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Use of Genetic Programming in the Identification of Rational Model Structures

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Book cover Genetic Programming (EuroGP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1802))

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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.

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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)

    Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • Billings, S.A., Zhu, Q.M.: Rational Model Identification Using an Extended Least-Squares Algorithm. Int. J. Control 54(3), 529–546 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, S., Billings, S.A.: Representation of Non-Linear Systems: the NARMAX Model. Int. J. Control 49(3), 1013–1032 (1989)

    MATH  MathSciNet  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  • Langdon, W.B.: Evolving Data Structures with Genetic Programming. In: Eshelman (ed.) 6th ICGA, pp. 295–302 (1995)

    Google Scholar 

  • 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)

    Google Scholar 

  • Ljung, L.S.: System Identification: Theory for the User. Prentice Hall, Englewood Cliffs (1987)

    MATH  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • Mühlenbetn, H., Schlierkamp-voosen, D.: Predictive Models for the Breeder Genetic Algorithm. Evolutionary Computation 1(1), 25–49 (1993)

    Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • Rodríguez-Vázquez, K., Fleming, P.J.: Multiobjective Genetic Programming for Non-Linear System Identification. Electronics Letters 34(9), 930–931 (1998a)

    Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    Google Scholar 

  • Sontag, E.D.: Polynomial Response Maps. Lectures Notes in Control and Information Sciences, vol. 13. Springer, Heidelberg (1979)

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. DISCA-IIMAS-UNAM, P.O. Box 20-726, Alvaro Obregón, 01000, México, D.F., Mexico

    Katya Rodríguez-Vázquez

  2. Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, S1 3JD, Sheffield, United Kingdom

    Peter J. Fleming

Authors
  1. Katya Rodríguez-Vázquez
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  2. Peter J. Fleming
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Editor information

Editors and Affiliations

  1. Department of Computing and Electronic Systems, University of Essex, Wivenhoe Park, CO4 3SQ, Colchester, UK

    Riccardo Poli

  2. Department of Computer Science, Memorial University of Newfoundland, Canada

    Wolfgang Banzhaf

  3. Departments of Mathematical, Biological Sciences and Computing and Electronic Systems, University of Essex, UK

    William B. Langdon

  4. School of Computer Science, The University of Birmingham, B15 2TT, Edgbaston, Birmingham, UK

    Julian Miller

  5. Dept. of Physical Rescource Theory, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Peter Nordin

  6. School of Computing, Information Systems and Mathematics, South Bank University, SE1 0AA, London, UK

    Terence C. Fogarty

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© 2000 Springer-Verlag Berlin Heidelberg

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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

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  • 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

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