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
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the numerical estimation techniques for solving the updating equations;
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the influence of different model parametrisations defining the type and the location of the erroneous parameters;
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the type of the residuals formed by the test/analysis differences to be minimised;
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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.
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References
Natke (1992), Einführung in théorie und praxis der zeitreihen und modalanalyse, Vieweg Verlag, Braunschweig/Wiesbaden.
Friswell and Mottershead, J.E. (1995), Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht.
Lallement, G. (1988), Localisation techniques, Proc. of Workshop “Structural Safety Evaluation Based on System Identification Approaches”, Vieweg Verlag, Braunschweig/Wiesbaden.
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.
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.
Demmel (1997), Applied numerical linear algebra, S1AM, Philadelphia, PA, U.S.A.
Soederstroem and Stoica, P. (1989), System Identification, Prentice Hall Int., UK.
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.
Tikhonov and Arsenin, V.Y. (1977), Solutions of Ill-posed Problems, J. Wiley, New York.
Natke (1991), On regularization methods applied to the error localization of mathematical models, Proc. Int. Modal Analysis Conf. IMAC IX, Florence, Union College, Schenectady.
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.
Prells (1995), Eine regularisierungsmethode für die lineare fehlerlokalisierung von modellen elastomechanischer systeme, Dissertation, Univ. Hannover.
Hansen, C. (1992), Analysis of discrete ill-posed problems by means of the L — curve, Siam Review, Vol. 34, No. 4, 561–580.
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.
Hansen, C., Régularisation Tools: a MATLAB package for analysis and solution of discrete ill-posed problems, Technical University of Denmark, Lyngby, Denmark
Natke, Collmann, D. and Zimmermann, H. (1974), Beitrag zur korrektur des rechenmodells eines elastomechanischen systems anhand von Versuchsergebnissen, VDI-Berichte 221, 23–32.
Natke, Lallement, G. and Cottin, N. (1995), Properties of various residuals within updating of mathematical models, Inverse Problems in Engineering., Vol. 1, 329-348.
Fox and Kapoor, M. (1968), Rate of change of eigenvalues and eigenvectors, AIAA Journal, Vol. 6, 2426–2429.
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.
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.
Balmes, E. (1998), Efficient sensitivity analysis based on finite element model reduction, Proc. of 16th Int. Modal Analysis Conf., IMACXVI, Santa Barbara, USA.
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.
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.
Targoff (1976), Orthogonality check and correction of measured modes, AIAA Journal, Vol. 14, No. 2,164–167.
Baruch and Bar-Itzhack, I.Y. (1978), Optimal weighted orthogonalisation of measured modes, AIAA Journal, Vol. 16, No. 4, 346–351.
Baruch (1982), Optimal correction of mass and stiffness matrices using measured modes, AIAA Journal Vol. 20, No. 11, 1623–1626.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Niedbal (1984), Analytical determination of real normal modes from measured complex modes, AIAA Paper 84–0995.
Gladwell and Ahmadian, H. (1995), Generic element matrices suitable for finite element model updating, Mechanical Systems and Signal Processing, Vol. 9.
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© 1999 Springer Science+Business Media Dordrecht
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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
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DOI: https://doi.org/10.1007/978-94-011-4503-9_14
Publisher Name: Springer, Dordrecht
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