Chaos in Nonlinear Dynamic Systems: Helicopter Vibration Mechanisms

Abstract – The nonlinear dynamic behavior of a helicopter is considered in this paper, using only real-time flight data analysis. The main objective of this study is to characterize the vibration mechanism(s), based on the analysis of the time-series data of the dynamical system, specifically acceleration for two different airspeeds with a sampling rate of 1024 Hz. We explore the possibility of the presence of chaotic behavior in the time-series data, using a systematic, detailed approach. Some background in the theory of chaos in nonlinear dynamical systems is discussed, and techniques for the identification of chaos in time-series data are presented. Several topics including delay-coordinate embedding theory, delay time and dimension calculation, and Lyapunov exponent computation for chaotic systems are described. In each section, time-series data sets from the helicopter are analyzed and examined; in some sections classical examples such as the Hénon Map and Lorenz System are also considered to provide illustrative results. Finally, implications regarding the possibility of chaotic behavior in the dynamical system is discussed, and the next steps in this study are presented. I