A high dimensional delay selection for the reconstruction of proper phase space with cross auto-correlation

Adaptive symbolic transfer entropy and its applications in modeling for complex industrial systems

Directed coupling between variables is the foundation of studying the dynamical behavior of complex systems. We propose an adaptive symbolic transfer entropy (ASTE) method based on the principle of equal probability division. First, the adaptive kernel density method is used to obtain an accurate probability density function for an observation series. Second, the complete phase space of the system can be obtained by using the multivariable phase space reconstruction method. This provides common parameters for symbolizing a time series, including delay time and embedding dimension. Third, an optimization strategy is used to select the appropriate symbolic parameters of a time series, such as the symbol set and partition intervals, which can be used to convert the time series to a symbol sequence. Then the transfer entropy between the symbolic sequences can be carried out. Finally, the proposed method is analyzed and validated using the chaotic Lorenz system and typical complex industrial systems. The results show that the ASTE method is superior to the existing transfer entropy and symbolic transfer entropy methods in terms of measurement accuracy and noise resistance, and it can be applied to the network modeling and performance safety analysis of complex industrial systems.

Nonuniform State Space Reconstruction for Multivariate Chaotic Time Series

State space reconstruction is the foundation of chaotic system modeling. Selection of reconstructed variables is essential to the analysis and prediction of multivariate chaotic time series. As most existing state space reconstruction theorems deal with univariate time series, we have presented a novel nonuniform state space reconstruction method using information criterion for multivariate chaotic time series. We derived a new criterion based on low dimensional approximation of joint mutual information for time delay selection, which can be solved efficiently through the use of an intelligent optimization algorithm with low computation complexity. The embedding dimension is determined by conditional entropy, after which the reconstructed variables have relatively strong independence and low redundancy. The scheme, which integrates nonuniform embedding and feature selection, results in better reconstructions for multivariate chaotic systems. Moreover, the proposed nonuniform state space reconstruction method shows good performance in forecasting benchmark and actual multivariate chaotic time series.

Complexity in congestive heart failure: A time-frequency approach

Reconstruction of phase space is an effective method to quantify the dynamics of a signal or a time series. Various phase space reconstruction techniques have been investigated. However, there are some issues on the optimal reconstructions and the best possible choice of the reconstruction parameters. This research introduces the idea of gradient cross recurrence (GCR) and mean gradient cross recurrence density which shows that reconstructions in time frequency domain preserve more information about the dynamics than the optimal reconstructions in time domain. This analysis is further extended to ECG signals of normal and congestive heart failure patients. By using another newly introduced measure-gradient cross recurrence period density entropy, two classes of aforesaid ECG signals can be classified with a proper threshold. This analysis can be applied to quantifying and distinguishing biomedical and other nonlinear signals.