Amplitude- and Fluctuation-Based Dispersion Entropy

Tsallis Entropy-Based Complexity-IPE Casualty Plane: A Novel Method for Complex Time Series Analysis

Due to its capacity to unveil the dynamic characteristics of time series data, entropy has attracted growing interest. However, traditional entropy feature extraction methods, such as permutation entropy, fall short in concurrently considering both the absolute amplitude information of signals and the temporal correlation between sample points. Consequently, this limitation leads to inadequate differentiation among different time series and susceptibility to noise interference. In order to augment the discriminative power and noise robustness of entropy features in time series analysis, this paper introduces a novel method called Tsallis entropy-based complexity-improved permutation entropy casualty plane (TC-IPE-CP). TC-IPE-CP adopts a novel symbolization approach that preserves both absolute amplitude information and inter-point correlations within sequences, thereby enhancing feature separability and noise resilience. Additionally, by incorporating Tsallis entropy and weighting the probability distribution with parameter q, it integrates with statistical complexity to establish a feature plane of complexity and entropy, further enriching signal features. Through the integration of multiscale algorithms, a multiscale Tsallis-improved permutation entropy algorithm is also developed. The simulation results indicate that TC-IPE-CP requires a small amount of data, exhibits strong noise resistance, and possesses high separability for signals. When applied to the analysis of heart rate signals, fault diagnosis, and underwater acoustic signal recognition, experimental findings demonstrate that TC-IPE-CP can accurately differentiate between electrocardiographic signals of elderly and young subjects, achieve precise bearing fault diagnosis, and identify four types of underwater targets. Particularly in underwater acoustic signal recognition experiments, TC-IPE-CP achieves a recognition rate of 96.67%, surpassing the well-known multi-scale dispersion entropy and multi-scale permutation entropy by 7.34% and 19.17%, respectively. This suggests that TC-IPE-CP is highly suitable for the analysis of complex time series.

Fault Diagnosis of Wind Turbine Gearbox Based on Modified Hierarchical Fluctuation Dispersion Entropy of Tan-Sigmoid Mapping

Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach based on modified hierarchical fluctuation dispersion entropy of tan-sigmoid mapping (MHFDE_TANSIG) and northern goshawk optimization-support vector machine (NGO-SVM) for wind turbine gearboxes. The tan-sigmoid (TANSIG) mapping function replaces the normal cumulative distribution function (NCDF) of the hierarchical fluctuation dispersion entropy (HFDE) method. Additionally, the hierarchical decomposition of the HFDE method is improved, resulting in the proposed MHFDE_TANSIG method. The vibration signals of wind turbine gearboxes are analyzed using the MHFDE_TANSIG method to extract fault features. The constructed fault feature set is used to intelligently recognize and classify the fault type of the gearboxes with the NGO-SVM classifier. The fault diagnosis methods based on MHFDE_TANSIG and NGO-SVM are applied to the experimental data analysis of gearboxes with different operating conditions. The results show that the fault diagnosis model proposed in this paper has the best performance with an average accuracy rate of 97.25%.

Benefits of Zero-Phase or Linear Phase Filters to Design Multiscale Entropy: Theory and Application

In various applications, multiscale entropy (MSE) is often used as a feature to characterize the complexity of the signals in order to classify them. It consists of estimating the sample entropies (SEs) of the signal under study and its coarse-grained (CG) versions, where the CG process amounts to (1) filtering the signal with an average filter whose order is the scale and (2) decimating the filter output by a factor equal to the scale. In this paper, we propose to derive a new variant of the MSE. Its novelty stands in the way to get the sequences at different scales by avoiding distortions during the decimation step. To this end, a linear-phase or null-phase low-pass filter whose cutoff frequency is well suited to the scale is used. Interpretations on how the MSE behaves and illustrations with a sum of sinusoids, as well as white and pink noises, are given. Then, an application to detect attentional tunneling is presented. It shows the benefit of the new approach in terms of p value when one aims at differentiating the set of MSEs obtained in the attentional tunneling state from the set of MSEs obtained in the nominal state. It should be noted that CG versions can be replaced not only for the MSE but also for other variants.

