Skip to main content

Updating of Analytical Models — Basic Procedures and Extensions

  • Chapter
Modal Analysis and Testing

Part of the book series: NATO Science Series ((NSSE,volume 363))

Abstract

In the paper basic procedures for computational updating of analytical model parameters are presented. The procedures have been investigated thoroughly in recent years with respect to

  • the numerical estimation techniques for solving the updating equations;

  • the influence of different model parametrisations defining the type and the location of the erroneous parameters;

  • the type of the residuals formed by the test/analysis differences to be minimised;

  • the requirements to be posed on the initial analysis model.

The residuals presented are formed by force and response equation errors, by eigenfrequency and mode shape errors and by frequency response errors. The procedures have been derived to handle incomplete test vectors, where the number of measured degrees of freedom (DOF) is much less than the DOF no. of the computational model. Finally an example of updating a laboratory test structure is reported including some recommendations and experiences.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Natke (1992), Einführung in théorie und praxis der zeitreihen und modalanalyse, Vieweg Verlag, Braunschweig/Wiesbaden.

    MATH  Google Scholar 

  2. Friswell and Mottershead, J.E. (1995), Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht.

    MATH  Google Scholar 

  3. Lallement, G. (1988), Localisation techniques, Proc. of Workshop “Structural Safety Evaluation Based on System Identification Approaches”, Vieweg Verlag, Braunschweig/Wiesbaden.

    Google Scholar 

  4. Flores, O., Link, M. (1993), Localization techniques for parametric updating of dynamic mathematical models, Proc. of Int. Forum On Aeroelasticity and Structural Dynamics, Strassbourg, France, Association Aeronautic et Astronautic de France (Hrsg), 75782 Paris.

    Google Scholar 

  5. Ahmadian, G.M.L., Gladwell and Ismail, F., Parameter selection strategies in finite element model updating, ASME, J. of Vibration and Acoustics 119, 37–45.

    Google Scholar 

  6. Demmel (1997), Applied numerical linear algebra, S1AM, Philadelphia, PA, U.S.A.

    Google Scholar 

  7. Soederstroem and Stoica, P. (1989), System Identification, Prentice Hall Int., UK.

    MATH  Google Scholar 

  8. Link, M. (1993), Updating of analytical models-procedures and experience, Proc. of Conf. on Modern Practice in Stress and Vibration Analysis, J.L. Wearing (ed.), Sheffield Academic Press, 35–52.

    Google Scholar 

  9. Tikhonov and Arsenin, V.Y. (1977), Solutions of Ill-posed Problems, J. Wiley, New York.

    Google Scholar 

  10. Natke (1991), On regularization methods applied to the error localization of mathematical models, Proc. Int. Modal Analysis Conf. IMAC IX, Florence, Union College, Schenectady.

    Google Scholar 

  11. Mottershead and Foster, C.D. (1991), On the treatment of ill-conditioning in spatial parameter estimation from measured vibration data, Mechanical Systems and Signal Processing, Vol. 5, No. 2, 139–154.

    Article  Google Scholar 

  12. Prells (1995), Eine regularisierungsmethode für die lineare fehlerlokalisierung von modellen elastomechanischer systeme, Dissertation, Univ. Hannover.

    Google Scholar 

  13. Hansen, C. (1992), Analysis of discrete ill-posed problems by means of the L — curve, Siam Review, Vol. 34, No. 4, 561–580.

    Article  MathSciNet  MATH  Google Scholar 

  14. Ahmadian, Mottershead, J.E. and Friswell, M.I. (1998), Régularisation methods for finite element model updating, Mechanical Systems and Signal Processing, Vol. 12, No. 1.

    Google Scholar 

  15. Hansen, C., Régularisation Tools: a MATLAB package for analysis and solution of discrete ill-posed problems, Technical University of Denmark, Lyngby, Denmark

    Google Scholar 

  16. Natke, Collmann, D. and Zimmermann, H. (1974), Beitrag zur korrektur des rechenmodells eines elastomechanischen systems anhand von Versuchsergebnissen, VDI-Berichte 221, 23–32.

    Google Scholar 

  17. Natke, Lallement, G. and Cottin, N. (1995), Properties of various residuals within updating of mathematical models, Inverse Problems in Engineering., Vol. 1, 329-348.

