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Identification of Time-Varying Nonlinear Systems Using Differential Evolution Algorithm

  • Nevena Perisic
  • Peter L Green
  • Keith Worden
  • Poul Henning Kirkegaard
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

Online monitoring of modal and physical parameters which change due to damage progression and aging of mechanical and structural systems is important for the condition and health monitoring of these systems. Usually, only the limited number of imperfect, noisy system state measurements is available, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution (DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus of the further work will be on the convergence study with respect to parameters of DE and on applying the method to experimental data.

Keywords

Differential evolution Time-varying systems Coulomb friction Nonlinear system identification 

Notes

Acknowledgements

The financial support by the SYSWIND project, funded by the Marie Curie Actions under the Seventh Framework Programme for Research and Technology Development of the EU, is gratefully acknowledged.

References

  1. 1.
    Ljung L (1987) System identification: theory for the user. Prentice-Hall, Englewood Cliffs, p 519, ISBN 0-13-881640Google Scholar
  2. 2.
    Price KV, Storn RM, Lampinen JA (2005) Differential evolution a practical approach to global optimization. Springer, Berlin/New YorkGoogle Scholar
  3. 3.
    Gross D, Harris CM (1985) Fundamentals of queuing theory. Wiley, New YorkGoogle Scholar
  4. 4.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680Google Scholar
  5. 5.
    Rechenberg I (1973) Evolutionstrategie. Frommann-Holzboog, StuttgartGoogle Scholar
  6. 6.
    Schwefel HP (1994) Evolution and optimum seeking. Wiley, New YorkGoogle Scholar
  7. 7.
    Holland JH (1962) Outline for a logical theory of adaptive systems. J assoc comput mach 8:212–229Google Scholar
  8. 8.
    Goldberg DE (1989) Genetic algorithms in search optimization and machine learning. Addison-Wesley, ReadingGoogle Scholar
  9. 9.
    Storn R, Price KV (1995) Differential evolution – a simple and efficient adaptive scheme for global optimization over continous spaces. Technical report TR-95-012, ICSIGoogle Scholar
  10. 10.
    Kyprianou A, Worden K, Panet M (2001) Identification of hysteretic systems using the differential evolution algorithm. J Sound Vib 248: 289–314Google Scholar
  11. 11.
    Worden K, Manson G (2011) On the Identification of Hysteretic Systems, Part I: an Extended Evolutionary Scheme. In: Nonlinear modeling and applications, vol 2 conference proceedings of the society for experimental mechanics series, Proceedings of the 28th IMAC, A Conference on Structural Dynamics, February 1–4, 2010, Jacksonville, Florida, USA, vol 11, pp 67–75Google Scholar

Copyright information

© The Society for Experimental Mechanics 2014

Authors and Affiliations

  • Nevena Perisic
    • 1
  • Peter L Green
    • 2
  • Keith Worden
    • 2
  • Poul Henning Kirkegaard
    • 1
  1. 1.Department of Civil EngineeringAalborg UniversityAalborgDenmark
  2. 2.Department of Mechanical EngineeringUniversity of SheffieldSheffieldUK

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