Identification and verification of chaotic dynamics in a missile system from experimental time series

Abstract

This article is concerned with the chaotic dynamics in a missile system. Five channels of acceleration signals were measured at different locations and/or orientations of the missile during a test flight. Based on these data, the existence of chaotic behaviour is determined using common techniques for nonlinear time series analysis, such as phase-space reconstruction, Poincaré map, correlation dimension and maximum Lyapunov exponent. It is found that the vibration behaviour of the missile system represents high-order (eight dimensional) chaos. Chaotic dynamics exist in three (out of the five) channels of acceleration signals. As typical in experimental time series, the acceleration signals are contaminated with random noises. In order to determine whether deterministic chaos dominates in the three acceleration signals, a sequence of two statistical tests, the BDS test and the Kaboudan test, is applied. The BDS test rules out the possibility that the three acceleration signals are purely random. The subsequent Kaboudan test indicates that deterministic chaotic dynamics indeed dominate in two acceleration signals where the seeker is located.

Keywords:

• chaotic dynamics
• experimental time series
• missile system
• BDS statistical test

Acknowledgements

This research is supported by the National Science Council, Taiwan, Republic of China, under the grant NSC 93-2623-7-194-002.