Identifying Chaotic Dynamics in a Flying Vibratory System

This paper determines whether chaotic dynamics exists in a flying vibratory system. Acceleration signals were measured at nine different locations or orientations of the flying object during a test flight. Steady-state acceleration data were extracted to reconstruct pseudo phase-space trajectories from which two dynamical indices including the correlation dimension and the maximum Lyapunov exponent are calculated. Although generally the correlation dimension depends on the embedding dimension, it is found that in three out of the nine-channel acceleration signals, the correlation dimension saturates when the embedding dimension reaches a critical value. The phenomenon indicates a possible existence of chaotic motion. The maximum Lyapunov exponents calculated for the same three-channel data are all positive which again implies the possible existence of chaos. To determine whether the experimental time series that demonstrate chaotic characteristics are in fact deterministic (rather than random noise), a sequence of two statistical tests is applied. Based on these tests, the possibility of those three-channel acceleration data being random noise is excluded.