Modelizing a non-linear system: a computational effcient adaptive neuro-fuzzy system tool based on matlab
In a great diversity of knowledge areas, the variables that are involved in the behavior of a complex system, perform normally, a non-linear system. The search of a function that express those behavior, requires techniques as mathematics optimization techniques or others. The new paradigms introduced in the soft computing, as fuzzy logic, neuronal networks, genetics algorithms and the fusion of them like the neuro-fuzzy systems, and so on, represent a new point of view to deal this kind of problems due to the approximation properties of those systems (universal approximators).
This work shows a methodology to develop a tool based on a neuro-fuzzy system of ANFIS (Adaptive Neuro-Fuzzy Inference System) type with piecewise multilinear (PWM) behaviour (introducing some restrictions on the membership functions -triangular- chosen in the ANFIS system). The obtained tool is named PWM-ANFIS Tool, that allows modelize a n-dimensional system with one output and, also, permits a comparison between the neuro-fuzzy system modelized, a purely PWM-ANFIS model, with a generic ANFIS (Gaussian membership functions) modelized with the same tool. The proposed tool is an efficient tool to deal non-linearly complicated systems.
Keywords: ANFIS model, Function approximation, Matlab environment, Neuro-Fuzzy CAD tool, Neuro-Fuzzy modelling.
K. Ray, J. Ghoshal, Neuro fuzzy approach to pattern recognition, Neural Networks 10 (1) (1997) 161-182.
S. K. Pal, S. Mitra, Neuro-Fuzzy Pattern Recognition: Methods in Soft Computing, Wiley-Interscience, 1999.
P. Rusu, E. M. Petriu, T. E. Whalen, A. C. and. H. J. W. Spoelder, Behavior-based neuro-fuzzy controller for mobile robot navigation, IEEE Transaction on Instrumentation and Measurement 52 (4) (2003) 1335-1340.
H. Wongsuwarn, D. Laowattana, Neuro-fuzzy algorithm for a biped robotic system, World Academy of Science, Engineering and Technology 15 (2006) 138-144.
R. Babuska, H. Verbruggen, Neuro-fuzzy methods for nonlinear systems identication, Annual Reviews in Control 27 (2003) 73-85.
P. Panchariya, A. Palit, D. Popovic, A. Sharmal, Nonlinear system identication using takagi-sugeno type neuro-fuzzy model, in: Second IEEE International Conference on Intelligent Systems, IEEE, 2004, pp. 76-81.
C. Li, K.-B. Tsai, Adaptive interference signal processing with intelligent neuro-fuzzy approach, in: IC-COMP'06 Proceedings of the 10th WSEAS international conference on Computers, 2006, pp. 393-398.
S. Chabaa, A. Zeroual, J. Antari, Application of adaptive neuro-fuzzy inference systems for analyzing non-gaussian signal, in: International Conference on Multimedia Computing and Systems. ICMCS '09, 2009, pp.377 - 380.
G. Acampora, V. Loia, A proposal of ubiquitous fuzzy computing for ambient intelligence, Information Science 178 (2008) 631- 646.
Y. Kishino, T. Terada, M. Tsukamoto, T. Yoshihisa, K. Hayakawa, A. Kashitani, S. Nishio, A rule-based discovery mechanism of network topology among ubiquitous chips, in: International Conference on Pervasive Services (ICPS 05), 2005, pp. 198- 207.
Y. Kawahara, M. Minami, H.Morikawa, T. Aoyama, Design and implementation of a sensor network node for ubiquitous computing environment, in: IEEE 58th Vehicular Technology Conference. VTC 2003, Vol. 5, 2003, pp. 3005 - 3009.
J. Buckley, Sugeno type controllers are universal controllers, Fuzzy Sets Systems 53 (1) (1993) 299-303.
J. Castro, Fuzzy logic controllers are universal approximators, IEEE Transactions on Systems, Man, and Cyberbetics 25 (4) (1995) 629-635.
