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.
Bayesian Model Screening for the Identification of Nonlinear Mechanical Structures
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.
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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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