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Nonlinear Dynamics

, 58:393 | Cite as

Parametric identification of nonlinear hysteretic systems

  • Y. Rochdi
  • F. Giri
  • F. Ikhouane
  • F. Z. Chaoui
  • J. Rodellar
Original Paper

Abstract

The hysteretic behavior is an essential feature of many physical systems (e.g. mechanical structures, buildings dampers). Such a feature is conveniently accounted for in hysteretic systems’ modeling through the well-known Bouc–Wen equations. But these involve several unknown parameters and internal signals that are not all accessible to measurements. Furthermore, not all parameters come in linearly. All these difficulties make the identification of hysteretic systems a challenging problem. To cope with these issues, previous works have simplified the problem by supposing that the system displacements are large, the restoring force (and other internal signals) are accessible to measurements, the displacement is the actual control signal, the unknown parameter entering nonlinearly is known or is an integer, etc. In fact, these restrictive assumptions amount to supposing, among others, that the Bouc–Wen equations describe an isolated physical element in which ‘hysteretis’ is the only dynamic feature. The point is that the control input should be an external driving force and not the displacement. In this paper, the hysteretic equations are let to be what they really are in most practical situations: just a part of the system dynamics. Such a more realistic problem statement has a cost, which is in additional unknown parameters. A multi-stage parametric identification scheme is designed in this paper and shown to recover consistently the unknown system parameters. The proposed solution is suitable for systems not tolerating large displacements (e.g. buildings) as well as for situations where force, velocity and acceleration sensors are not available.

Keywords

Nonlinear system identification Hysteretic systems Bouc–Wen model 

References

  1. 1.
    Smith, A.W., Masri, S.F., Chassiakos, A.G., Caughey, T.K.: On-line parametric identification of MDOF non-linear hysteretic systems. J. Eng. Mech. 125(2), 133–142 (1999) CrossRefGoogle Scholar
  2. 2.
    Ikhouane, F., Rodellar, J.: On the hysteretic Bouc–Wen model. Part I: Forced limit cycle characterization. Nonlinear Dyn. 42, 63–78 (2005a) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Ikhouane, F., Rodellar, J.: On the hysteretic Bouc–Wen model. Part II: Robust parametric identification. Nonlinear Dyn. 42, 79–95 (2005b) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Macki, J.W., Nistri, P., Zecca, P.: Mathematical models for hysteresis. SIAM Rev. 35(1), 94–123 (1993) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Nagarajaiah, S., Xiaohong, S.: Response of base-isolated USC hospital building in Northridge earthquake. J. Struct. Eng. 126(10), 1177–1186 (2000) CrossRefGoogle Scholar
  6. 6.
    Savaresia, S.M., Bittantia, S., Montigliob, M.: Identification of semi-physical and black-box non-linear models: The case of MR-dampers for vehicles control. Automatica 41, 113–127 (2005) CrossRefGoogle Scholar
  7. 7.
    Wen, Y.K.: Method of random vibration of hysteretic systems. ASCE J. Eng. Mech. Div. 102(2), 249–263 (1976) Google Scholar
  8. 8.
    Ni, Y.Q., Ko, J.M., Wong, C.W.: Identification of non-linear hysteretic isolators from periodic vibration tests. J. Sound Vib. 217, 737–756 (1998) CrossRefGoogle Scholar
  9. 9.
    Erlicher, S., Point, N.: Thermodynamic admissibility of Bouc–Wen type hysteresis models. C. R. Mecanique 332, 51–57 (2004) zbMATHCrossRefGoogle Scholar
  10. 10.
    Ma, F., Zhang, H., Bockstedte, A., Foliente, G.C., Paevere, P.: Parametric analysis of the differential model of hysteresis. J. Appl. Mech. 71, 342–349 (2004) zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Y. Rochdi
    • 1
  • F. Giri
    • 1
  • F. Ikhouane
    • 2
  • F. Z. Chaoui
    • 1
  • J. Rodellar
    • 2
  1. 1.GREYCUniversity of Basse-NormandieCaenFrance
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain

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