Analysis and Identification of Chaotic Dynamics in a Flying Vibratory System

This paper aims at determining whether chaotic dynamics exist in a flying vibratory system. It is important to identify chaotic behavior in a flying system since it may jeopardize the structure of the flying object and cause instability subsequently. It can also cause uncomfortable experience for passengers in a passenger airplane or inaccurate targeting for a missile. Identification of chaotic dynamics from experimental time series is a nontrivial task, since the data is likely to be contaminated with random noise that possesses similar properties to chaos. In this work, acceleration signals were measured at nine different locations or orientations of the flying object during a test fly. Steady-state acceleration signals were extracted and analyzed. The analysis is based on the pseudo phase-space trajectories reconstructed from the experimental time series using the method of delays. Two indices, the correlation dimension and the maximum Lyapunov exponent, are employed to identify the chaotic behavior and to distinguish it from random noise. In general, the correlation dimension calculated from the pseudo trajectory depends on the embedding dimension. It is found in three of the nine-channel signals that the correlation dimension saturates when the embedding dimension is larger than a critical value. The critical embedding dimension is the minimum dimension required for fully un-stretching the phase-space trajectories. This phenomenon indicates a possible existence of chaotic dynamics. It is also found that the maximum Lyapunov exponents calculated from the same acceleration signals are all positive, which further verifies the possibility of the existence of chaotic motion. In addition, some computational issues regarding the embedding dimension, correlation dimension, and maximum Lyapunov exponent are discussed in this paper.