Gas-liquid two-phase flow is complex and has uncertainty in phase interfaces

which make the two-phase flow look very complicated. Even though the flow behavior (e.g. coalescence

crushing and separation) of single bubble or bubble groups in the liquid phase looks random

combining some established characteristics and methodologies can find regularities among the randomness. In order to excavate the nonlinear dynamic characteristics of gas-liquid two-phase flow

the authors developed an improved matrix pencil (IMP) method to analyze the pressure difference signals of the two-phase flow. This paper elucidates the influence of signal length on MP calculation results and the anti-noise-interference ability of the MP method. An IMP algorithm was applied to the fluctuation signals of gas-liquid two-phase flow to extract themode frequency and damping ratio

which were combined with the component energy index (CEI) entropy to identify the different flow patterns. It is also found that frequency

damping ratio

CEI entropy and stability diagram together not only identify flow patterns

but also provide a new way to examine and understand the evolution mechanism of physical dynamics embedded in flow patterns. Combining these characteristics and methods

the evolution of the nonlinear dynamic physical behavior of gas bubbles is revealed.