LAUSR

Multivariate time series are routinely measured in real complex systems, and effective multivariate multiscale methods for uncovering the complexity of multivariate complex systems are certainly needed. In this paper, a new complexity measure for multiscale analysis of multivariate time series, namely multivariate multiscale increment entropy (MMIE), is proposed and applied to detect the nonlinear dynamic complexity of flow pattern transition in oil–gas–water three-phase flow. The MMIE can map each increment into a word of two letters, which contains sign information and magnitude information, and make coupling analysis of multivariate time series. These endow the MMIE an ability to detect the complexity of multivariate time series. The simulation analysis of typical time series shows the importance of multiscale coupling analysis of multivariate time series and the effectiveness of MMIE in mining the complexity of different multivariate time series. Finally, the MMIE is employed to analyze the multichannel sensor signals of oil–gas–water three-phase flow system, which are of multivariate and correlated. The results indicate that MMIE can effectively reveal the dynamic complexity of different flow patterns and their evolution behavior with the change of flow condition.