Dispersion complexity-entropy curves: An effective method to characterize the structures of nonlinear time series

The complexity-entropy curve (CEC) is a valuable tool for characterizing the structure of time series and finds broad application across various research fields. Despite its widespread usage, the original permutation complexity-entropy curve (PCEC), which is founded on permutation entropy (PE), exhibits a notable limitation: its inability to take the means and amplitudes of time series into considerations. This oversight can lead to inaccuracies in differentiating time series. In this paper, drawing inspiration from dispersion entropy (DE), we propose the dispersion complexity-entropy curve (DCEC) to enhance the capability of CEC in uncovering the concealed structures within nonlinear time series. Our approach initiates with simulated data including the logistic map, color noises, and various chaotic systems. The outcomes of our simulated experiments consistently showcase the effectiveness of DCEC in distinguishing nonlinear time series with diverse characteristics. Furthermore, we extend the application of DCEC to real-world data, thereby asserting its practical utility. A novel approach is proposed, wherein DCEC-based feature extraction is combined with multivariate support vector machine for the diagnosis of various types of bearing faults. This combination achieved a high accuracy rate in our experiments. Additionally, we employ DCEC to assess stock indices from different countries and periods, thereby facilitating an analysis of the complexity inherent in financial markets. Our findings reveal significant insights into the dynamic regularities and distinct structures of these indices, offering a novel perspective for analyzing financial time series. Collectively, these applications underscore the potential of DCEC as an effective tool for the nonlinear time series analysis.

Exploring the Hidden Complexity: Entropy Analysis in Pulse Oximetry of Female Athletes

This study examines the relationship between physiological complexity, as measured by Approximate Entropy (ApEn) and Sample Entropy (SampEn), and fitness levels in female athletes. Our focus is on their association with maximal oxygen consumption (VO2,max). Our findings reveal a complex relationship between entropy metrics and fitness levels, indicating that higher fitness typically, though not invariably, correlates with greater entropy in physiological time series data; however, this is not consistent for all individuals. For Heart Rate (HR), entropy measures suggest stable patterns across fitness categories, while pulse oximetry (SpO2) data shows greater variability. For instance, the medium fitness group displayed an ApEn(HR) = 0.57±0.13 with a coefficient of variation (CV) of 22.17 and ApEn(SpO2) = 0.96±0.49 with a CV of 46.08%, compared to the excellent fitness group with ApEn(HR) = 0.60±0.09 with a CV of 15.19% and ApEn(SpO2) =0.85±0.42 with a CV of 49.46%, suggesting broader physiological responses among more fit individuals. The larger standard deviations and CVs for SpO2 entropy may indicate the body's proficient oxygen utilization at higher levels of physical demand. Our findings advocate for combining entropy metrics with wearable sensor technology for improved biomedical analysis and personalized healthcare.

NLDyn - An open source MATLAB toolbox for the univariate and multivariate nonlinear dynamical analysis of physiological data

BACKGROUND AND OBJECTIVE

We present NLDyn, an open-source MATLAB toolbox tailored for in-depth analysis of nonlinear dynamics in biomedical signals. Our objective is to offer a user-friendly yet comprehensive platform for researchers to explore the intricacies of time series data.

METHODS

NLDyn integrates approximately 80 distinct methods, encompassing both univariate and multivariate nonlinear dynamics, setting it apart from existing solutions. This toolbox combines state-of-the-art nonlinear dynamical techniques with advanced multivariate entropy methods, providing users with powerful analytical capabilities. NLDyn enables analyses with or without a sliding window, and users can easily access and customize default parameters.

RESULTS

NLDyn generates results that are both exportable and visually informative, facilitating seamless integration into research and presentations. Its ongoing development ensures it remains at the forefront of nonlinear dynamics analysis.

CONCLUSIONS

NLDyn is a valuable resource for researchers in the biomedical field, offering an intuitive interface and a wide array of nonlinear analysis tools. Its integration of advanced techniques empowers users to gain deeper insights from their data. As we continually refine and expand NLDyn's capabilities, we envision it becoming an indispensable tool for the exploration of complex dynamics in biomedical signals.

