Multivariate Multiscale Entropy Research Articles

Analysis and identification of gas-liquid two-phase flow pattern based on multivariate multi-scale dispersion entropy and interconnected dispersion pattern complex network

Gas-liquid two-phase flow is polymorphic and unstable. The investigation of the flow behavior of two-phase flow is vital for the application of gas-liquid transport in ocean engineering areas. We propose an analytical framework that combines multivariate multi-scale dispersion entropy (mvMDE) and interconnected dispersion pattern complex networks (IDPCN) for flow patterns. The resistance sensor array is used to capture the two-phase flow fluctuation signals in the riser, and the dimensionally reduced time series are nonlinearly mapped into a multivariate symbolic sequence. The mvMDE of the multivariate symbolic sequence is computed to measure the complexity of the flow pattern signals at the level of amplitude variation. In addition, a new multis-cale complex network based on the symbolic sequence is proposed to study the pseudo spatial coupling behavior of flow patterns. The evolution of the flow pattern from bubble to churn flow is quantitatively characterized using the mean value of the complex network indices in the optimal scale range. Finally, we construct the joint plane of mvMDE and two network indices to complete flow pattern identification. The research results show that the framework can effectively fuse multi-channel flow pattern information at different time scales to reveal the evolution mechanism of gas-liquid two-phase flow.

Eigen-entropy based time series signatures to support multivariate time series classification

Most current algorithms for multivariate time series classification tend to overlook the correlations between time series of different variables. In this research, we propose a framework that leverages Eigen-entropy along with a cumulative moving window to derive time series signatures to support the classification task. These signatures are enumerations of correlations among different time series considering the temporal nature of the dataset. To manage dataset’s dynamic nature, we employ preprocessing with dense multi scale entropy. Consequently, the proposed framework, Eigen-entropy-based Time Series Signatures, captures correlations among multivariate time series without losing its temporal and dynamic aspects. The efficacy of our algorithm is assessed using six binary datasets sourced from the University of East Anglia, in addition to a publicly available gait dataset and an institutional sepsis dataset from the Mayo Clinic. We use recall as the evaluation metric to compare our approach against baseline algorithms, including dependent dynamic time warping with 1 nearest neighbor and multivariate multi-scale permutation entropy. Our method demonstrates superior performance in terms of recall for seven out of the eight datasets.

Refined composite multivariate multiscale fuzzy dispersion entropy: Theoretical analysis and applications

Multivariate multiscale sample entropy (mvMSE) is a popular method to quantify the irregularity of multi-channel time series. However, mvMSE generates either undefined or unreliable results for short-length signals and has a high computational cost. To address these issues, multivariate multiscale dispersion entropy (mvMDE) was recently developed, but it depends on its parameters and overlooks some data information. To address these limitations, we herein propose an extension of fuzzy dispersion entropy (FDE) by incorporating fuzzy set theory, multidimensional embedding reconstruction theory, and dispersion patterns. This leads to the multivariate multiscale FDE (mvMFDE) and refined composite mvMFDE (RCmvMFDE) measures. (RC)mvMFDE is the first multivariate analysis based on Shannon entropy that uses the fuzzification concept. Some sets of time series have been synthesized and analyzed using several concepts in multivariate signal processing to evaluate the advantages of our introduced mvMFDE and RCmvMFDE. The results indicated that the proposed methods are less sensitive to their parameters, signal length, and noise, providing more stable results compared to the existing approaches mvMSE and mvMDE. On multi-channel noise signals and bivariate autoregressive processes, mvMSE, mvMDE, and mvMFDE produced similar finding although mvMFDE exhibited superior discriminative capabilities. When applied to one physiological dataset and two mechanical datasets, RCmvMFDE distinguished the diverse dynamics of multichannel signals exceptionally well.

