As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the $LS{E}^{FSTE100}$ and $LS{E}^{S\&P500}$ are higher than $LS{E}^{SZI}$, which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy.

As effective tools for time series analyzing, a variety of information entropies have been widely applied in engineering, economic, biomedicine and other fields. In this paper, we define a new distance between finite sequence based on inversion and derive a new entropy, Fuzzy Permutation Entropy(FPE). A comparison of recognition performance for WGN, 1/f noise, periodical, or chaotic sequence and sine waves shows that FPE is valid on distinguishing deterministic signals from stochastic signals. Further contrast studying versus FE and PE shows that FPE is more sensitive to the alteration of the complexity of time series and more effective on separating different signals. Moreover, FPE is used to explore the distinction of the complexity of various traffic flows via the time headways which is simulated from the improved brake light rule model. We hope it is conducive to design Intelligent Transportation Management System.

As effective representations of complex systems, complex networks have attracted scholarly attention for their many practical applications. They also represent a new tool for time series analysis. In order to characterize the underlying dynamic features, the structure of transformed networks should be encoded with the systematic evolution information that always hides behind the time series data. Thus, the way of mapping segments of the time series into nodes of the network is particularly crucial, but it is liable to be unstable under noise and missing values. In this paper, we propose a coarse-graining based on statistics of segments (CBS) founded complex network method, which can make it immune to interference to a certain degree. The time series is divided into many segments by a slide window, of which the width is determined by the multi-scale entropy of the data. We use a multi-dimensional symbol to represent the motion state of every segment. Due to the utilization of the distribution information of the fragments’ numerical characteristics, the coarse-graining process is self-adaptive to some extent. The complex network is then established based on the adjacent relations of the symbolic sequence. With our method, the differences in the network measurements between the periodic and chaotic motion is easily observable. Furthermore, we investigated the robustness of CBS by adding noise and missing values. We found that CBS is still valid, even with strong noise and 15% missing values, and simulation shows that it is more robust than the VG and LS approaches. By mapping a time series into a complex network, we provide a new tool for understanding the dynamic evolution mechanism of a complex system. This method has been applied in various fields, such as physics, engineering, medicine and economics. However, the interference of noise may greatly affects the reliability of judgment, which is based on the structures of transformed networks. An insufficient robustness is mostly to blame for the transformation from a time series to a symbolic sequence. In this paper, we suggest a new approach to the coarse-graining process which is self-adaptive for threshold choosing. Simulations show that even with strong disturbances, our network structure is easily distinguishable under different dynamic mechanisms.

Distinguishing between chaotic and stochastic dynamics given an input series is a widely studied topic within the time series analysis due to high demand from the practitioners in various fields. Due to one of the fundamental properties of chaotic systems, namely, being sensitive to parameters and initial conditions, chaotic time series exhibit features also observed in randomly generated signals. In this paper, we introduce distance as a measure of similarity between segments based on the ordinal structure. Furthermore, we introduce a new fuzzy entropy, Fuzzy Permutation Entropy (FPE), which can be used to detect determinism in time series. FPE immunes from repeated equal values in signals to some extent, especially for chaotic series. With specific embedding dimensions, it can be employed to distinguish chaotic signals from noise. We show an example for white Gaussian noise, autoregressive moving-average, continuous or discrete chaotic time series, and test FPE’s performance with additive observational noise. We show an application of FPE on rolling bearings’ fault diagnosis.

Construction the complex network paradigm, it is evidenced a new tool for exploring the dynamic mechanism hiding in the time series data which is a trajectory of complex system. This method has been applied in various domains gradually, such as physics, engineering, medicine and economics. In this paper, a new method for network paradigm transforming based on separating with the isoprobability is proposed, then it is applied in EEG signal analysis. The measures of transformed networks from 62-electrods ESI NeuroScan platform were used to construct EEG map. A three-layer convolutional neural network with 15 input channels were built so as to implement EEG-based emotion assessment. By nine fold cross validation, the structure of the convolutional neural network is improved. The simulation shows that our approach is better than differential entropy features based method.