Abstract
This paper demonstrates how genetic programming can be used for solving problems in the field of non-linear system identification of rational models. By using a two-tree structure rather than introducing the division operator in the function set, this genetic programming approach is able to determine the “true” model structure of the system under investigation. However, unlike use of the polynomial, which is linear in the parameters, use of rational model is non-linear in the parameters and thus noise terms cannot be estimated properly. By means of a second optimisation process (real-coded GA) which has the aim of tunning the coefficients to the “true” values, these parameters are then correctly computed. This approach is based upon the well-known NARMAX model representation, widely used in non-linear system identification.
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
Angeline, P.J.: An Investigation into the Sensitivity of Genetic Programming to the Frequency of Leaf Selection During Subtree Crossover. In: Koza, et al. (eds.) Annual GP Conference, pp. 21–29 (1996)
Billings, S.A., Chen, S.: Identification of Non-Linear Rational Systems Using a Prediction Error Estimation Algorithm. Int. J. Systems Sci. 20(3), 467–494 (1989)
Billings, S.A., Zhu, Q.M.: Rational Model Identification Using an Extended Least-Squares Algorithm. Int. J. Control 54(3), 529–546 (1991)
Chen, S., Billings, S.A.: Representation of Non-Linear Systems: the NARMAX Model. Int. J. Control 49(3), 1013–1032 (1989)
Iba, H., Kurita, T., de Garis, H., Sato, T.: System Identification Using Structured Genetic Algorithms. In: Proc. of the 5th ICGA, pp. 467–491 (1993)
Iba, P.L., de Garis, H., Sato, T.: Genetic Programming Using a Minimum Description Length. In: Kinnear (ed.) Advance in Genetic Programming, pp. 265–284 (1994)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)
Langdon, W.B.: Evolving Data Structures with Genetic Programming. In: Eshelman (ed.) 6th ICGA, pp. 295–302 (1995)
Leontaritis, I.J., Billings, S.A.: Input-Output Parametric Models for Non-Linear Systems. Part I and Part II. Int. J. Control 41(2), 304–344 (1985)
Ljung, L.S.: System Identification: Theory for the User. Prentice Hall, Englewood Cliffs (1987)
Marenbach, P., Bettenhausen, K.D., Freyer, S.: Signal Path Oriented Approach for Generation of Dynamic Process Models. In: Koza, et al.: pp. 327–332 (1996)
McKay, B., Willis, M.J., Barton, G.W.: Using a Tree Structures Genetic Algorithm to Perform Symbolic Regression. In: 1st. Int. Conf. on Genetic Algorithms in Engineering Systems: Innovations and Applications, pp. 487–492. IEE (1995)
Mühlenbetn, H., Schlierkamp-voosen, D.: Predictive Models for the Breeder Genetic Algorithm. Evolutionary Computation 1(1), 25–49 (1993)
Rodríguez-Vázquez, K., Fonseca, C.M., Fleming, P.J.: An Evolutionary Approach to Non-Linear Polynomial System Identification. In: 11th IFAC Symposium on System Identification, vol. 3, pp. 1395–1400 (1997a)
Rodríguez-Vázquez, K., Fonseca, C.M., Fleming, P.J.: Multiobjective Genetic Programming: A Non-Lineat System Identification Application. In: Late Breaking Paper at the GP 1997 Conference, pp. 207–212 (1997b)
Rodríguez-Vázquez, K., Fleming, P.J.: Multiobjective Genetic Programming for Non-Linear System Identification. Electronics Letters 34(9), 930–931 (1998a)
Rodríguez-Vázquez, K., Fleming, P.J.: Multiobjective Genetic Programming for a Gas Turbine Engine Model Identification. In: International Conference on Control 1998, pp. 1385–1390 (1998b)
Schoenauer, M., Sebag, M., Jouve, T., Lamy, B., Maitouram, H.: Evolutionary Identification of Macro-Mechanical Models. In: Angeline, Kinnear (eds.) Adavances in Genetic Programming, vol. 2, pp. 467–488 (1996)
Sontag, E.D.: Polynomial Response Maps. Lectures Notes in Control and Information Sciences, vol. 13. Springer, Heidelberg (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rodríguez-Vázquez, K., Fleming, P.J. (2000). Use of Genetic Programming in the Identification of Rational Model Structures. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds) Genetic Programming. EuroGP 2000. Lecture Notes in Computer Science, vol 1802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46239-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-46239-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67339-2
Online ISBN: 978-3-540-46239-2
eBook Packages: Springer Book Archive