Multi-Scale Permutation Entropy: A Complexity Measure for Discriminating Two-Phase Flow Dynamics

We propose an improved permutation entropy method, i.e., multi-scale permutation entropy (MSPE), for discriminating two-phase flow dynamics. We first take the signals from different typical dynamical systems as examples to demonstrate the effectiveness of the methods. In particular, we compute the MSPE values of sinusoidal signal, logistic, Lorenz and Chen chaotic signals and their signals with white Gaussian noise added. We find that the MSPE method can be an effective tool for analyzing the time series with distinct dynamics. We finally calculate the multi-scale permutation entropy and rate of MSPE from 66 groups of conductance fluctuating signals and find that these two measures can be used to identify different flow patterns and further explore dynamical characteristics of gas-liquid flow patterns. These results suggest that the MSPE can potentially be a useful tool for revealing the dynamical complexity of two-phase flow on different scales.