Skip to main content

Forecasting Daily Water Demand Using Fuzzy Cognitive Maps

  • Conference paper
  • First Online:
Time Series Analysis and Forecasting

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

In this chapter, we describe the design of a multi-regressive forecasting model based on fuzzy cognitive maps (FCMs). Growing window approach and 1-day ahead forecasting are assumed. The proposed model is retrained every day as more data become available. To improve forecasting accuracy, mean daily temperature and precipitation are applied as additional explanatory variables. The designed model is trained and tested using data gathered from a water distribution system. Comparative experiments provide evidence for the superiority of the proposed approach over the selected state-of-the-art competitive methods.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adamowski, J., Adamowski, K., Prokoph, A.: A spectral analysis based methodology to detect climatological influences on daily urban water demand. Math. Geosci. 45(1), 49–68 (2013)

    Article  MathSciNet  Google Scholar 

  2. Bianco, V., Manca, O., Nardini, S.: Electricity consumption forecasting in Italy using linear regression models. Energy 34(9), 1413–1421 (2009)

    Article  Google Scholar 

  3. Cortez, P., Rocha, M., Neves, J.: Genetic and evolutionary algorithms for time series forecasting. In: Engineering of Intelligent Systems, 14th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, IEA/AIE 2001, Budapest, Hungary, June 4–7, 2001, Proceedings, pp. 393–402 (2001)

    Google Scholar 

  4. Cowpertwait, P.S.P., Metcalfe, A.V.: Introductory Time Series with R, 1st edn. Springer, New York (2009)

    MATH  Google Scholar 

  5. Dickerson, J., Kosko, B.: Virtual worlds as fuzzy cognitive maps. Presence 3(2), 173–189 (1994)

    Article  Google Scholar 

  6. Dickey, D.A., Fuller, W.A.: Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74(366), 427–431 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. Donkor, E., Mazzuchi, T., Soyer, R., Alan Roberson, J.: Urban water demand forecasting: review of methods and models. J. Water Resour. Plan. Manag. 140(2), 146–159 (2014)

    Article  Google Scholar 

  8. Du, W., Leung, S.Y.S., Kwong, C.K.: A multiobjective optimization-based neural network model for short-term replenishment forecasting in fashion industry. Neurocomputing 151(Part 1), 342–353 (2015)

    Google Scholar 

  9. Froelich, W., Juszczuk, P.: Predictive capabilities of adaptive and evolutionary fuzzy cognitive maps - a comparative study. In: Nguyen, N.T., Szczerbicki, E. (eds.) Intelligent Systems for Knowledge Management, Studies in Computational Intelligence, vol. 252, pp. 153–174. Springer, New York (2009)

    Google Scholar 

  10. Froelich, W., Salmeron, J.L.: Evolutionary learning of fuzzy grey cognitive maps for the forecasting of multivariate, interval-valued time series. Int. J. Approx. Reason. 55(6), 1319–1335 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Froelich, W., Papageorgiou, E.I., Samarinas, M., Skriapas, K.: Application of evolutionary fuzzy cognitive maps to the long-term prediction of prostate cancer. Appl. Soft Comput. 12(12), 3810–3817 (2012)

    Article  Google Scholar 

  12. Glykas, M. (ed.): Fuzzy Cognitive Maps, Advances in Theory, Methodologies, Tools and Applications. Studies in Fuzziness and Soft Computing. Springer, Berlin (2010)

    MATH  Google Scholar 

  13. Han, A., Hong, Y., Wan, S.: Autoregressive conditional models for interval-valued time series data. In: The 3rd International Conference on Singular Spectrum Analysis and Its Applications, p. 27 (2012)

    Google Scholar 

  14. Johansen, S.: Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models. Econometrica 59(6), 1551–1580 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  15. Juszczuk, P., Froelich, W.: Learning fuzzy cognitive maps using a differential evolution algorithm. Pol. J. Environ. Stud. 12(3B), 108–112 (2009)

    Google Scholar 

  16. Kosko, B.: Fuzzy cognitive maps. Int. J. Man Mach. Stud. 24, 65–75 (2010)

    Article  MATH  Google Scholar 

  17. Kwiatkowski, D., Phillips, P.C., Schmidt, P., Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econ. 54(1–3), 159–178 (1992)

    Article  MATH  Google Scholar 

  18. Ljung G.M, Box G.E.P.: On a measure of lack of fit in time series models. Biometrika 65(2), 297–303 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lu, W., Pedrycz, W., Liu, X., Yang, J., Li, P.: The modeling of time series based on fuzzy information granules. Expert Syst. Appl. 41, 3799–3808 (2014)

