Multiscale Complexity-entropy Causality Plane Research Articles

Refined composite multivariate multiscale complexity-entropy causality plane analysis for gas-liquid two-phase flow

Abstract This paper presents a refined composite multivariate multiscale complexity-entropy causality plane (RCMMCECP) to explore the dynamics features of gas–liquid two-phase flow. Firstly, we employ a series of typical nonlinear time series to confirm the effectiveness of the RCMMCECP, including seven chaotic systems, two random processes, and one periodic process. The comparison results of the proposed method and conventional multivariate multiscale complexity-entropy causality plane (MMCECP) confirm the stability performance of the proposed RCMMCECP. Above all, the RCMMCECP enhances the reliability of the statistical complexity measure over large time scales and exhibits good continuity and noise-resistant ability in multiscale analysis. Then, we employ the RCMMCECP to analyze the upstream and downstream conductance signals. The experimental results demonstrate that the RCMMCECP can characterize the change of complexity and structural stability in the gas-liquid two-phase flow evolution process, effectively revealing its dynamics features.

Multivariate multiscale complexity-entropy causality plane analysis for complex time series

The multivariate multiscale complexity-entropy causality plane (MMCECP) is introduced for evaluating the dynamical complexity and long-range correlations of multivariate nonlinear systems. Numerical simulations from different classes of systems are applied to confirm the effectiveness of the proposed measure. We observe that the MMCECP not only can characterize the deterministic properties of the systems, but also can distinguish Gaussian and non-Gaussian processes. Moreover, it is immune to varying degrees of noises at large scales. Then we apply it to financial time series analysis, mainly investigating the classification of stock market dynamics. Empirical results illustrate that the MMCECP is robust and valid to detect the physical structures of stock markets.

Characterization of dynamic behavior of combustion noise and detection of blowout in a laboratory-scale gas-turbine model combustor

We present an experimental study on characterizing the dynamic behavior of flow velocity field during combustion noise from the viewpoints of statistical complexity and complex-network theory, involving the detection of a precursor of blowout. The multiscale complexity-entropy causality plane clearly shows the possible presence of two dynamics, (1) stochastic dynamics in the injector rim region and (2) noisy chaos in the shear layer between a vortex breakdown bubble in a wake of a centerbody and the outer recirculation region in a dump plate. The turbulence network is used to study the vortical interactions during combustion noise. The weighted permutation entropy incorporating the amplitude information of pressure fluctuations is useful for capturing a precursor of blowout.

Effect of gravity on nonlinear dynamics of the flow velocity field in turbulent fire

We numerically study the effect of gravity on the dynamic behavior of flow velocity field in a turbulent fire from the viewpoints of symbolic dynamics, statistical complexity, and complex networks. The randomness of streamwise flow velocity fluctuations significantly increases with increasing gravity, which is found to be correlated with the mean permutation entropy and the Froude number. The multiscale complexity-entropy causality plane clearly shows that under high gravity, high-dimensional deterministic chaos starts to be formed in the near field. We observe the appearance, disappearance, and reappearance of a scale-free structure in weighted networks between vortices under high gravity, clearly showing the presence of power-law decay in the lifetime of the scale-free structure.

Dynamic behavior of temperature field in a buoyancy-driven turbulent fire

We study the dynamic behavior of temperature field in a buoyancy-driven turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. The permutation entropy and the horizontal visibility network entropy allow us to capture the subtle changes in temperature fluctuations. The possible existence of deterministic chaos in temperature fluctuations, as well as in streamwise flow velocity fluctuations [Takagi et al., Phys. Rev. E 96 (2017) 052223], is clearly verified using the multiscale complexity-entropy causality plane.

Multi-scale nonlinear analysis of drying dynamics in the mixed pulsed drying fluidized beds

Abundant information resides in the pressure signal of a fluidized bed, especially when the pressure signal of that bed is mixed with steady flow, and the pulsed flow is more prevalent. In this paper, the authors established a stable and pulsed flow fluidized bed experiment platform. They also collected pressure signals with different times, different frequencies and different gas flow rates in the drying process. The pressure signals were analyzed by two approaches. One is based on the use of the multi-scale complexity entropy causality plane, and the other relies on a recurrence plot. With the drying characteristics of wet particles in the bed and flow pattern, the focus was on influence factors such as time lapse, air intake ratio and pulse frequency on both drying efficiency and the characteristics of complex nonlinear dynamics were analyzed. A study of the micro and macro mechanism of flow characteristics is also presented. The results show that the two approaches (i.e., methods) have a higher accuracy in judging the change of the interaction force between moist particles and the change of flow characteristics. The drying efficiency can be deduced by analysis of the dynamic characteristics of the fluidized bed; thus, the multi-scale complexity entropy causality plane and the structure of the recurrence plot corresponding to the best drying efficiency are obtained. A recommended reference range of the three parameters of a recurrence plot that are good for drying will be presented, which corresponds to the ratio of the stable flow and the pulsed flow.