Use of Intrinsic Entropy to Assess the Instantaneous Complexity of Thoracoabdominal Movement Patterns to Indicate the Effect of the Iso-Volume Maneuver Trial on the Performance of the Step Test

The recent surge in interest surrounds the analysis of physiological signals with a non-linear dynamic approach. The measurement of entropy serves as a renowned method for indicating the complexity of a signal. However, there is a dearth of research concerning the non-linear dynamic analysis of respiratory signals. Therefore, this study employs a novel method known as intrinsic entropy (IE) to assess the short-term dynamic changes in thoracoabdominal movement patterns, as measured by respiratory inductance plethysmography (RIP), during various states such as resting, step test, recovery, and iso-volume maneuver (IVM) trials. The findings reveal a decrease in IE of thoracic wall movement (TWM) and an increase in IE of abdominal wall movement (AWM) following the IVM trial. This suggests that AWM may dominate the breathing exercise after the IVM trial. Moreover, due to the high temporal resolution of IE, it proves to be a suitable measure for assessing the complexity of thoracoabdominal movement patterns under non-stationary states such as the step test and recovery. The results also demonstrate that the instantaneous complexity of TWM and AWM can effectively capture instantaneous changes during non-stationary states, which may prove valuable in understanding the respiratory mechanism for healthcare purposes in daily life.

Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis

Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE-FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE's performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.

Ensemble Improved Permutation Entropy: A New Approach for Time Series Analysis

Entropy quantification approaches have gained considerable attention in engineering applications. However, certain limitations persist, including the strong dependence on parameter selection, limited discriminating power, and low robustness to noise. To alleviate these issues, this paper introduces two novel algorithms for time series analysis: the ensemble improved permutation entropy (EIPE) and multiscale EIPE (MEIPE). Our approaches employ a new symbolization process that considers both permutation relations and amplitude information. Additionally, the ensemble technique is utilized to reduce the dependence on parameter selection. We performed a comprehensive evaluation of the proposed methods using various synthetic and experimental signals. The results illustrate that EIPE is capable of distinguishing white, pink, and brown noise with a smaller number of samples compared to traditional entropy algorithms. Furthermore, EIPE displays the potential to discriminate between regular and non-regular dynamics. Notably, when compared to permutation entropy, weighted permutation entropy, and dispersion entropy, EIPE exhibits superior robustness against noise. In practical applications, such as RR interval data classification, bearing fault diagnosis, marine vessel identification, and electroencephalographic (EEG) signal classification, the proposed methods demonstrate better discriminating power compared to conventional entropy measures. These promising findings validate the effectiveness and potential of the algorithms proposed in this paper.

EEG Signal Complexity Measurements to Enhance BCI-Based Stroke Patients' Rehabilitation

The second leading cause of death and one of the most common causes of disability in the world is stroke. Researchers have found that brain-computer interface (BCI) techniques can result in better stroke patient rehabilitation. This study used the proposed motor imagery (MI) framework to analyze the electroencephalogram (EEG) dataset from eight subjects in order to enhance the MI-based BCI systems for stroke patients. The preprocessing portion of the framework comprises the use of conventional filters and the independent component analysis (ICA) denoising approach. Fractal dimension (FD) and Hurst exponent (Hur) were then calculated as complexity features, and Tsallis entropy (TsEn) and dispersion entropy (DispEn) were assessed as irregularity parameters. The MI-based BCI features were then statistically retrieved from each participant using two-way analysis of variance (ANOVA) to demonstrate the individuals' performances from four classes (left hand, right hand, foot, and tongue). The dimensionality reduction algorithm, Laplacian Eigenmap (LE), was used to enhance the MI-based BCI classification performance. Utilizing k-nearest neighbors (KNN), support vector machine (SVM), and random forest (RF) classifiers, the groups of post-stroke patients were ultimately determined. The findings show that LE with RF and KNN obtained 74.48% and 73.20% accuracy, respectively; therefore, the integrated set of the proposed features along with ICA denoising technique can exactly describe the proposed MI framework, which may be used to explore the four classes of MI-based BCI rehabilitation. This study will help clinicians, doctors, and technicians make a good rehabilitation program for people who have had a stroke.

