An air flow-driven micro-turbine, widely used in air-condition control systems in aircraft cabins, train coaches, etc., exhibits complex vibration behaviors under stable or unstable inlet flow conditions, and especially has a certain correlation with speeds. In this paper, the vibration responses of the micro-turbine undergoing stable and unstable inlet flows measured on a test rig are analyzed and compared by using different signal processing methods, which include time and frequency domain methods, and statistical and nonlinear methods. First, the test rig system of the airflow-driven micro-turbine, the instrument system and four typical experimental cases are introduced. Then the measured vibration signals are analyzed and compared by time domain characteristic parameters (peak-to-peak value, RMS value and kurtosis value), statistical parameters (auto-correlation and BDS), and amplitude spectra in the frequency domain, statistic spectrum indicators (SSI) based on Welch's periodogram of power spectra, and the spectra of selected IMF components based on Hilbert-Huang Transform (HHT). In particular, some nonlinear feature analyzing methods, including Pseudo-Poincare mapping diagrams and Lempel-Ziv(LZ) complexity, are also used for analyzing measured vibration responses. The obtained results using the above multiple methods are compared and show that, when the inlet flow of the turbine fluctuates significantly, the nonlinear characteristics of the turbine bearings are significantly higher than those of the relatively stable inlet flow and speed conditions. Under these circumstances, commonly used time-frequency analysis methods cannot characterize the different speed operating state of the turbine, and LZ-Complexity and other nonlinear characterization methods should be used to better understand the characteristics of different speeds under unstable conditions.This study provides references for the aerodynamic stability monitoring of the micro-turbine and its design improvement.