A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems (Lorenz and Rossler) to examine the anti-noise ability for complex systems. Results show that the nonlinear dynamic system analysis method resists noise and reveals the internal dynamics of a weak signal from noise pollution. On this basis, the vertical upward gas-liquid two-phase flow in a 2 mm x 0.81 mm small rectangular channel is investigated. The frequency and energy distributions of the main oscillation mode are revealed by analyzing the time-frequency spectra of the pressure signals of different flow patterns. The positive power spectral density of singular-value frequency entropy and the damping ratio are extracted to characterize the evolution of flow patterns and achieve accurate recognition of different vertical upward gas-liquid flow patterns (bubbly flow: 100%, slug flow: 92%, churn flow: 96%, annular flow: 100%). The proposed analysis method will enrich the dynamics theory of multi-phase flow in small channel. (C) 2015 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.