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Published September 2003 | public
Book Section - Chapter

Updating Nonlinear Dynamical Models using Response Measurements Only

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 update 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 presented directly for multiple-degree-of-freedom systems. Examples using simulated data for a Duffing oscillator and a four-DOF inelastic structure are presented to illustrate the proposed approach.

Additional Information

The first author would like to acknowledge the generous financial support by California Institute of Technology during his PhD study.

Additional details

Created:
August 19, 2023
Modified:
October 19, 2023