How to mine the abnormal information of power transformers: An efficient tool for quantifying the fault characteristics via multi-vibration signals

The new power system puts forward higher requirements for the reliability of power equipment. Mining the intrinsic information of equipment operation from massive data is the key challenge to determining fault early warning. The transformer fault diagnosis through vibration signal analysis has gained increasing prominence. However, the vibration signals produced by power transformers exhibit complex nonlinear and multivariate fluctuations due to the interaction of electromagnetic and mechanical factors. Unfortunately, the traditional fault diagnosis models lack the capability to capture extensive global fault information, resulting in inadequate performance in fault identification. This paper proposes the enhanced hierarchical multivariate multiscale fuzzy entropy (EHMvMFE) as an effective method for quantifying defect information in multivariate transformer signals to overcome the challenge. Firstly, the enhanced hierarchical decomposition method and time series coarse-graining theory are introduced into multivariate fuzzy entropy to develop EHMvMFE, which can comprehensively reflect the feature information of multivariate signals from the full range of frequencies. Then, EHMvMFE is utilized to extract the features via multivariate vibration signals of the transformer. Finally, the extreme learning machine is conducted to achieve effective identification of abnormal conditions. The proposed method is applied to two categories of transformer fault cases, and the diagnostic indicators are at least higher than 99.70 % and 91.82 %, which indicates a strong advantage in comparison with other popular models. The approach could be flexibly extended to the fault diagnosis of other power equipment, which is a potentially effective tool for improving the reliability of power systems.

Multivariate multi-scale cross-fuzzy entropy and SSA-SVM-based fault diagnosis method of gearbox

Abstract Fuzzy entropy (FuzzyEn) is widely recognized as a powerful tool for analyzing nonlinear dynamics and measuring the complexity of time series data. It has been utilized as an effective indicator to capture nonlinear fault features in gearbox vibration signals. However, FuzzyEn only measures complexity at a single scale, ignoring the valuable information contained in large-scale features of the time series. Furthermore, FuzzyEn does not account for coupling characteristics between related or synchronized time series. To address these limitations, a novel entropy-based approach called multivariate multi-scale cross-fuzzy entropy (MvMCFE) is proposed in this paper for measuring the complexity and mutual predictability of two multivariate time series. Relying on the advantages of MvMCFE in nonlinear feature extraction, a new fault diagnosis method for gearboxes is proposed based on MvMCFE and an optimized support vector machine (SVM) using the salp swarm algorithm (SSA-SVM). Ultimately, the proposed gearbox diagnostic method is employed to analyze the gearbox experimental data and a comparison with existing fault diagnosis approaches is conducted. The comparison results indicate that the proposed method can effectively extract nonlinear fault features of gearboxes and achieve the highest recognition rate compared to the other methods.

Unbiased multivariate multiscale sample entropy

The development of multi-channel data acquisition techniques has provided richer prior information for studying the nonlinear dynamic characteristics of complex systems. However, conventional nonlinear feature extraction algorithms prove unsuitable in the context of multi-channel data. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although the MMSE algorithm generalized the multiscale sample entropy algorithm, presenting a novel method for multidimensional data analysis, it remains deficient in theoretical underpinning and suffers from shortcomings, such as missing cross-channel correlation information and having biased estimation results. In this paper, unbiased multivariate multiscale sample entropy algorithm (UMMSE) is proposed. UMMSE increases the embedding dimension from <i>M</i> to <i>M</i> + <i>p</i>. This increasing strategy facilitates the reconstruction of a deterministic phase space. By virtue of theoretical scrutiny grounded in probability theory and subsequent experimental validation, this paper illustrates the algorithm's effectiveness in extracting inter-channel correlation information through the integration of cross-channel conditional probabilities. The computation of similarities between sample points across different channels is recognized as a potential source of bias and instability in algorithms.Through simulation experiments, this study delineates the parameter selection range for the UMMSE algorithm. Subsequently, diverse simulation signals are employed to showcase the UMMSE algorithm’s efficacy in extracting both within-channel and cross-channel correlation information. Ultimately, this paper demonstrates that the new algorithm has the lowest computational cost compared with traditional MMSE algorithms.

