Updating Properties of Nonlinear Dynamical Systems with Uncertain Input
Publication: Journal of Engineering Mechanics
Volume 129, Issue 1
Abstract
A spectral density approach for the identification of linear systems is extended to nonlinear dynamical systems using only incomplete noisy response measurements. A stochastic model is used for the uncertain input and a Bayesian probabilistic approach is used to quantify the uncertainties in the model parameters. The proposed spectral-based approach utilizes important statistical properties of the Fast Fourier Transform and their robustness with respect to the probability distribution of the response signal in order to calculate the updated probability density function for the parameters of a nonlinear model conditional on the measured response. This probabilistic approach is well suited for the identification of nonlinear systems and does not require huge amounts of dynamic data. The formulation is first presented for single-degree-of-freedom systems and then for multiple-degree-of freedom systems. Examples using simulated data for a Duffing oscillator, an elastoplastic system and a four-story inelastic structure are presented to illustrate the proposed approach.
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Published In
Journal of Engineering Mechanics
Volume 129 • Issue 1 • January 2003
Pages: 9 - 20
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Oct 8, 2001
Accepted: May 20, 2002
Published online: Dec 13, 2002
Published in print: Jan 2003
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