This paper deals with the modeling and the prediction of the dynamic behavior of uncertain nonlinear systems. An efficient method is proposed to treat these problems. It is based on the Wiener–Haar chaos concept resulting from the polynomial chaos theory and it generalizes the use of the multiresolution analysis well known in the signal processing theory. The method provides a powerful tool to describe stochastic processes as series of orthonormal piecewise functions whose weighting coefficients are identified using the Mallat pyramidal algorithm. This paper shows that the Wiener–Haar model allows an efficient description and prediction of the dynamic behavior of nonlinear systems with probabilistic uncertainty in parameters. Its contribution, compared to the representation using the generalized polynomial chaos model, is illustrated by evaluating the two models via their application to the problems of the modeling and the prediction of the dynamic behavior of a self-excited uncertain nonlinear system.
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September 2012
Research Papers
Wiener–Haar Expansion for the Modeling and Prediction of the Dynamic Behavior of Self-Excited Nonlinear Uncertain Systems
Evelyne Aubry
Evelyne Aubry
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Lyes Nechak
Sébastien Berger
Evelyne Aubry
J. Dyn. Sys., Meas., Control. Sep 2012, 134(5): 051011 (11 pages)
Published Online: July 27, 2012
Article history
Received:
March 6, 2011
Revised:
February 21, 2012
Published:
July 26, 2012
Online:
July 27, 2012
Citation
Nechak, L., Berger, S., and Aubry, E. (July 27, 2012). "Wiener–Haar Expansion for the Modeling and Prediction of the Dynamic Behavior of Self-Excited Nonlinear Uncertain Systems." ASME. J. Dyn. Sys., Meas., Control. September 2012; 134(5): 051011. https://doi.org/10.1115/1.4006371
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