    Article  Google Scholar 

  20. MatíAs, J.M., Febrero-Bande, M., González-Manteiga, W., Reboredo, J.C.: Boosting garch and neural networks for the prediction of heteroskedastic time series. Math. Comput. Model. 51(3–4), 256–271 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Papageorgiou, E.I., Froelich, W.: Application of evolutionary fuzzy cognitive maps for prediction of pulmonary infections. IEEE Trans. Inf. Technol. Biomed. 16(1), 143–149 (2012)

    Article  Google Scholar 

  22. Papageorgiou, E.I., Froelich, W.: Multi-step prediction of pulmonary infection with the use of evolutionary fuzzy cognitive maps. Neurocomputing 92, 28–35 (2012)

    Article  Google Scholar 

  23. Pearson, R.: Outliers in process modelling and identification. IEEE Trans. Control Syst. Technol. 10(1), 55–63 (2002)

    Article  Google Scholar 

  24. Pulido-Calvo, I., Gutiérrez-Estrada, J.C.: Improved irrigation water demand forecasting using a soft-computing hybrid model. Biosyst. Eng. 102(2), 202–218 (2009)

    Article  Google Scholar 

  25. Pulido-Calvo, I., Montesinos, P., Roldán, J., Ruiz-Navarro, F.: Linear regressions and neural approaches to water demand forecasting in irrigation districts with telemetry systems. Biosyst. Eng. 97(2), 283–293 (2007)

    Article  Google Scholar 

  26. Qi, C., Chang, N.B.: System dynamics modeling for municipal water demand estimation in an urban region under uncertain economic impacts. J. Environ. Manag. 92(6), 1628–1641 (2011)

    Article  Google Scholar 

  27. Riedmiller, M., Braun, H.: A direct adaptive method for faster backpropagation learning: the RPROP algorithm. In: Proceedings of the IEEE International Conference on Neural Networks (ICNN), pp. 586–591 (1993)

    Google Scholar 

  28. Stach, W., Kurgan, L., Pedrycz, W., Reformat, M.: Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst. 153(3), 371–401 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Stach, W., Kurgan, L.A., Pedrycz, W.: Numerical and linguistic prediction of time series with the use of fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 16(1), 61–72 (2008)

    Article  Google Scholar 

  30. Stach, W., Kurgan, L., Pedrycz, W.: A divide and conquer method for learning large fuzzy cognitive maps. Fuzzy Sets Syst. 161, 2515–2532 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Teräsvirta, T., Lin, C.F., Granger, C.W.J.: Power of the neural network linearity test. J. Time Ser. Anal. 14(2), 209–220 (1993)

    Article  Google Scholar 

  32. R Development Core Team (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org

    Google Scholar 

  33. Homenda W., Jastrzȩbska A., Pedrycz W.: Joining concept’s based fuzzy cognitive map model with moving window technique for time series modeling. In: IFIP International Federation for Information Processing, CISIM 2014. Lecture Notes in Computer Science, vol. 8838. pp. 397–408 (2014)

    Google Scholar 

  34. Homenda W., Jastrzȩbska A., Pedrycz W.: Modeling time series with fuzzy cognitive maps. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 2055–2062 (2014)

    Google Scholar 

  35. Homenda W., Jastrzȩbska A., Pedrycz W.: Time series modeling with fuzzy cognitive maps: simplification strategies, the case of a posteriori removal of nodes and weights. In: IFIP International Federation for Information Processing, CISIM 2014. Lecture Notes in Computer Science, vol. 8838, pp. 409–420 (2014)

    Article  Google Scholar 

  36. Yasar, A., Bilgili, M., Simsek, E.: Water demand forecasting based on stepwise multiple nonlinear regression analysis. Arab. J. Sci. Eng. 37(8), 2333–2341 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The work was supported by ISS-EWATUS project which has received funding from the European Union’s Seventh Framework Programme for research, technological development, and demonstration under grant agreement no. 619228. The authors would like to thank the water distribution company in Sosnowiec (Poland) for gathering water demand data and the personal of the weather station of the University of Silesia for collecting and preparing meteorological data.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jose L. Salmeron .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Salmeron, J.L., Froelich, W., Papageorgiou, E.I. (2016). Forecasting Daily Water Demand Using Fuzzy Cognitive Maps. In: Rojas, I., Pomares, H. (eds) Time Series Analysis and Forecasting. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28725-6_24

Download citation

Publish with us

Policies and ethics