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Suitable Algorithms for Model Updating and their Deployment for Smart Structures

  • M. W. Zehn
  • O. Martin
Conference paper
  • 179 Downloads
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 89)

Abstract

Smart structures can sense and actuate in a controlled manner in response to variable ambient stimuli combined with load carrying functions. If we are using finite element analysis up-front to design parts of our smart structures it is beset with problems like uncertainties from the manufacturing and in material properties. Attempts to improve the model with more detailed, sophisticated, refined discretised models are limited in either way. Hence, uncertainties not can be eliminated by shear mesh refinement or more detailed modelling in general. Moreover, model reduction techniques might be necessary to make a dynamical simulation feasible. Model updating aims to correct or at least alleviate invalid assumptions, omissions, and uncertainties as well as model reduction errors by processing vibration test results so that the theoretical model is closer to reality. Yet, model updating is limited in its applicability as well by the choice of the right parameters and weighting matrices. It also requires substantial computational effort because of the inverse character of the mathematical problem it involves; successful application requires a number of preparatory steps. Several methods for validation and error localisation should be applied to the FE model and a good selection of correction parameters (either sensitive or representative - a big problem). Today a wide variety of different model updating methods exist. We will confine ourselves to iterative updating methods. The updating of FE model parameters is based on a minimisation of a cost or penalty function at each iteration. These parameter estimation methods depend on the proper choice of the weighting matrices used ensure a good initial in the numerical process, and in the results.

Keywords

Weighting Matrice Smart Structure Sensitivity Matrix Parameter Estimation Method Suitable Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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7. References

  1. 1.
    Zehn, M.W., Martin, O., Offinger R.: Influence of Parameter Estimation Procedures on the Updating Process of Large Finite Element Models, 2nd International Conference on “Identification in Engineering Systems” (1999), University of Wales Swansea, pp. 240–250.Google Scholar
  2. 2.
    Zehn, M.W., Schmidt, G.: FE-Modellierungen und Modellverbesserungen von CFK-Laminaten miteingebetteten Piezokeramiken auf der Grundlage experimenteller Untersuchungen, 4. Magdeburger Maschinenbautage “Entwicklungsmethoden und Entwicklungsprozesse im Maschinenbau” (1999), Magdeburg, pp. 361–368.Google Scholar
  3. 3.
    Friswell, M.I., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht, 1995.CrossRefzbMATHGoogle Scholar
  4. 4.
    Cressie, N.A.C.: Statistics for spatial data, John Wiley & Sons, New York, 1993.Google Scholar
  5. 5.
    Zehn, M.W., Saitov, A.: Determination of spatially distributed probability density functions for parameter estimation in modal updating procedures, Proceedings “ISMA25 — 2000 International Conference on Noise and Vibration Engineering”, P. Sas (ed.), 13.–15. September 2000, Leuven/Belgium, pp. 155–162.Google Scholar
  6. 6.
    Fox, R., Kapoor, M.: Rates of Change of Eigenvalues and Eigenvectors, AIAA Journal 6(1968), pp. 2426–2429.CrossRefzbMATHGoogle Scholar
  7. 7.
    Lim, K., Junkins, J., Wang, B.: Re-examination of Eigenvector Derivatives, AIAA Journal of Guidance, Control and Dynamics, 10(1987), pp. 581–587.CrossRefzbMATHGoogle Scholar
  8. 8.
    Natke, H.: Einführung in die Theorie und Praxis der Zeitreihen-und Modalanalyse, Vieweg-Verlag, Braunschweig, Wiesbaden, 1992.Google Scholar
  9. 9.
    Nelson, R.B.: Simplified Calculation of eigenvector derivatives, AIAA Journal, 9(1976), pp. 1201–1205.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • M. W. Zehn
    • 1
  • O. Martin
    • 1
  1. 1.Institute of MechanicsOtto-von-Guericke-University MagdeburgMagdeburgGermany

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