Multi Modal Feature Extraction for Classification of Vascular Dementia in Post-Stroke Patients Based on EEG Signal

Dementia is a term that represents a set of symptoms that affect the ability of the brain's cognitive functions related to memory, thinking, behavior, and language. At worst, dementia is often called a major neurocognitive disorder or senile disease. One of the most common types of dementia after Alzheimer's is vascular dementia. Vascular dementia is closely related to cerebrovascular disease, one of which is stroke. Post-stroke patients with recurrent onset have the potential to develop dementia. An accurate diagnosis is needed for proper therapy management to ensure the patient's quality of life and prevent it from worsening. The gold standard diagnostic of vascular dementia is complex, includes psychological tests, complete memory tests, and is evidenced by medical imaging of brain lesions. However, brain imaging methods such as CT-Scan, PET-Scan, and MRI have high costs and cannot be routinely used in a short period. For more than two decades, electroencephalogram signal analysis has been an alternative in assisting the diagnosis of brain diseases associated with cognitive decline. Traditional EEG analysis performs visual observations of signals, including rhythm, power, and spikes. Of course, it requires a clinician expert, time consumption, and high costs. Therefore, a quantitative EEG method for identifying vascular dementia in post-stroke patients is discussed in this study. This study used 19 EEG channels recorded from normal elderly, post-stroke with mild cognitive impairment, and post-stroke with dementia. The QEEG method used for feature extraction includes relative power, coherence, and signal complexity; the evaluation performance of normal-mild cognitive impairment-dementia classification was conducted using Support Vector Machine and K-Nearest Neighbor. The results of the classification simulation showed the highest accuracy of 96% by Gaussian SVM with a sensitivity and specificity of 95.6% and 97.9%, respectively. This study is expected to be an additional criterion in the diagnosis of dementia, especially in post-stroke patients.

Refined composite multiscale fluctuation-based dispersion Lempel-Ziv complexity for signal analysis

Dispersion Lempel-Ziv complexity (DLZC) and multiscale DLZC (MDLZC) are very recently introduced complexity indicators to quantify the dynamic change of time series in acoustics signals. They introduce the mapping steps of dispersion entropy (DE), which can effectively identify time series with different characteristics, but ignore the fluctuation information and have poor stability. In order to overcome these shortcomings, this paper firstly adds fluctuation information to DLZC and proposes fluctuation-based DLZC (FDLZC) as an alternative to the classical time series complexity index, followed by introducing an improved coarse-graining operation to propose the refined composite multiscale FDLZC (RCMFDLZC), which increases the number of features and also ensures the stability of FDLZC, and finally select the subsequence containing the most information by the minimum redundancy maximum relevance (mRMR) feature selection algorithm for subsequent experiments. The experimental results show that the extracted RCMFDLZC features have the strongest separability and better clustering effect in both bearing fault signals and ship radiated noise signals, and the RCMFDLZC-based signal analysis method also has higher recognition rate compared with other methods in bearing fault diagnosis and ship signal classification.

Assessment and Comparison of Nonlinear Measures in Resting-State Magnetoencephalograms in Alzheimer's Disease and Mild Cognitive Impairment

BACKGROUND

Nonlinear dynamical measures, such as fractal dimension (FD), entropy, and Lempel-Ziv complexity (LZC), have been extensively investigated individually for detecting information content in magnetoencephalograms (MEGs) from patients with Alzheimer's disease (AD).

OBJECTIVE

To compare systematically the performance of twenty conventional and recently introduced nonlinear dynamical measures in studying AD versus mild cognitive impairment (MCI) and healthy control (HC) subjects using MEG.