Optimized multivariate multiscale slope entropy for nonlinear dynamic analysis of mechanical signals

Slope entropy (SloEn) is an effective nonlinear dynamic method to represent the complexity of time series, which has been extensively applied to various mechanical signal processing. However, it is only applicable to the analysis of single-channel time series at a single scale. Additionally, thresholds γandδ of SloEn can affect the division of symbols. To address these limitations, this paper firstly develops multivariate SloEn (mvSloEn) and extends it to multiscale mvSloEn (mvMSloEn), which not only accounts for the correlation of time series complexity within and across channels, but also mirrors the complexity of multi-channel time series over multiple scales. Furthermore, the sea-horse optimization-mvMSloEn (SHO-mvMSloEn) is proposed through utilizing the sea-horse optimizer (SHO) to fine-tune the thresholds for improved performance. Finally, the proposed SHO-mvMSloEn is applied to three real-world datasets and the highest classification accuracies are all over 98 %, superior to the existing multivariate multiscale dispersion entropy (mvMDE), multivariate multiscale fuzzy entropy (mvMFE), and multivariate multiscale sample entropy (mvMSE), which demonstrates that the proposed SHO-mvMSloEn always exhibits the best feature extraction capability.

The less complex temporal patterns of resting‑state EEG activity, the lower the visual temporal order threshold.

Speech understanding, watching a movie, listening to music etc., requires perception of the temporal order of at least two incoming events. A history of performing these tasks may be reflected in spontaneous brain activity. Here, we examined the relationship between the complexity (temporal dynamics) of resting‑state EEG (rsEEG) signal, assessed using the multivariate MultiScale Entropy (mMSE) algorithm, and the perception of event ordering, indexed by a visual temporal order threshold (TOT), i.e., the minimum duration necessary to correctly identify the before‑after relation between two stimuli. Healthy adolescents and young adults performed a psychophysical task measuring the TOT and underwent an eyes‑closed rsEEG study. The features of mMSE vectors, namely the area under curve (AUC) that represents total signal complexity, as well as the MaxSlope and the AvgEnt, corresponding to the entropy at fine‑ and coarse‑grained timescales, respectively, were obtained for the central (midline), anterior, middle and posterior channel sets. The greater the AUC and AvgEnt values in the central, left and right posterior areas, and the higher AUC in the right middle region, the higher the TOT. The most significant relationships were found for the midline electrodes (Fz, Cz, Pz, Oz). There were no significant correlations between the MaxSlope values and the TOT. To the best of our knowledge, this is the first study demonstrating that spontaneous EEG signal complexity is associated with the temporal order perception of two stimuli presented in rapid succession. Our findings may indicate that low total and coarse entropy levels of rsEEG signal are beneficial for visual temporal order judgments.

Multivariate multiscale entropy (mMSE) as a tool for understanding the resting-state EEG signal dynamics: the spatial distribution and sex/gender-related differences

BackgroundThe study aimed to determine how the resting-state EEG (rsEEG) complexity changes both over time and space (channels). The complexity of rsEEG and its sex/gender differences were examined using the multivariate Multiscale Entropy (mMSE) in 95 healthy adults. Following the probability maps (Giacometti et al. in J Neurosci Methods 229:84–96, 2014), channel sets have been identified that correspond to the functional networks. For each channel set the area under curve (AUC), which represents the total complexity, MaxSlope—the maximum complexity change of the EEG signal at thefine scales (1:4 timescales), and AvgEnt—to the average entropy level at coarse-grained scales (9:12 timescales), respectively, were extracted. To check dynamic changes between the entropy level at the fine and coarse-grained scales, the difference in mMSE between the #9 and #4 timescale (DiffEnt) was also calculated.ResultsWe found the highest AUC for the channel sets corresponding to the somatomotor (SMN), dorsolateral network (DAN) and default mode (DMN) whereas the visual network (VN), limbic (LN), and frontoparietal (FPN) network showed the lowest AUC. The largest MaxSlope were in the SMN, DMN, ventral attention network (VAN), LN and FPN, and the smallest in the VN. The SMN and DAN were characterized by the highest and the LN, FPN, and VN by the lowest AvgEnt. The most stable entropy were for the DAN and VN while the LN showed the greatest drop of entropy at the coarse scales. Women, compared to men, showed higher MaxSlope and DiffEnt but lower AvgEnt in all channel sets.ConclusionsNovel results of the present study are: (1) an identification of the mMSE features that capture entropy at the fine and coarse timescales in the channel sets corresponding to the main resting-state networks; (2) the sex/gender differences in these features.

