Investigation of Internal Functioning of the Radial-Basis-Function Neural Network River Flow Forecasting Models
Publication: Journal of Hydrologic Engineering
Volume 14, Issue 3
Abstract
This paper deals with the challenging problem of hydrological interpretation of the internal functioning of artificial neural networks (ANNs) by extracting knowledge from their solutions. The neural network used in this study is based on the structure of the radial-basis-function neural network (RBFNN), which is considered as an alternative to the multilayer perceptron for solving complex modeling problems. This network consists of input, hidden, and output layers. The network is trained using the daily data of two catchments having different characteristics and from two different regions in the world. The present day and antecedent observed discharges are used as inputs to the network to forecast the flow one day ahead. A range of quantitative and qualitative techniques are used for hydrological interpretation of the internal functioning by examining the responses of the hidden layer nodes. The results of the study show that a single hidden layered RBFNN is an effective tool to forecast the daily flows and that the activation of the hidden layer nodes are far from arbitrary, but appear to represent flow components of the predicted hydrograph. The results of the study confirm that the three nodes in the hidden layer of this model effectively divide the input data space in such a way that the contribution from each node dominates in one of the flow domains—low, medium, or high—and form, in a crude manner, the base flow, interflow and surface runoff components of the hydrograph.
Get full access to this article
View all available purchase options and get full access to this article.
References
Chau, K. W. (2006). “Particle swarm optimization training algorithm for ANNs in stage prediction of Shing Mun River.” J. Hydrol., 329(3–4), 363–367.
Chau, K. W., Wu, C. L., and Li, Y. S. (2005). “Comparison of several flood forecasting models in Yangtze River.” J. Hydrol. Eng., 10(6), 485–491.
Chen, S., and Billings, S. A. (1989). “Extended model set, global data and threshold model identification of several nonlinear systems.” Int. J. Control, 50(5), 1897–1923.
Chen, S., Billings, S. A., Cowen, C. F. N., and Grant, P. M. (1990). “Nonlinear systems identification using radial-basis functions.” Int. J. Syst. Sci., 21(12), 77–93.
Coppola, J. E., Poulton, M., Charles, E., Dustman, J., and Szidarovszky, F. (2003). “Application of artificial neural networks to complex groundwater management problems.” Nat. Resour Res., 12(4), 303–320.
Dawson, C. W., Abrahart, R. J., Shamseldin, A. Y., and Wilby, R. L. (2006). “Flood estimation at ungauged sites using artificial neural networks.” J. Hydrol., 319(1–4), 391–409.
De Vos, N. J., and Rientjes, T. H. M. (2005). “Constraints of artificial neural networks for rainfall-runoff modelling: trade-offs in hydrological state representation and model evaluation.” Hydrology Earth Syst. Sci., 9, 111–126.
Dibike, Y. B., Solomatine, D. P., and Abbott, M. B. (1999). “On the encapsulation of numerical-hydraulic models in artificial neural network.” J. Hydraul. Res., 37(2), 147–161.
Fernando, A. K., and Shamseldin, A. Y. (2007). “Role of hidden neurons in a RBF type ANN in stream flow forecasting.” MODSIM 2007—Int. Congress on Modelling and Simulation, 2306–2311.
Fernando, D. A. K., and Jayawardena, A. W. (1998). “Runoff forecasting using RBF networks with OLS algorithm.” J. Hydrol. Eng., 3(3), 203–209.
Garson, G. D. (1991). “Interpreting neural-network connection weights.” AI Expert, 6(4), 46–51.
Gaume, E., and Gosset, R. (2003). “Over-parameterisation, a major obstacle to the use of artificial neural networks in hydrology?” Eur. J. Emerg. Med., 7(5), 693–706.
Hartman, E. J., Keeler, J. D., and Kowalski, J. M. (1990). “Layered neural networks with Gaussian hidden units as universal approximations.” Neural Comput., 2(2), 210–215.
Hayking, S. (1999). Neural networks: A comprehensive foundation, 2nd Ed., Prentice-Hall, N.J.
Jain, A., Sudheer, A. P., and Srinivasulu, S. (2004). “Identification of physical processes inherent in artificial neural network rainfall runoff models.” Hydrolog. Process., 18(3), 571–581.
Jayawardena, A. W., and Fernando, D. A. K. (1998). “Use of radial-basis function type artificial neural networks for runoff simulation.” Comput. Aided Civ. Infrastruct. Eng., 13(2), 91–99.
Leonard, J. A., Kramer, M. A., and Unger, L. H. (1992). “Using radial-basis functions to approximate a function and its error bounds.” IEEE Trans. Neural Netw., 3(4), 624–627.
Lozowski, A., Cholewo, T. J., and Zurada, J. M. (1996). “Crisp rule extraction from perceptron network classifiers.” IEEE Int. Conf. on Neural Networks: Plenary, Panel and Special Sessions, 94–99.
Luo, F. L., and Unbehauen, R. (1999). Applied neural networks for signal processing, Cambridge University Press, Cambridge, U.K.
Park, J., and Sandberg, I. W. (1991). “Universal approximations using radial-basis-function networks.” Neural Comput., 3(2), 246–257.
Park, J., and Sandberg, I. W. (1993). “Approximation and radial-basis function networks.” Neural Comput., 5(2), 305–316.
Rabuñal, J. R., Dorado, J., Pazos, A., Pereira, J., and Rivero, D. (2004). “A new approach to the extraction of ANN rules and to their generalization capacity through GP.” Neural Comput., 16(7), 1483–1523.
Shamseldin, A. Y., Abrahart, R. J., and See, L. M. (2005). “Neural network river discharge forecasts: An empirical investigation of hidden unit processing functions based on two different catchments.” International Conf. on Neural Networks.
Shepherd, T. J., and Broomhead, D. S. (1990). “Nonlinear signal processing using radial-basis functions.” SPE Adv. Signal Process. Algorithms, Architectures, and Implementations, 1348, 51–61.
Specht, D. F. (1991). “A general regression neural network.” IEEE Trans. Neural Netw., 2(6), 568–576.
Sudheer, K. P., and Jain, S. K. (2003). “Radial basis function neural network for modeling rating curves.” J. Hydrol. Eng., 8(3), 161–164.
Sutcliffe, J. V., and Parks, Y. P. (1999). “The hydrology of the Nile.” IAHS Spec. Publ., 5, 179.
Tickle, A., Andrews, R., Golea, M., and Diederich, J. (1998). “The truth will come to light: Directions and challenges in extracting knowledge embedded within trained artificial neural network.” IEEE Trans. Neural Netw., 9(6), 1057–1068.
Wilby, R. L., Abrahart, R. J., and Dawson, C. W. (2003). “Detection of conceptual model rainfall-runoff processes inside an artificial neural network.” Hydrol. Sci. J., 48(2), 163–181.
Wu, J. S., Han, J., Annambhotla, S., and Bryant, S. (2005). “Artificial neural networks for forecasting watershed runoff and stream flows.” J. Hydrol. Eng., 10(3), 216–222.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Sep 10, 2007
Accepted: Jul 3, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.