J. Jang, C. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing, Prentice Hall, 1997.
D. Nauck, R. Kruse, Neuro-fuzzy systems for function approximation, Fuzzy Sets and Systems 101 (1999) 261-271.
L.-X. Wang, C. Wei, Approximation accuracy of some neuro-fuzzy appoaches, IEEE Transactions on Fuzzy Systems 8 (4) (2000) 470-478.
W. Wu, L. Li, J. Yang, Y. Liub, A modied gradient-based neuro-fuzzy learning algorithm and its convergence, Information Sciences 180 (2010) 1630-1642.
G. Bosque, I. del Campo, J. Echanobe, J. Tarela, Modelling and synthesis of computational ecient adaptive neuro-fuzzy systems based on matlab, in: Springer (Ed.), Articial Neural Networks - ICANN 2008 – LNCS 5164, Vol. 2, 2008, pp. 131-140.
J.-S. Jang, Ans: Adaptive-network-based fuzzy inference system, IEEE Transactions on Systems, Man, and Cybernetics 23 (1993) 665-685.
J.-S. R. Jang, C.-T. Sun, Neuro-fuzzy modeling and control, Proceedings of the IEEE 83 (3) (1995) 378-406.
S.-K. Oh, W. Pedrycz, B.-J. Park, Relation-based neuro-fuzzy networks with evolutionary data granulation, Mathematical and Computer Modelling 40 (2004) 891-921.
B. Kosko, Fuzzy systems and universal approximators, IEEE Transactions Computing 43 (11) (1994) 1329-1333.
X.-J. Zeng, M. Singh, Approximation theory of fuzzy systems-siso case, IEEE Transactions on Fuzzy Systems 2 (2) (1994) 162-176.
X.-J. Zeng, M. Singh., Approximation theory of fuzzy systems-mimo case, IEEE Transactions on Fuzzy Systems 3 (2) (1995) 219-235.
X.-J. Zeng, M. Singh, Approximation accuracy analys of fuzzy systems as function approximators, IEEE Transactions on Fuzzy Systems 4 (1) (1996) 44-63.
R. Rovatti, Fuzzy piecewise multilinear and piecewise linear systems as universal approximator in sobolev norms, IEEE Transactions on Fuzzy Systems 6 (2) (1998) 235-249.
S. Cao, N. Rees, G. Feng, Mamdani-type fuzzy controllers are universal fuzzy approximators, IEEE Transactions Computer 123 (3) (2001) 359-367.
T. Takagi, M. Sugeno, Fuzzy identication of systems and its applications to modelling and control, IEEE Transactions on Systems, Man and Cybernetics 15 (1985) 116-132.
M. Sugeno, G. Kang, Structure identication of fuzzy model, Fuzzy Sets Systems 28 (1) (1988) 15-33.
W. Pedrycz, Why triangular membership functions?, Fuzzy Sets and Systems 64 (1994) 21-30.
K. Basterretxea, I. del Campo, J. M. Tarela, G. Bosque, An experimental study on non-linear function computation for neural/fuzzy hardware design, IEEE Transactions on Neural Networks 18 (2007) 266-283.
G. Bosque, I. del Campo, J. Echanobe, Ecient hardware/software implementation of a neuro-fuzzy system on a sopc, in: Recent Advanced in Soft Computing (RASC), 2006.
J. Echanobe, I. del Campo, G. Bosque, An adaptive neuro-fuzzy system for ecient implementations, Information Science 178 (9) (May 2008) 2150-2162.
I. del Campo, J. Echanobe, G. Bosque, J. Tarela, Ecient hardware/software implementation of an adaptive neuro-fuzzy system, IEEE Transactions on Fuzzy Systems 16 (3) (Junne 2008) 761-778.
G. Bosque, I. del Campo, J. Echanobe, J. Tarela, Implementacin de un sistema neuro-fuzzy sobre un sopc, in: Congreso Espaol sobre Tecnologas y Lgica Fuzzy (Estylf 2004), European Society for Fuzzy Logic and Technology (EUSFLAT), 2004, pp. 587-592.
S. Lee, C. Ouyang, Neuro-fuzzy system modeling with self-constructing rule generation and hybrid svd-based learning, IEEE Transactions on Fuzzy Systems 11 (3) (2003) 341-353.