Gas–liquid two-phase flow structure in the multi-scale weighted complexity entropy causality plane

• We test both MS-WCECP and MS-CECP on typical nonlinear dynamic systems.
• MS-WCECP shows better anti-noise ability and signal distinguishing ability.
• We apply both algorithms to study gas–liquid two-phase flow system.
• MS-WCECP can more accurately indicate gas–liquid two-phase flow structures.

The multi-scale weighted complexity entropy causality plane (MS-WCECP) is proposed for characterizing the physical structure of complex system. Firstly we use the method to investigate typical nonlinear time series. Compared with the multi-scale complexity entropy causality plane (MS-CECP), the MS-WCECP can not only uncover the dynamic information loss of complex system with the increase of scale, but also can characterize the complexity of nonlinear dynamic system. In particular, the algorithm of MS-WCECP performs strong anti-noise ability. Then we calculate the MS-WCECP for the conductance fluctuating signals measured from vertical upward gas–liquid two-phase flow experiments in a small diameter pipe, the results demonstrate that the MS-WCECP is a useful approach for exploring the stability and complexity in gas–liquid two-phase flows.