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

A new rotating machinery fault diagnosis method for different speeds based on improved multivariate multiscale fuzzy distribution entropy

Multivariate Multiscale Entropy: An Approach to Estimating Vigilance of Driver

Various driver’s vigilance estimation techniques currently exist in the literature. But none of them estimates the driver’s vigilance in the complexity domain. In this research, we propose the recently introduced multivariate multiscale entropy method to fill the above mentioned research gap. We apply this technique to differential entropy features of electroencephalogram and electrooculogram signals to detect driver’s vigilance. Also, we employ it to the percentage of eye closure values to analyse the driver’s cognitive states (awake, tired and drowsy) in the complexity domain. The contribution of this research is to efficiently classify the driver’s cognitive states using a new feature based on multivariate multiscale entropy. The experimental complexity profile curves show the statistically significant differences (p < 0.01) among brain electroencephalogram, forehead electroencephalogram and electrooculogram signals. Moreover, the difference in the multivariate sample entropy across all scales in awake (1.0828 ± 0.4664), tired (0.7841 ± 0.3183) and drowsy (0.2938 ± 0.1664) states are statistically significant (p <0.01). Also, the support vector machine, a machine learning technique, discriminates the driver’s cognitive states with a promising classification accuracy of 76.2%. Therefore, the complexity profile of driver’s cognitive states could be an indicator for vigilance estimation.

Improved multivariate multiscale sample entropy and its application in multi-channel data.

Entropy, as a nonlinear feature in information science, has drawn much attention for time series analysis. Entropy features have been used to measure the complexity behavior of time series. However, traditional entropy methods mainly focus on one-dimensional time series originating from single-channel transducers and are incapable of handling the multidimensional time series from multi-channel transducers. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although MMSE generalizes multiscale sample entropy and provides a new method for multidimensional data analysis, it lacks necessary theoretical support and has shortcomings, such as missing cross-channel correlation information and having biased estimation results. This paper proposes an improved multivariate multiscale sample entropy (IMMSE) algorithm to overcome these shortcomings. This paper highlights the existing shortcomings in MMSE under the generalized algorithm. The rationality of IMMSE is theoretically proven using probability theory. Simulations and real-world data analysis have shown that IMMSE is capable of effectively extracting cross-channel correlation information and demonstrating robustness in practical applications. Moreover, it provides theoretical support for generalizing single-channel entropy methods to multi-channel situations.

Coating Damage Detection of Vessels Using Machine Learning-Based Underwater Electric Field

There has been extensive research on corrosion electric fields because of their special characteristics. There are apparent distribution characteristics corresponding to different coating damage regions of a vessel. To accurately detect where the coating damage region is located on vessels using underwater electric field signature, in this study, a method called “refined composite multivariate multiscale fluctuation reverse dispersion entropy (RCMMFRDE)” was proposed. This method effectively extracted the multichannel signal in a complex environment of poor stability and high noise. By combining RCMMFRDE and hierarchical prototype (HP), a novel coating damage detection method was developed. First, the accumulated differential value was calculated to determine the side on which the vessel had the damaged coating. Second, RCMMFRDE was used to extract the features of electric field signals. Then, feature vector dimensionality reduction was carried out using pair-wise feature proximity (PWFP). The low-dimensional features were given as input to the HP classifier to detect the damaged region. Finally, a series of numerical and physical scale experiments were conducted to validate the feasibility of the proposed method. The damaged region was efficiently predicted, achieving satisfactory accuracy of 96.67% and 92.00% in numerical and measurement data respectively; thus, it is a suitable alternative to conventional methods, especially when there is a lack of previous environmental information.

