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Updating Properties of Nonlinear Dynamical Systems with Uncertain Input

Yuen, Ka-Veng and Beck, James L. (2003) Updating Properties of Nonlinear Dynamical Systems with Uncertain Input. Journal of Engineering Mechanics, 129 (1). pp. 9-20. ISSN 0733-9399.

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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.

Item Type:Article
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Additional Information:©ASCE. The manuscript for this paper was submitted for review and possible publication on October 8, 2001; approved on May 20, 2002.
Subject Keywords:Bayesian analysis, Nonlinear systems, Spectral density function
Record Number:CaltechAUTHORS:20120810-111806039
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33085
Deposited By: Sydney Garstang
Deposited On:13 Aug 2012 18:15
Last Modified:24 Feb 2014 19:10

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