Estimating largest Lyapunov exponents in aeroelastic signals

Abstract

The characterization of experimental signals from nonlinear systems is of fundamental importance for the development of precise mathematical models. Aeroelastic systems are intrinsically nonlinear, leading to unpredictable and sometimes uncontrollable situations. Experimental signal analysis still represents the most effective way to characterize most of the phenomena that occur in the different operating conditions of aircraft. Nonlinear signal analysis tools allow the identification and characterization of a nonlinear system, where one of the most important characteristics is the classification of the behavior between stability, instability and the type of instability so that prevention or control techniques can be implemented. However, techniques for characterizing nonlinear behavior, such as determining the largest Lyapunov exponent from the reconstructed state space, can be affected by noise, always present in experimental signals, resulting in an incorrect characterization. In this work, the singular value decomposition method is first applied as state space reconstruction and as a digital filter to the well-known Lorenz attractor at different levels of noise contamination. The effects of noise on the estimation of the largest Lyapunov exponent and the efficiency of the proposed signal filtering technique are discussed. With the procedure verified, the method is applied in experimental aeroelastic signals from a wind tunnel test of a three degrees of freedom aeroelastic wing with freeplay nonlinearity in the control surface. Subsequently, the largest Lyapunov exponent is estimated to characterize the nonlinear behavior.