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Maximum entropy approach to the identification of stochastic reduced-order models of nonlinear dynamical systems

Published online by Cambridge University Press:  03 February 2016

M. Arnst ,
R. Ghanem  and
S. Masri
M. Arnst
Affiliation:
arnst@usc.edu
R. Ghanem
Affiliation:
University of Southern California, Los Angeles, USA
S. Masri
Affiliation:
University of Southern California, Los Angeles, USA
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Abstract

Data-driven methodologies based on the restoring force method have been developed over the past few decades for building predictive reduced-order models (ROMs) of nonlinear dynamical systems. These methodologies involve fitting a polynomial expansion of the restoring force in the dominant state variables to observed states of the system. ROMs obtained in this way are usually prone to errors and uncertainties due to the approximate nature of the polynomial expansion and experimental limitations. We develop in this article a stochastic methodology that endows these errors and uncertainties with a probabilistic structure in order to obtain a quantitative description of the proximity between the ROM and the system that it purports to represent. Specifically, we propose an entropy maximization procedure for constructing a multi-variate probability distribution for the coefficients of power-series expansions of restoring forces. An illustration in stochastic aeroelastic stability analysis is provided to demonstrate the proposed framework.

Type
Research Article
Information
The Aeronautical Journal , Volume 114 , Issue 1160 , October 2010 , pp. 637 - 650
Copyright
Copyright © Royal Aeronautical Society 2010 

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