METHODS

We compared twenty nonlinear measures to distinguish MEG recordings from 36 AD (mean age = 74.06±6.95 years), 18 MCI (mean age = 74.89±5.57 years), and 26 HC subjects (mean age = 71.77±6.38 years) in different brain regions and also evaluated the effect of the length of MEG epochs on their performance. We also studied the correlation between these measures and cognitive performance based on the Mini-Mental State Examination (MMSE).

RESULTS

The results obtained by LZC, zero-crossing rate (ZCR), FD, and dispersion entropy (DispEn) measures showed significant differences among the three groups. There was no significant difference between HC and MCI. The highest Hedge's g effect sizes for HC versus AD and MCI versus AD were respectively obtained by Higuchi's FD (HFD) and fuzzy DispEn (FuzDispEn) in the whole brain and was most prominent in left lateral. The results obtained by HFD and FuzDispEn had a significant correlation with the MMSE scores. DispEn-based techniques, LZC, and ZCR, compared with HFD, were less sensitive to epoch length in distinguishing HC form AD.

CONCLUSIONS

FuzDispEn was the most consistent technique to distinguish MEG dynamical patterns in AD compared with HC and MCI.

EEG Entropy in REM Sleep as a Physiologic Biomarker in Early Clinical Stages of Alzheimer's Disease

BACKGROUND

Alzheimer's disease (AD) is associated with EEG changes across the sleep-wake cycle. As the brain is a non-linear system, non-linear EEG features across behavioral states may provide an informative physiologic biomarker of AD. Multiscale fluctuation dispersion entropy (MFDE) provides a sensitive non-linear measure of EEG information content across a range of biologically relevant time-scales.

OBJECTIVE

To evaluate MFDE in awake and sleep EEGs as a potential biomarker for AD.

METHODS

We analyzed overnight scalp EEGs from 35 cognitively normal healthy controls, 23 participants with mild cognitive impairment (MCI), and 19 participants with mild dementia due to AD. We examined measures of entropy in wake and sleep states, including a slow-to-fast-activity ratio of entropy (SFAR-entropy). We compared SFAR-entropy to linear EEG measures including a slow-to-fast-activity ratio of power spectral density (SFAR-PSD) and relative alpha power, as well as to cognitive function.

RESULTS

SFAR-entropy differentiated dementia from MCI and controls. This effect was greatest in REM sleep, a state associated with high cholinergic activity. Differentiation was evident in the whole brain EEG and was most prominent in temporal and occipital regions. Five minutes of REM sleep was sufficient to distinguish dementia from MCI and controls. Higher SFAR-entropy during REM sleep was associated with worse performance on the Montreal Cognitive Assessment. Classifiers based on REM sleep SFAR-entropy distinguished dementia from MCI and controls with high accuracy, and outperformed classifiers based on SFAR-PSD and relative alpha power.

CONCLUSION

SFAR-entropy measured in REM sleep robustly discriminates dementia in AD from MCI and healthy controls.

The complexity of spontaneous brain activity changes in schizophrenia, bipolar disorder, and ADHD was examined using different variations of entropy

Adult attention deficit/hyperactivity disorder (ADHD), schizophrenia (SCHZ), and bipolar disorder (BP) have common symptoms and differences, and the underlying neural mechanisms are still unclear. This article will thoroughly discuss the differences between ADHD, BP, and SCHZ (31 healthy control and 31 ADHD; 34 healthy control and 34 BP; 42 healthy control and 42 SCHZ) relative to healthy subjects in combination with three atlases (et al., the Brainnetome atlas, the Dosenbach atlas, the Power atlas) and seven entropies (et al., approximate entropy (ApEn), sample entropy (SaEn), permutation entropy (PeEn), fuzzy entropy (FuEn), differential entropy (DiffEn), range entropy (RaEn), and dispersion entropy (DispEn)), as well as the prominent significant brain regions, in the hope of giving information that is more suitable for analyzing different diseases' entropy. First, the reliability (et al., intraclass correlation coefficient [ICC]) of seven kinds of entropy is calculated and analyzed by using the MSC dataset (10 subjects and 100 sessions in total) and simulation data; then, seven types of entropy and multiscale entropy expanded based on seven kinds of entropy are used to explore the differences and brain regions of ADHD, BP, and SCHZ relative to healthy subjects; and finally, by verifying the classification performance of the seven information entropies on ADHD, BP, and SCHZ, the effectiveness of the seven entropy methods is evaluated through these three methods. The core brain regions that affect the classification are given, and DiffEn performed best on ADHD, SaEn for BP, and RaEn for SCHZ.

