Comprehensive Method of Chaotic Vibration Identification

When the parameters are in a special range, the response of a nonlinear vibration system is chaotic, which is different from the classical regular response such as primary, super-, sub-, ultra-sub-harmonic resonances. Because the chaotic time series looks like random signal, the characteristics of the chaos cannot be identified from the time history. This paper presents a comprehensive method to identify the chaotic vibration. The attractor of the system is reconstructed in the phase space, and thus the characteristics of the chaotic signal are reflected by the attractor. If the attractor is regular, the response may be periodic. If the topologic structure of the phase diagram is very complicate, the attractor is strange, that is, the system may be in a chaotic state. Correlation dimension and Lyapunov exponent are calculated to prove the conclusions above. It is clear that if the correlation dimension is fraction and the Lyapunov exponent is positive, the measured signal is chaotic. The difference between chaotic signal and noise is studied as well Results show that the comprehensive method can be applied to identify the chaotic vibration efficiently.