Abstract
The conventional forward RBF network construction methods, such as Orthogonal Least Squares (OLS) and the Fast Recursive Algorithm (FRA), can produce a sparse network with satisfactory generalization capability. However, the RBF width, as a nonlinear parameter in the network, is not easy to determine. In the aforementioned methods, the width is always pre-determined, either by trail-and-error, or generated randomly. This will inevitably reduce the network performance, and more RBF centres may then be needed to meet a desired modelling specification. This paper investigates a new forward construction algorithm for RBF networks. It utilizes the Particle Swarm Optimization (PSO) method to search for the optimal RBF centres and their associated widths. The efficiency of this network construction procedure is retained within the forward construction scheme. Numerical analysis shows that the FRA with PSO included only needs about two thirds of the computation involved in a PSO assisted OLS algorithm. The effectiveness of the proposed technique is confirmed by a numerical simulation example.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blum, C., Merkle, D.: Swarm intelligence: introduction and applications. Springer, New York (2008)
Chen, S., Cowan, C.F.N., Grant, P.M.: Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks 2(2), 302–309 (1991)
Chen, S., Hong, X., Harris, C.J.: Sparse kernel density construction using orthogonal forward regression with leave-one-out test score and local regularization. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(4), 1708–1717 (2004)
Chen, S., Hong, X., Luk, B.L., Harris, C.J.: Non-linear system identification using particle swarm optimisation tuned radial basis function models. International Journal of Bio-Inspired Computation 1(4), 246–258 (2009)
Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proc. Congress on Evolutionary Computation, vol. 1, pp. 84–88 (2000)
Hong, X., Sharkey, P.M., Warwick, K.: Automatic nonlinear predictive model-construction algorithm using forward regression and the press statistic. IEE Proceedings: Control Theory and Applications 150(3), 245–254 (2003)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proc. IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE, Australia (1995)
Li, K., Peng, J.X., Bai, E.W.: A two-stage algorithm for identification of nonlinear dynamic systems. Automatica 42(7), 1189–1197 (2006)
Li, K., Peng, J.X., Irwin, G.W.: A fast nonlinear model identification method. IEEE Transactions on Automatic Control 50(8), 1211–1216 (2005)
Li, Y.H., Qiang, S., Zhuang, X.Y., Kaynak, O.: Robust and adaptive backstepping control for nonlinear systems using RBF neural networks. IEEE Transactions on Neural Networks 15(3), 693–701 (2004)
McLoone, S., Brown, M.D., Irwin, G.W., Lightbody, G.: A hybrid linear/nonlinear training algorithm for feedforward neural networks. IEEE Transactions on Neural Networks 9(4), 669–684 (1998)
Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Networks 1(1), 4–27 (1990)
Nelles, O.: Nonlinear System Identification. Springer, Heidelberg (2001)
Rajakarunakaran, S., Devaraj, D., Suryaprakasa Rao, K.: Fault detection in centrifugal pumping systems using neural networks. International Journal of Modelling, Identification and Control 3(2), 131–139 (2008)
Sutanto, E.L., Mason, J.D., Warwick, K.: Mean-tracking clustering algorithm for radial basis function centre selection. International Journal of Control 67(6), 961–977 (1997)
Tipping, M.E.: Sparse baesian learning and the relevance vector machine. Journal of Machine Learning Research 1(3), 211–244 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Deng, J., Li, K., Irwin, G.W., Fei, M. (2010). Fast Forward RBF Network Construction Based on Particle Swarm Optimization. In: Li, K., Fei, M., Jia, L., Irwin, G.W. (eds) Life System Modeling and Intelligent Computing. ICSEE LSMS 2010 2010. Lecture Notes in Computer Science, vol 6329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15597-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-15597-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15596-3
Online ISBN: 978-3-642-15597-0
eBook Packages: Computer ScienceComputer Science (R0)