    Google Scholar 

  18. Fox and Kapoor, M. (1968), Rate of change of eigenvalues and eigenvectors, AIAA Journal, Vol. 6, 2426–2429.

    Article  MATH  Google Scholar 

  19. Sutter, T. R., Camarda. Ch.J., Walsh, J.L. and Adelman, H. M. (1988), Comparison of several methods for calculating vibration mode shape derivatives, AIAA J., Vol. 26, No. 12.

    Google Scholar 

  20. Lallement, G. and Zhang, Q. (1989), Selective structural modifications, applications to the problems of eigensolution sensitivity and model adjustment, Mechanical Systems and Signal Processing, Vol. 3, No. 1.

    Google Scholar 

  21. Balmes, E. (1998), Efficient sensitivity analysis based on finite element model reduction, Proc. of 16th Int. Modal Analysis Conf., IMACXVI, Santa Barbara, USA.

    Google Scholar 

  22. Link, M. and Mardorf, J. (1996), The role of finite element idealisation and test data errors in model updating, Proc. 2 nd Int. Conf. Structural Dynamics Modelling, NAFEMS, Glasgow, 493–504.

    Google Scholar 

  23. Link, M. (1998), Updating analytical models by using local and global parameters and relaxed optimisation requirements, Mechanical Systems and Signal Processing, Vol. 12, No. 1.

    Google Scholar 

  24. Targoff (1976), Orthogonality check and correction of measured modes, AIAA Journal, Vol. 14, No. 2,164–167.

    Article  Google Scholar 

  25. Baruch and Bar-Itzhack, I.Y. (1978), Optimal weighted orthogonalisation of measured modes, AIAA Journal, Vol. 16, No. 4, 346–351.

    Article  Google Scholar 

  26. Baruch (1982), Optimal correction of mass and stiffness matrices using measured modes, AIAA Journal Vol. 20, No. 11, 1623–1626.

    Article  Google Scholar 

  27. Link, M. (1991), Localisation of errors in computational models using dynamic test data, Proc. of the European Conf. on Struct. Dynamics, EURODYN ′90, Structural Dynamics, W. B. Kraetzig et al (eds.), A. A. Balkema.

    Google Scholar 

  28. Link, M. (1992), Experiences with different procedures for updating structural parameters of analytical models using test data, Proc. Int. Modal Analysis Conf., IMAC X, San Diego, Union College, Schenectady, NY, USA.

    Google Scholar 

  29. Fritzen, P. and Kiefer, T. (1992), Localisation and correction of errors in finite element models based on experimental data, Proc. Int. Modal Analysis Conf., IMAC X, San Diego, Union College, Schenectady, NY, USA.

    Google Scholar 

  30. Larsson and Sas, P. (1992), Model updating based on forced vibration testing using numerically stable formulation, Proc. Int. Modal Analysis Conf., IMAC X, San Diego, Union College, Schenectady, NY, USA.

    Google Scholar 

  31. D’Ambrogio and Fregolent, A. (1998), On the use of consistent and significant information to reduce ill-conditioning in dynamic model updating, Mechanical Systems and Signal Processing, Vol. 12, No. 1.

    Google Scholar 

  32. Ibrahim, Teichert, W. and Brunner, O. (1998), Frequency response function FE model updating using multi perturbed analytical models and information density matrix, Proc. Int. Modal Analysis Conf, IMAC XVI, Santa Barbara, USA.

    Google Scholar 

  33. Pascual, Golinval, J.C. and Razeto, M. (1997), A frequency domain correlation technique for model correlation and updating, Proc. Int. Modal Analysis Conf, IMAC 15, Orlando, USA.

    Google Scholar 

  34. Cogan, S., Lenoir, D. and Lallement, G. (1996), An improved frequency response residual for model correction, Proc. Int. Modal Analysis Conf, IMAC 14, Dearborn, USA.

    Google Scholar 

  35. Link, M., Weiland, M. and Moreno-Barragan, J. (1987), Direct physical matrix identification as compared to phase resonance testing, Proc. Int. Modal Analysis Conf., IMAC 5, London, UK.

    Google Scholar 

  36. Niedbal (1984), Analytical determination of real normal modes from measured complex modes, AIAA Paper 84–0995.

    Google Scholar 

  37. Gladwell and Ahmadian, H. (1995), Generic element matrices suitable for finite element model updating, Mechanical Systems and Signal Processing, Vol. 9.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Link, M. (1999). Updating of Analytical Models — Basic Procedures and Extensions. In: Silva, J.M.M., Maia, N.M.M. (eds) Modal Analysis and Testing. NATO Science Series, vol 363. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4503-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4503-9_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5894-7

  • Online ISBN: 978-94-011-4503-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics