Y. R., & Vijaya, T. (2008). Modelling groundwater levels in an urban coastal aquifer using artificial neural networks. Hydrological Processes, 22, 1180–1188.

    Article  Google Scholar 

  • Krzysztofowicz, R. (1999). Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resources Research, 35(9), 2739–2750.

    Article  Google Scholar 

  • Kumar V., & Schuhmacher M. (2005). Fuzzy uncertainty analysis in system modeling. European Symposium on Computer Aided Process Engineering, 391–396.

  • Kumar, M., & Yadav, N. (2011). Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. Computers and Mathematics with Applications, 62, 3796–3811.

    Article  Google Scholar 

  • Lin, K. P., & Pai, P. F. (2010). A fuzzy support vector regression model for business cycle predictions. Expert Systems with Applications, 37, 5430–5435.

    Article  Google Scholar 

  • Liong, S. Y., & Sivapragasam, C. (2002). Flood stage forecasting with support vector machines. Journal of the American Water Resources Association, 38(1), 173–196.

    Article  Google Scholar 

  • Ma, T. S., Sophocleous, M., & Yu, Y. S. (1999). Geostatistical applications in ground-water modeling in south–central Kansas. Journal of Hydrologic Engineering, 4(1), 57–64.

    Article  Google Scholar 

  • Maier, H. R., & Dandy, G. C. (2000). Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environmental Modeling and Software, 101–124.

  • Morshed, J., & Kaluarachchi, J. J. (2012). Parameter estimation using artificial neural network and genetic algorithm for free-product migration and recovery. Water Resources Research, 34(5), 1101–1113.

    Article  Google Scholar 

  • Nikoo, M. R. & Mahjouri, N. (2013) Water quality zoning using probabilistic support vector machines: two case studies, Water Resources Management, Springer, 27, 2577–2594

    Google Scholar 

  • Ovaska, S. J. (2005). Computationally intelligent hybrid systems. Piscataway, New Jersey: Wiley-IEEE Press.

    Google Scholar 

  • Rogers, D. (1996). Some theory and examples of genetic function approximation with comparison to evolutionary techniques. In J. Devillers (Ed.), Genetic algorithms in molecular modeling (pp. 87–107). London: Academic Press.

    Chapter  Google Scholar 

  • Schölkopf, B., & Smola, A. J. (2002). Learning with kernels: support vector machines, regularization, optimization, and beyond. Cambridge: MIT Press. 626.

    Google Scholar 

  • Shevade, S. K., Keerthi, S. S., Bhattacharyya, C., & Murthy, K. R. K. (2000). Improvements to the SMO algorithm for SVM regression. IEEE Trans on Neural Netw, 11, 1188–1193.

    Article  CAS  Google Scholar 

  • Shrestha, D. L., & Solomatine, D. P. (2006). Experiments with AdaBoost. RT, an improved boosting scheme for regression. Neural Computation, 18, 1678–1710.

    Article  CAS  Google Scholar 

  • Sivapragasam, C., Liong, S. Y., & Pasha, M. F. K. (2001). Rainfall and runoff forecasting with SSA–SVM approach. Journal of Hydroinformatics, 3(3), 141–152.

    Google Scholar 

  • Szidarovszky, F., Coppola, E. A., Long, J., Hall, A. D., & Poulton, M. M. (2007). A hybrid artificial neural network-numerical model for ground water problems. Ground Water, 45(5), 590–600.

    Article  CAS  Google Scholar 

  • Tanaka, H., Uejima, S., & Asai, K. (1982). Linear regression analysis with fuzzy model. IEEE Transactions on Systems Man and Cybernetics, 12(6), 903–907.

    Article  Google Scholar 

  • Task Committee, A. S. C. E. (2000). Artificial neural networks in hydrology. II: hydrologic applications. Journal of Hydrologic Engineering, ASCE, 5(2), 124–137.

    Article  Google Scholar 

  • Tutmez, B., Hatipoglu, Z., & Kaymak, U. (2006). Modelling electrical conductivity of groundwater using an adaptive neurofuzzy inference system. Computers & Geosciences, 32, 421–433.

    Article  CAS  Google Scholar 

  • Vapnik, V. (1995). The nature of statistical learning theory. New York: Springer-Verlag.

    Book  Google Scholar 

  • Vapnik, V. (1999). An overview of statistical learning theory. IEEE Transactions on Neural Networks, l0(5), 988–999.

    Article  Google Scholar 

  • Varma, M., & Babu, B. R. (2009). More generality in efficient multiple kernel learning. In proceedings of the 26th annual international conference on machine learning (ICML) (pp. 1065–1072). New York: ACM.

    Google Scholar 

  • Ward, M. H., deKok, T. M., Levallois, P., Brender, J., Gulis, G., Nolan, B. T., et al. (2005). Workgroup report: drinking-water nitrate and health—recent findings and research needs. Environmental Health Perspectives, 113(11), 1607–1614.

    Article  CAS  Google Scholar 

  • Winneberger, J.H. (1982). Nitrogen, Public health and the environment. Ann Arbor, Michigan: Ann Arbor Science publishers, Inc.

  • Winston, W. L., & Venkataramanan, M. (2003). Introduction to Mathematical Programming. Pacific Grove: Brooks/Cole.

    Google Scholar 

  • Wu, Q. (2011). The complex fuzzy system forecasting model based on triangular fuzzy robust wavelet m-support vector machine. Expert Systems with Applications, 38, 14478–14489.

    Article  Google Scholar 

  • Wu, C. L., & Chau, K. W. (2006). A flood forecasting neural network model with genetic algorithm. International Journal of Environment and Pollution, 28(3/4), 261–272.

    Article  Google Scholar 

  • Yao, C. C., & Yu, P. T. (2006). Fuzzy regression based on asymmetric support vector machines. Applied Mathematics and Computation, 182, 175–193.

    Google Scholar 

  • Yen, K. K., Goshray, S., & Roig, G. (1999). A linear regression model using triangular fuzzy number coefficients. Fuzzy Sets and Systems, 106, 166–177.

    Article  Google Scholar 

  • Yoon, H., Jun, S. C., Hyun, Y., Bae, G. O., & Lee, K. K. (2011). A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology, 396, 128–138.

    Article  Google Scholar 

  • Yu, X. Y., & Liong, S. Y. (2007). Forecasting of hydrology time series with ridge regression in feature space. Journal of Hydrology, 332(3–4), 290–302.

    Article  Google Scholar 

  • Yu, P. S., Chen, S. T., & Chang, I. F. (2006). Support vector regression for real-time flood stage forecasting. Journal of Hydrology, 328(3–4), 704–716.

    Article  Google Scholar 

  • Zahraie, B., & Hosseini, S. M. (2009). Development of reservoir operation policies considering variable agricultural water demands. Expert Systems with Applications, 36, 4980–4987.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Natural Geography Department, University of Tehran, Tehran, 14155-6465, Iran

    Seiyed Mossa Hosseini

  2. Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Najmeh Mahjouri

Authors
  1. Seiyed Mossa Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Najmeh Mahjouri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Seiyed Mossa Hosseini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hosseini, S.M., Mahjouri, N. Developing a fuzzy neural network-based support vector regression (FNN-SVR) for regionalizing nitrate concentration in groundwater. Environ Monit Assess 186, 3685–3699 (2014). https://doi.org/10.1007/s10661-014-3650-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10661-014-3650-8

Keywords

Search

Navigation