Forecasting Daily Water Demand Using Fuzzy Cognitive Maps
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.
KeywordsForecasting water demand Fuzzy cognitive maps
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.
- 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
- 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
- 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
- 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
- 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
- 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)CrossRefGoogle Scholar