Which Multivariate Multi-Scale Entropy Algorithm Is More Suitable for Analyzing the EEG Characteristics of Mild Cognitive Impairment?

So far, most articles using the multivariate multi-scale entropy algorithm mainly use algorithms to analyze the multivariable signal complexity without clearly describing what characteristics of signals these algorithms measure and what factors affect these algorithms. This paper analyzes six commonly used multivariate multi-scale entropy algorithms from a new perspective. It clarifies for the first time what characteristics of signals these algorithms measure and which factors affect them. It also studies which algorithm is more suitable for analyzing mild cognitive impairment (MCI) electroencephalograph (EEG) signals. The simulation results show that the multivariate multi-scale sample entropy (mvMSE), multivariate multi-scale fuzzy entropy (mvMFE), and refined composite multivariate multi-scale fuzzy entropy (RCmvMFE) algorithms can measure intra- and inter-channel correlation and multivariable signal complexity. In the joint analysis of coupling and complexity, they all decrease with the decrease in signal complexity and coupling strength, highlighting their advantages in processing related multi-channel signals, which is a discovery in the simulation. Among them, the RCmvMFE algorithm can better distinguish different complexity signals and correlations between channels. It also performs well in anti-noise and length analysis of multi-channel data simultaneously. Therefore, we use the RCmvMFE algorithm to analyze EEG signals from twenty subjects (eight control subjects and twelve MCI subjects). The results show that the MCI group had lower entropy than the control group on the short scale and the opposite on the long scale. Moreover, frontal entropy correlates significantly positively with the Montreal Cognitive Assessment score and Auditory Verbal Learning Test delayed recall score on the short scale.

Fault diagnosis of bearing based on refined piecewise composite multivariate multiscale fuzzy entropy

As one of the key components of the train, the condition of the bearing is related to the train's safe operation. The vibration signal of the bearing is usually nonlinear and nonstationary, which makes it difficult to extract fault features and leads to low diagnostic accuracy. Entropy theory can effectively measure the change of nonlinearity and complexity of the vibration signal. However, the conventional entropy algorithm cannot extract the characteristics of a multi-channel signal simultaneously. A bearing fault diagnosis method based on refined piecewise composite multivariate multiscale fuzzy entropy (RPCMMFE) and convolutional neural network (CNN) is proposed. The proposed method can fully extract fault features and improve fault diagnosis accuracy. Firstly, based on multivariate multiscale fuzzy entropy (MMFE), RPCMMFE is proposed by introducing refined theory and piecewise composite theory. Then, the RPCMMFE of different fault signals is calculated, and RPCMMFE is considered to be a feature vector that acts as an input into the CNN for fault diagnosis. Finally, it is verified by two groups of experiments. The experimental results show that the features extracted by this method have better stability and discrimination ability and can identify bearing faults more accurately. The average accuracy rates are 99% and 99.17%, respectively.

Entropy-Based Emotion Recognition from Multichannel EEG Signals Using Artificial Neural Network.

Humans experience a variety of emotions throughout the course of their daily lives, including happiness, sadness, and rage. As a result, an effective emotion identification system is essential for electroencephalography (EEG) data to accurately reflect emotion in real-time. Although recent studies on this problem can provide acceptable performance measures, it is still not adequate for the implementation of a complete emotion recognition system. In this research work, we propose a new approach for an emotion recognition system, using multichannel EEG calculation with our developed entropy known as multivariate multiscale modified-distribution entropy (MM-mDistEn) which is combined with a model based on an artificial neural network (ANN) to attain a better outcome over existing methods. The proposed system has been tested with two different datasets and achieved better accuracy than existing methods. For the GAMEEMO dataset, we achieved an average accuracy ± standard deviation of 95.73% ± 0.67 for valence and 96.78% ± 0.25 for arousal. Moreover, the average accuracy percentage for the DEAP dataset reached 92.57% ± 1.51 in valence and 80.23% ± 1.83 in arousal.