Nonlinear determinism in degenerated combustion instability in a gas-turbine model combustor

We present a detailed study on the dynamic behavior of pressure fluctuations in degenerated combustion instability [Gotoda et al. Phys. Rev. E 92 (2015) 052906] in a lean premixed gas-turbine model combustor in terms of symbolic dynamics, statistical complexity, complex networks, and nonlinear forecasting. The permutation spectrum test enables us to extract nonlinear determinism in degenerated combustion instability. The possible presence of chaotic dynamics in degenerated combustion instability is reasonably shown by considering the multiscale complexity–entropy causality plane incorporating a scale-dependent approach.

Dynamic behavior of combustion instability in a cylindrical combustor with an off-center installed coaxial injector.

We have intensively studied the dynamic behavior of combustion instability in a cylindrical combustor with an off-center installed coaxial injector. The most interesting discovery in this study is the appearance of a deterministic chaos in a transition from a dynamically stable state to well-developed high-frequency thermoacoustic combustion oscillations with increasing the volume flow rate of nitrogen with which oxygen is diluted. The presence of deterministic chaos is reasonably identified by considering an extended version of the Sugihara-May algorithm [G. Sugihara and R. May, Nature 344, 734 (1990)] as a local predictor and the multiscale complexity-entropy causality plane based on statistical complexity.

Characterization and detection of thermoacoustic combustion oscillations based on statistical complexity and complex-network theory.

We present an experimental study on the characterization of dynamic behavior of flow velocity field during thermoacoustic combustion oscillations in a turbulent confined combustor from the viewpoints of statistical complexity and complex-network theory, involving detection of a precursor of thermoacoustic combustion oscillations. The multiscale complexity-entropy causality plane clearly shows the possible presence of two dynamics, noisy periodic oscillations and noisy chaos, in the shear layer regions (1) between the outer recirculation region in the dump plate and a recirculation flow in the wake of the centerbody and (2) between the outer recirculation region in the dump plate and a vortex breakdown bubble away from the centerbody. The vertex strength in the turbulence network and the community structure of the vorticity field can identify the vortical interactions during thermoacoustic combustion oscillations. Sequential horizontal visibility graph motifs are useful for capturing a precursor of themoacoustic combustion oscillations.

Detection of frequency-mode-shift during thermoacoustic combustion oscillations in a staged aircraft engine model combustor

We conduct an experimental study using time series analysis based on symbolic dynamics to detect a precursor of frequency-mode-shift during thermoacoustic combustion oscillations in a staged aircraft engine model combustor. With increasing amount of the main fuel, a significant shift in the dominant frequency-mode occurs in noisy periodic dynamics, leading to a notable increase in oscillation amplitudes. The sustainment of noisy periodic dynamics during thermoacoustic combustion oscillations is clearly shown by the multiscale complexity-entropy causality plane in terms of statistical complexity. A modified version of the permutation entropy allows us to detect a precursor of the frequency-mode-shift before the amplification of pressure fluctuations.

Nonlinear dynamics of a buoyancy-induced turbulent fire.

We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in ε-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.

Chaotic dynamics of a swirling flame front instability generated by a change in gravitational orientation.

We have intensively examined the dynamic behavior of flame front instability in a lean swirling premixed flame generated by a change in gravitational orientation [H. Gotoda, T. Miyano, and I. G. Shepherd, Phys. Rev. E 81, 026211 (2010)PLEEE81539-375510.1103/PhysRevE.81.026211] from the viewpoints of complex networks, symbolic dynamics, and statistical complexity. Here, we considered the permutation entropy in combination with the surrogate data method, the permutation spectrum test, and the multiscale complexity-entropy causality plane incorporating a scale-dependent approach, none of which have been considered in the study of flame front instabilities. Our results clearly show the possible presence of chaos in flame front dynamics induced by the coupling of swirl-buoyancy interaction in inverted gravity. The flame front dynamics also possesses a scale-free structure, which is reasonably shown by the probability distribution of the degree in ε-recurrence networks.

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

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.

Multi-scale complexity entropy causality plane: An intrinsic measure for indicating two-phase flow structures

We extend the complexity entropy causality plane (CECP) to propose a multi-scale complexity entropy causality plane (MS-CECP) and further use the proposed method to discriminate the deterministic characteristics of different oil-in-water flows. We first take several typical time series for example to investigate the characteristic of the MS-CECP and find that the MS-CECP not only describes the continuous loss of dynamical structure with the increase of scale, but also reflects the determinacy of the system. Then we calculate the MS-CECP for the conductance fluctuating signals measured from oil—water two-phase flow loop test facility. The results indicate that the MS-CECP could be an intrinsic measure for indicating oil-in-water two-phase flow structures.

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.