Fault detection of rotating machinery based on marine predator algorithm optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy

Feature extraction is the key to the fault detection of rotating machinery based on vibration signals, and the quality of the features influences the reliability of the detection. This paper develops a fault feature extraction method of rotating machinery based on optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy. First, resonance-based sparse signal decomposition is used to decompose the vibration signals adaptively. In order to obtain the resonance-based sparse signal decomposition algorithm with optimal performance, the marine predator algorithm is used for the parameters optimization with correlation kurtosis as the fitness function. Subsequently, based on the refined composite coarse-grained process and fluctuation dispersion entropy, a refined composite multiscale fluctuation dispersion entropy is developed, enabling a more accurate and comprehensive measure of the complexity of time series. Then, all feature matrices are input to the support matrix machine for fault identification. Experiments are conducted using two typical rotating machinery datasets for the validity of the proposed method, and comparisons are made with other methods. The results show that the proposed scheme outperforms other comparative methods regarding classification accuracy and stability. In addition, the proposed scheme can obtain relatively reliable classification results even when the data volume is small and the background noise is significant, demonstrating the scheme's potential for application in practical engineering.

A Novel Fault Diagnosis Method for Rolling Bearing Based on Hierarchical Refined Composite Multiscale Fluctuation-Based Dispersion Entropy and PSO-ELM

This paper proposes a novel fault diagnosis method for rolling bearing based on hierarchical refined composite multiscale fluctuation-based dispersion entropy (HRCMFDE) and particle swarm optimization-based extreme learning machine (PSO-ELM). First, HRCMFDE is used to extract fault features in the vibration signal at different time scales. By introducing the hierarchical theory algorithm into the vibration signal decomposition process, the problem of missing high-frequency signals in the coarse-grained process is solved. Fluctuation-based dispersion entropy (FDE) has the characteristics of insensitivity to noise interference and high computational efficiency based on the consideration of nonlinear time series fluctuations, which makes the extracted feature vectors more effective in describing the fault information embedded in each frequency band of the vibration signal. Then, PSO is used to optimize the input weights and hidden layer neuron thresholds of the ELM model to improve the fault identification capability of the ELM classifier. Finally, the performance of the proposed rolling bearing fault diagnosis method is verified and analyzed by using the CWRU dataset and MFPT dataset as experimental cases, respectively. The results show that the proposed method has high identification accuracy for the fault diagnosis of rolling bearings with varying loads and has a good load migration effect.

Stratified Multivariate Multiscale Dispersion Entropy for Physiological Signal Analysis

Multivariate entropy quantification algorithms are becoming a prominent tool for the extraction of information from multi-channel physiological time-series. However, in the analysis of physiological signals from heterogeneous organ systems, certain channels may overshadow the patterns of others, resulting in information loss. Here, we introduce the framework of Stratified Entropy to prioritize each channels' dynamics based on their allocation to respective strata, leading to a richer description of the multi-channel time-series. As an implementation of the framework, three algorithmic variations of the Stratified Multivariate Multiscale Dispersion Entropy are introduced. These variations and the original algorithm are applied to synthetic time-series, waveform physiological time-series, and derivative physiological data. Based on the synthetic time-series experiments, the variations successfully prioritize channels following their strata allocation while maintaining the low computation time of the original algorithm. In experiments on waveform physiological time-series and derivative physiological data, increased discrimination capacity was noted for multiple strata allocations in the variations when benchmarked to the original algorithm. This suggests improved physiological state monitoring by the variations. Furthermore, our variations can be modified to utilize a priori knowledge for the stratification of channels. Thus, our research provides a novel approach for the extraction of previously inaccessible information from multi-channel time series acquired from heterogeneous systems.

