Abstract
B-spline neural network (BSNN), a type of basis function neural network, is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of an artificial immune network inspired optimization method ( the opt-aiNet ( to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods useful for building a good BSNN model for the nonlinear identification of an experimental nonlinear ball-and-tube system.
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
Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks 1(1), 4–27 (1990)
Karayiannis, N.B., Randolph-Gips, M.M.: On the construction and training of reformulated radial basis function neural networks. IEEE Transactions on Neural Networks 14(14), 835–846 (2003)
Mcloone, S., et al.: A hybrid linear/nonlinear training algorithm for feedforward neural networks. IEEE Transactions on Neural Networks 9(4), 669–684 (1998)
Sierakowski, C.A., Guerra, F.A., Coelho, L.S.: Particle swarm optimization approach for multi-step-ahead prediction using radial basis function neural network. In: Proceedings of 16th IFAC World Congress, Prague, Czech Republic (2005)
Yingwei, L., Sundararajsn, N., Saratchandran, P.: Identification of time-varying nonlinear systems using minimal radial basis function neural networks. IEE Proc.-Control Theory Applications 144(2), 202–208 (1997)
Harris, C.J., Moore, C.G., Brown, M.: Intelligent control: aspects of fuzzy logic and neural nets. World Scientific, Singapore (1993)
Zhang, Q., Benveniste, A.: Wavelet networks. IEEE Transactions on Neural Networks 3(6), 889–898 (1992)
Lightbody, G., et al.: Neural modelling of chemical plant using MLP and B-spline networks. Control Engineering Practice 5(11), 1501–1515 (1997)
Newmann, W.M., Sproull, R.F.: Principles of interactive computer graphics. McGraw-Hill, New York (1979)
Wang, K., Lei, B.: Using B-splines neural network to extract fuzzy rules for a centrifugal pump monitoring. Journal of Intelligent Manufacturing 12(1), 5–11 (2001)
Wang, H., Oyebande, B.: On the application of neural network modeling to a wet end chemical process in paper making. In: Proceedings of IEEE Conference on Control Applications, Albany, NY, pp. 657–662. IEEE Computer Society Press, Los Alamitos (1995)
Starrenburg, G., et al.: Learning feedforward controller for a mobile robot vehicle. Control Engineering Practice 4(9), 1221–1230 (1996)
Zhang, J., Knoll, A.: Designing fuzzy controllers by rapid learning. Fuzzy Sets and Systems 101, 287–301 (1999)
Yiu, K.F.C., et al.: Nonlinear system modeling via knot-optimizing B-spline networks. IEEE Trans. on Neural Networks 12(4), 1013–1022 (2001)
Saranli, A., Baykal, B.: Complexity reduction in radial basis function (RBF) networks by using radial B-spline functions. Neurocomputing 18(1-3), 183–194 (1998)
Shimojima, K., Fukuda, T., Arai, F.: Self-tuning fuzzy inference based on spline function. In: Proceedings of IEEE International Conference on Fuzzy Systems, Orlando, FL, USA, pp. 690–695. IEEE Computer Society Press, Los Alamitos (1994)
Chua, V.K., Tomizuka, M.: Rule generation for fuzzy systems based on B-splines. In: Proc. IEEE Int. Conference on Neural Networks, Perth, Australia, pp. 608–611. IEEE Computer Society Press, Los Alamitos (1995)
Chan, C.W., et al.: An adaptive learning rate for the training of B-spline networks. In: Proc. UKACC Int. Conf. Control, Swansea, UK, pp. 342–347 (1998)
Wang, W.-Y., et al.: GA-based learning of BMF fuzzy-neural network. In: Proc. Int. Conference on Fuzzy Systems, Honolulu, HI, USA, pp. 1234–1238 (2002)
Coelho, L.S., Krohling, R.A.: Nonlinear system identification based on B-spline neural network and modified particle swarm optimization. In: Proc.IEEE World Conference on Computational Intelligence (WCCI), Int. Joint-Conf. on Neural Networks, Vancouver, Canada, IEEE, Los Alamitos (2006)
Ishida, Y., et al. (eds.): Immunity-based systems – intelligent systems by artificial immune systems (in Japonese). Corona Pub. Co., Tokyo (1998)
Dasrupta, D. (ed.): Artificial immune systems and their applications. Springer, Heidelberg (1999)
De Castro, L.N., Timmis, J.I.: Artificial immune systems as a novel soft computing paradigm. Soft Computing Journal 7(7), 526–544 (2003)
De Castro, L.N., Von Zuben, F.: AINET: an artificial immune network for data analysis. In: Abbas, H., Sarker, R., Newton, C. (eds.) Data Mining: a heuristic approach, Idea Group Publishing, Hershey (2001)
De Castro, L.N., Timmis, J.: An artificial immune network for multimodal function optimization. In: Proc. IEEE Congress on Evolutionary Computation, Hawaii, USA, pp. 699–704. IEEE Computer Society Press, Los Alamitos (2002)
Timmis, J., Edmonds, C.: A comment on opt-AiNET: an immune network algorithm for optimisation. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 308–317. Springer, Heidelberg (2004)
Campelo, F., et al.: A modified immune network algorithm for multimodal electromagnetic problems. IEEE Transactions on Magnetics 42(4), 1111–1114 (2006)
Schaible, B., Xie, H., Lee, Y.C.: Fuzzy logic models for ranking process effects. IEEE Transactions on Fuzzy Systems 5(4), 545–556 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
dos Santos Coelho, L., Assunção, R. (2007). B-Spline Neural Network Using an Artificial Immune Network Applied to Identification of a Ball-and-Tube Prototype. In: Saad, A., Dahal, K., Sarfraz, M., Roy, R. (eds) Soft Computing in Industrial Applications. Advances in Soft Computing, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70706-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-70706-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70704-2
Online ISBN: 978-3-540-70706-6
eBook Packages: EngineeringEngineering (R0)