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Shock and Vibration
Volume 13, Issue 4-5, Pages 393-407

On the Investigation of State Space Reconstruction of Nonlinear Aeroelastic Response Time Series

Flávio D. Marques, Eduardo M. Belo, Vilma A. Oliveira, José R. Rosolen, and Andréia R. Simoni

Department of Aeronautical Engineering, Engineering School of Sao Carlos, University of Sao Paulo, Av. Trabalhador Sancarlense, 400, 13561-020, Sao Carlos, SP, Brazil

Received 19 July 2006; Revised 19 July 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Stall-induced aeroelastic motion may present severe non-linear behavior. Mathematical models for predicting such phenomena are still not available for practical applications and they are not enough reliable to capture physical effects. Experimental data can provide suitable information to help the understanding of typical non-linear aeroelastic phenomena. Dynamic systems techniques based on time series analysis can be adequately applied to non-linear aeroelasticity. When experimental data are available, the methods of state space reconstruction have been widely considered. This paper presents the state space reconstruction approach for the characterization of the stall-induced aeroelastic non-linear behavior. A wind tunnel scaled wing model has been tested. The wing model is subjected to different airspeeds and dynamic incidence angle variations. The method of delays is used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. To obtain an estimate of the time delay used in the state space reconstruction from time series, the autocorrelation function analyis is used. For the calculation of the embedding dimension the correlation integral approach is considered. The reconstructed attractors can reveal typical non-linear structures associated, for instance, to chaos or limit cycles.