Optimized Ship-Radiated Noise Feature Extraction Approaches Based on CEEMDAN and Slope Entropy

Slope entropy (Slopen) has been demonstrated to be an excellent approach to extracting ship-radiated noise signals (S-NSs) features by analyzing the complexity of the signals; however, its recognition ability is limited because it extracts the features of undecomposed S-NSs. To solve this problem, in this study, we combined complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to explore the differences of Slopen between the intrinsic mode components (IMFs) of the S-NSs and proposed a single-IMF optimized feature extraction approach. Aiming to further enhance its performance, the optimized combination of dual-IMFs was selected, and a dual-IMF optimized feature extraction approach was also proposed. We conducted three experiments to demonstrate the effectiveness of CEEMDAN, Slopen, and the proposed approaches. The experimental and comparative results revealed both of the proposed single- and dual-IMF optimized feature extraction approaches based on Slopen and CEEMDAN to be more effective than the original ship signal-based and IMF-based feature extraction approaches.

MVME-RCMFDE framework for discerning hyper-responsivity in Autism Spectrum Disorders

BACKGROUND

Autism Spectrum Disorder (ASD), characterized by impaired sensory processing, has a wide range of clinical heterogeneity, which handicaps effective therapeutic interventions. Therefore, it is imperative to develop potential mechanisms for delineating clinically meaningful subgroups, so as to provide individualised medical treatment. In this study, an attempt is being made to differentiate the hyper-responsive subgroup from ASD by analysing the complexity pattern of Visual Evoked Potentials (VEPs), recorded from a group of 30 ASD participants, in the presence of vertical achromatic sinewave gratings at varying contrast conditions of low (5%), medium (50%) and high (90%).

METHOD

This study proposes a new diagnostic framework incorporating a novel signal decomposition method termed as Modified Variational Mode Extraction (MVME) and a multiscale entropy approach. MVME segments the signal into five constituent modes with less spectral overlap in lower frequencies. Refined Composite Multiscale Fluctuation-based Dispersion entropy (RCMFDE) is extracted from these constituent modes, thereby facilitating the identification of hyper-responsive subgroup in ASD.

RESULTS

When tested on both simulated and real VEPs, MVME displays appreciable performance in terms of root mean square error and minimal spectral overlap in the lower frequencies, in comparison with the other state-of-the-art techniques. Relative Complexity analysis with RCMFDE exhibits a rising trend in 43%-50% of ASD in modes 1, 2, 3 and 4.

CONCLUSION

The proposed MVME-RCMFDE approach is efficient in discriminating the hyper-responsive subgroup in ASD in multiple modes namely mode 1, 2, 3 and 4, which correspond to delta, theta, alpha and beta frequency bands of brain signals.

Combination of Optimized Variational Mode Decomposition and Deep Transfer Learning: A Better Fault Diagnosis Approach for Diesel Engines

Extracting features manually and employing preeminent knowledge is overly utilized in methods to conduct fault diagnosis. A diagnosis approach utilizing intelligent methods of the optimized variational mode decomposition and deep transfer learning is proposed in this manuscript to deal with fault diagnosis. Firstly, the variational mode decomposition is optimized by K values of the dispersion entropy to realize an adaptive decomposition and reduce the noise of the signal. Secondly, an image with two dimensions is generated by a vibration signal with one dimension utilizing a short-time Fourier transform, after conducting noise reduction. Then, the ResNet18 network model is used to pre-train the model. Finally, the model transfer method is used to detect faults of a diesel engine. The results show that the proposed method outperforms the deep learning methods available in the literature. Besides, better noise reduction ability and higher diagnostic accuracy are attained.

