As a novel form of visual analysis technique, the Poincaré plot has been used to identify correlation patterns in time series that cannot be detected using traditional analysis methods. In this work, based on the nonextensive of EEG, Poincaré plot nonextensive distribution entropy (NDE) is proposed to solve the problem of insufficient discrimination ability of Poincaré plot distribution entropy (DE) in analyzing fractional Brownian motion time series with different Hurst indices. More specifically, firstly, the reasons for the failure of Poincaré plot DE in the analysis of fractional Brownian motion are analyzed; secondly, in view of the nonextensive of EEG, a nonextensive parameter, the distance between sector ring subintervals from the original point, is introduced to highlight the different roles of each sector ring subinterval in the system. To demonstrate the usefulness of this method, the simulated time series of the fractional Brownian motion with different Hurst indices were analyzed using Poincaré plot NDE, and the process of determining the relevant parameters was further explained. Furthermore, the published sleep EEG dataset was analyzed, and the results showed that the Poincaré plot NDE can effectively reflect different sleep stages. The obtained results for the two classes of time series demonstrate that the Poincaré plot NDE provides a prospective tool for single-channel EEG time series analysis.

To evaluate the synchronization of bivariate time series has been a hot topic, and a number of measures have been proposed. In this work, by introducing the ordinal pattern transition network into the crossplot, a new method for measuring the synchronization of bivariate time series is proposed. After the crossplot been partitioned and coded, the coded partitions are defined as network nodes and a directed weighted network is constructed based on the temporal adjacency of the nodes. The crossplot transition entropy of the network is proposed as an indicator of the synchronization between two time series. To test the characteristics and performance of the method, it is used to analyse the unidirectional coupled Lorentz model and compared it with existing methods. The results showed the new method had the advantages of easy parameter setting, efficiency, robustness, good consistency and suitability for short time series. Finally, electroencephalogram (EEG) data from auditory-evoked potential EEG-biometric dataset are investigated, and some useful and interesting results are obtained.

The complex network nature of human brains has led an increasing number of researchers to adopt a complex network to assess the cognitive load. The method of constructing complex networks has a direct impact on assessment results. During the process of using the cross-permutation entropy (CPE) method to construct complex networks for cognitive load assessment, it is found that the CPE method has the shortcomings of ignoring the transition relationship between symbols and the analysis results are vulnerable to parameter settings. In order to address this issue, a new method based on the CPE principle is proposed by combining the advantages of the transition networks and the bubble entropy. From an interaction perspective, this method suggested that the node-wise out-link transition entropy of the cross-transition network between two time series is used as the edge weight to build a complex network. The proposed method was tested on the unidirectional coupled Henon model and the results demonstrated its suitability for the analysis of short time series by decreasing the influence of the embedding dimension and improving the reliability under the weak coupling conditions. The proposed method was further tested on the publicly available EEG dataset and showed significant superiority compared with the conventional CPE method.

Motor current signal analysis is a common method that can be applied to the monitoring and diagnosis of electromechanical equipment. Three-phase unbalance will increase the line power loss and affect the safe operation of power-using equipment. To quickly analyze motor current three-phase unbalance, we propose a method to analyze three-phase unbalance by calculating the coefficient of variation of the three-phase current’s instantaneous frequency and instantaneous amplitude. Simulations were conducted to analyze the effects of amplitude deviation and phase deviation on the coefficient of variation of instantaneous frequency and instantaneous amplitude. The three-phase unbalance with continuous amplitude change was simulated and its instantaneous performance was analyzed. Experiments were conducted to compare and analyze the instantaneous information characteristics of the motor with the continuous changing of three-phase unbalance under different speed conditions. Simulations and experiments show that the proposed method in this paper can analyze three-phase unbalance.