Multivariate Multiscale Cosine Similarity Entropy and Its Application to Examine Circularity Properties in Division Algebras

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.

An Equivalent Model of Wind Farm Based on Multivariate Multi-Scale Entropy and Multi-View Clustering

Wind farm (WF) equivalence is an effective method to achieve accurate and efficient simulation of large-scale WF. Existing equivalent models are generally suitable for one certain or very few scenarios, and have difficulty reflecting the multiple aspects of dynamic processes of WF. Aiming at these problems, this paper proposes an equivalent model of WF based on multivariate multi-scale entropy (MMSE) and multi-view clustering. Firstly, the influence of the factors on the dynamic process of the wind turbine (WT) is discussed, including control mode, wind speed and its wake effect, resistance of crowbar resistor and so on. The relationship between these factors and the dynamic equivalence of WF is analyzed. Secondly, an overview of MMSE is given, and the applicability of MMSE on WF equivalence is analyzed. On this basis, this paper proposes the extraction process of a WT clustering indicator using MMSE. Then, the multi-view fuzzy C means (MV-FCM) algorithm is used for the clustering of WTs, and the equivalent model of WF is obtained after calculating the equivalent parameters. Finally, the IEEE14 power system including WF is simulated. The results show that the equivalent model could be applied to dynamic process simulation in various fault scenarios of power systems, and the error is small when the cluster number is 4. Compared with the detailed model, the simulation time of the WF equivalent model proposed in this paper is shortened by 86%, and the simulation accuracy is improved by about 44% compared with the comparative model.

Combine Harvester Bearing Fault-Diagnosis Method Based on SDAE-RCmvMSE.

In the fault monitoring of rolling bearings, there is always loud noise, leading to poor signal stationariness. How to accurately and efficiently identify the fault type of rolling bearings is a challenge. Based on multivariate multiscale sample entropy (mvMSE), this paper introduces the refined composite mvMSE (RCmvMSE) into the fault extraction of the rolling bearing. A rolling bearing fault-diagnosis method based on stacked auto encoder and RCmvMSE (SDAE-RCmvMSE) is proposed. In the actual environment, the fault-diagnosis method use the multichannel vibration signals of the bearing as the input of stacked denoising autoencoders (SDAEs) to filter the noise of the vibration signals. The features of denoise signals are extracted by RCmvMSE and the rolling bearing operation-state diagnosis is completed with a support-vector machine (SVM) model. The results show that in the original test data, the accuracy rates of SDAE-RCmvMSE, RCmvMSE, and commonplace features of vibration signals combined with SVM (CFVS-SVM) methods are 99.5%, 100%, and 96% respectively. In the data with noise, the accuracy rates of RCmvMSE and CFVS-SVM are 97.75% and 93.08%, respectively, but the accuracy of SDAE-RCmvMSE is still 100%.

A MVMD–MMFE algorithm and its application in the flow patterns identification of horizontal oil–water two-phase flow

Abstract Aiming to extract the main information features of fluid multivariate conductance signals and identify the flow patterns under different flow velocities, we present a multichannel time series analysis algorithm based on the multivariate variational mode decomposition (MVMD) and multivariate multiscale fuzzy entropy (MMFE). Firstly, by simulating a multichannel complex signal and performing a series of sensitivity experiments within various noise intensities, we prove the feasibility of the MVMD in chaotic time series. Then, we employ the MVMD to decompose multivariate conductance signals into the intrinsic mode function (IMF) and calculate the MMFE of the IMFs for different flow patterns. Meanwhile, the multivariate empirical mode decomposition (MEMD) is also applied on the comparison of signal decomposition. Finally, we discuss the classification consequence under different mode values k to realize the optimal decomposition. The experimental results show that the MVMD–MMFE algorithm can extract the main information of fluid multichannel signals and distinguish three horizontal oil–water flow patterns effectively, which provides an idea for studying the nonlinear characteristics of the chaotic system.