In order to identify experimental chaotic vibration signals correctly, the measured data were analyzed by applying the methods of Poincaré section, return map, and phase space reconstruction. However, the nonlinear time series analysis based on phase space reconstruction is complex and time-consuming for large quantities of experimental signals. Besides, especially when the signal identification process should be completed online, the conventional method is unable to meet the requirements. The energy distribution features of signals in different frequency bands were extracted with the wavelet package analysis method, and the important characteristic vectors for chaos identification were provided. These methods were verified with numerical simulation first in this paper. Then, the nonlinear vibration system based on an air spring isolator was designed, which exhibits different responses with different parameters. In the experiment, the wavelet package technology and neural network were applied to identify the system behavior; results showed that the vibration system exhibited chaotic responses under special parameter ranges, and the parameter variation law was concluded, which is the foundation of linear spectra isolation for chaotic vibration control technology.