Advertisement

Residual States for Modal Models Identified from Accelerance Data

  • Mladen GibanicaEmail author
  • Thomas J. S. Abrahamsson
  • Randall J. Allemang
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

Residual stiffness and mass terms are often employed in frequency response synthesis to compensate for outside band eigenmodes in the identification of modal models from test data. For structures that have strongly participating modes above the test frequency band, it has been observed that in particular direct accelerances with strong outside-band modal contribution tend to render modal models that give poor fit to test data. For such problems it may be insufficient to just add residual mass and stiffness terms to the accelerance modal series to get a sufficiently improved fit. For accelerance, such residual terms are constant and quadratic in frequency. Another, residual term that is quasi-linear over the frequency range of interest has been found to augment the identified model. In this paper that complementary term is added to the constant and quadratic terms in a state-space model identification with a subspace state-space identification method. A comparison is performed to an alternative residualisation method. The methods’ results are compared on simulated finite element test data from of an automotive component.

Notes

Acknowledgements

Volvo Car Corporation is gratefully acknowledged for providing the funding for this paper.

References

  1. 1.
    Ljung, L.: System Identification: Theory for the User, 2nd edn., p. 672. Prentice Hall, Upper Saddle River (1999)Google Scholar
  2. 2.
    Ewins, D.J.: Modal Testing: Theory, Practice and Application, 2nd edn., p. 576. Wiley-Blackwell, Philadelphia (2000)Google Scholar
  3. 3.
    Abrahamsson, T.J.S., Kammer, D.C.: Finite element model calibration using frequency responses with damping equalization. Mech. Syst. Signal Process. 6263, 218–234 (2015)CrossRefGoogle Scholar
  4. 4.
    Friswell, M.I., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics. Solid Mechanics and Its Applications, vol. 38. Springer Netherlands, Dordrecht (1995)CrossRefGoogle Scholar
  5. 5.
    Sjövall, P., Abrahamsson, T.: Component system identification and state-space model synthesis. Mech. Syst. Signal Process. 21(7), 2697–2714 (2007)CrossRefGoogle Scholar
  6. 6.
    Liljerehn, A.: Machine tool dynamics – a constrained state-space substructuring approach. Doctoral thesis, Chalmers University of Technology (2016)Google Scholar
  7. 7.
    Klerk, D.D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review and classification of techniques. AIAA J. 46(5), 1169–1181 (2008)CrossRefGoogle Scholar
  8. 8.
    Peeters, B., Van der Auweraer, H., Guillaume, P., Leuridan, J.: The PolyMAX frequency-domain method: a new standard for modal parameter estimation? Shock Vib. 11(3), 395–409 (2004)CrossRefGoogle Scholar
  9. 9.
    Richardson, M.H., Formenti, D.L.: Parameter estimation from frequency response measurements using rational fraction polynomials. In: Proceedings of the 1st IMAC International Modal Analysis Conference, Orlando, pp. 167–186 (1982)Google Scholar
  10. 10.
    Allemang, R.J., Phillips, A.W.: The unified matrix polynomial approach to understanding modal parameter estimation: an update. In: Proceedings of the ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit, Leuven, pp. 2373–2408 (2004)Google Scholar
  11. 11.
    Allemang, R.J., Brown, D.L., Phillips, A.W.: Survey of modal techniques applicable to autonomous/semi-autonomous parameter identification. In: 24th International Conference on Noise and Vibration Engineering, ISMA 2010, Including the 3rd International Conference on Uncertainty in Structural Dynamics, USD 2010, Leuven, pp. 3331–3372 (2010)Google Scholar
  12. 12.
    McKelvey, T., Akcay, H., Ljung, L.: Subspace-based multivariable system identification from frequency response data. IEEE Trans. Autom. Control 41(7), 960–979 (1996)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Van Overschee, P., De Moor, B.: N4SID: subspace algorithms for the identification of combined deterministicstochastic systems. Automatica: Spec. Issue Stat. Signal Proces. Control 30(1), 75–93 (1994)CrossRefGoogle Scholar
  14. 14.
    Kay, S.M.: Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, 1st edn., p. 625. Prentice Hall, Englewood Cliffs (1993)Google Scholar
  15. 15.
    Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn., p. 662. Cambridge University Press, New York (2012)Google Scholar
  16. 16.
    Kailath, T.: Linear Systems, 1st edn., p. 682. Prentice-Hall, Inc., Englewood Cliffs (1980)Google Scholar
  17. 17.
    Gibanica, M., Abrahamsson, T.J.S.: Parameter estimation and uncertainty quantification of a subframe with mass loaded bushings. In: Barthorpe, R., et al. (eds.) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series, pp. 61–76. Springer International Publishing, Cham (2017)CrossRefGoogle Scholar
  18. 18.
    Heylen, W., Lammens, S.: FRAC: a consistent way of comparing frequency response functions. In: Proceedings of the Conference on Identification in Engineering Systems, pp. 48–57 (1996)Google Scholar
  19. 19.
    Allemang, R.J.: The modal assurance criterion – twenty years of use and abuse. Sound Vib. 37(8), 14–23 (2003)Google Scholar
  20. 20.
    Allemang, R.J., Brown, D.L.: A correlation coefficient for modal vector analysis. In: Proceedings of the 1st IMAC International Modal Analysis Conference, Orlando, pp. 110–116 (1982)Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2019

Authors and Affiliations

  • Mladen Gibanica
    • 1
    • 2
    Email author
  • Thomas J. S. Abrahamsson
    • 1
  • Randall J. Allemang
    • 3
  1. 1.Mechanics and Maritime SciencesChalmers University of TechnologyGöteborgSweden
  2. 2.Volvo Car CorporationGöteborgSweden
  3. 3.Structural Dynamics Research Laboratory, Department of Mechanical EngineeringUniversity of CincinnatiCincinnatiUSA

Personalised recommendations