The development of techniques for identification and updating of nonlinear mechanical structures has received increasing attention in recent years. In practical situations, there is not necessarily a priori knowledge about the nonlinearity. This suggests the need for strategies that allow inference of useful information from the data. The present study proposes an algorithm based on a Bayesian inference approach for giving insight into the form of the nonlinearity. A family of parametric models is defined to represent the nonlinear response of a system and the selection algorithm estimates the likelihood that each member of the family is appropriate. The (unknown) probability density function of the family of models is explored using a simple variant of the Markov Chain Monte Carlo sampling technique. This technique offers the advantage that the nature of the underlying statistical distribution need not be assumed a priori. Enough samples are drawn to guarantee that the empirical distribution approximates the true but unknown distribution to the desired level of accuracy. It provides an indication of which models are the most appropriate to represent the nonlinearity and their respective goodness-of-fit to the data. The methodology is illustrated using two examples, one of which comes from experimental data.
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e-mail: g.kerschen@ulg.ac.be
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July 2003
Technical Papers
Bayesian Model Screening for the Identification of Nonlinear Mechanical Structures
Gae¨tan Kerschen,
e-mail: g.kerschen@ulg.ac.be
Gae¨tan Kerschen
Vibrations & Identification des Structures, Department of Aerospace, Mechanics and Materials, University of Lie`ge, Chemin des Chevreuils 1 (B52), B-4000 Liege, Belgium
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Jean-Claude Golinval,
Jean-Claude Golinval
Vibrations & Identification des Structures, Department of Aerospace, Mechanics and Materials, University of Lie`ge, Chemin des Chevreuils 1 (B52), B-4000 Liege, Belgium
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Franc¸ois M. Hemez
Franc¸ois M. Hemez
Engineering Science & Applications Division, ESA-WR, Mail Stop P946, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
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Gae¨tan Kerschen
Vibrations & Identification des Structures, Department of Aerospace, Mechanics and Materials, University of Lie`ge, Chemin des Chevreuils 1 (B52), B-4000 Liege, Belgium
e-mail: g.kerschen@ulg.ac.be
Jean-Claude Golinval
Vibrations & Identification des Structures, Department of Aerospace, Mechanics and Materials, University of Lie`ge, Chemin des Chevreuils 1 (B52), B-4000 Liege, Belgium
Franc¸ois M. Hemez
Engineering Science & Applications Division, ESA-WR, Mail Stop P946, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 2002; Revised January 2003. Associate Editor: M. I. Friswell.
J. Vib. Acoust. Jul 2003, 125(3): 389-397 (9 pages)
Published Online: June 18, 2003
Article history
Received:
May 1, 2002
Revised:
January 1, 2003
Online:
June 18, 2003
Citation
Kerschen , G., Golinval, J., and Hemez, F. M. (June 18, 2003). "Bayesian Model Screening for the Identification of Nonlinear Mechanical Structures ." ASME. J. Vib. Acoust. July 2003; 125(3): 389–397. https://doi.org/10.1115/1.1569947
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