Particle Swarm Optimization Fractional Slope Entropy: A New Time Series Complexity Indicator for Bearing Fault Diagnosis

Slope entropy (SlEn) is a time series complexity indicator proposed in recent years, which has shown excellent performance in the fields of medical and hydroacoustics. In order to improve the ability of SlEn to distinguish different types of signals and solve the problem of two threshold parameters selection, a new time series complexity indicator on the basis of SlEn is proposed by introducing fractional calculus and combining particle swarm optimization (PSO), named PSO fractional SlEn (PSO-FrSlEn). Then we apply PSO-FrSlEn to the field of fault diagnosis and propose a single feature extraction method and a double feature extraction method for rolling bearing fault based on PSO-FrSlEn. The experimental results illustrated that only PSO-FrSlEn can classify 10 kinds of bearing signals with 100% classification accuracy by using double features, which is at least 4% higher than the classification accuracies of the other four fractional entropies.

Functional Connectivity and Complexity in the Phenomenological Model of Mild Cognitive-Impaired Alzheimer's Disease

Background

Functional connectivity and complexity analysis has been discretely studied to understand intricate brain dynamics. The current study investigates the interplay between functional connectivity and complexity using the Kuramoto mean-field model.

Method

Functional connectivity matrices are estimated using the weighted phase lag index and complexity measures through popularly used complexity estimators such as Lempel-Ziv complexity (LZC), Higuchi's fractal dimension (HFD), and fluctuation-based dispersion entropy (FDispEn). Complexity measures are estimated on real and simulated electroencephalogram (EEG) signals of patients with mild cognitive-impaired Alzheimer's disease (MCI-AD) and controls. Complexity measures are further applied to simulated signals generated from lesion-induced connectivity matrix and studied its impact. It is a novel attempt to study the relation between functional connectivity and complexity using a neurocomputational model.

Results

Real EEG signals from patients with MCI-AD exhibited reduced functional connectivity and complexity in anterior and central regions. A simulation study has also displayed significantly reduced regional complexity in the patient group with respect to control. A similar reduction in complexity was further evident in simulation studies with lesion-induced control groups compared with non-lesion-induced control groups.

Conclusion

Taken together, simulation studies demonstrate a positive influence of reduced connectivity in the model imparting a reduced complexity in the EEG signal. The study revealed the presence of a direct relation between functional connectivity and complexity with reduced connectivity, yielding a decreased EEG complexity.

EMD-based analysis of complexity with dissociated EEG amplitude and frequency information: a data-driven robust tool -for Autism diagnosis- compared to multi-scale entropy approach

OBJECTIVE

Autism spectrum disorder (ASD) is usually characterised by altered social skills, repetitive behaviours, and difficulties in verbal/nonverbal communication. It has been reported that electroencephalograms (EEGs) in ASD are characterised by atypical complexity. The most commonly applied method in studies of ASD EEG complexity is multiscale entropy (MSE), where the sample entropy is evaluated across several scales. However, the accuracy of MSE-based classifications between ASD and neurotypical EEG activities is poor owing to several shortcomings in scale extraction and length, the overlap between amplitude and frequency information, and sensitivity to frequency. The present study proposes a novel, nonlinear, non-stationary, adaptive, data-driven, and accurate method for the classification of ASD and neurotypical groups based on EEG complexity and entropy without the shortcomings of MSE.

APPROACH

The proposed method is as follows: (a) each ASD and neurotypical EEG (122 subjects × 64 channels) is decomposed using empirical mode decomposition (EMD) to obtain the intrinsic components (intrinsic mode functions). (b) The extracted components are normalised through the direct quadrature procedure. (c) The Hilbert transforms of the components are computed. (d) The analytic counterparts of components (and normalised components) are found. (e) The instantaneous frequency function of each analytic normalised component is calculated. (f) The instantaneous amplitude function of each analytic component is calculated. (g) The Shannon entropy values of the instantaneous frequency and amplitude vectors are computed. (h) The entropy values are classified using a neural network (NN). (i) The achieved accuracy is compared to that obtained with MSE-based classification. (j) The consistency of the results of entropy 3D mapping with clinical data is assessed.

MAIN RESULTS

The results demonstrate that the proposed method outperforms MSE (accuracy: 66.4%), with an accuracy of 93.5%. Moreover, the entropy 3D mapping results are more consistent with the available clinical data regarding brain topography in ASD.

SIGNIFICANCE

This study presents a more robust alternative to MSE, which can be used for accurate classification of ASD/neurotypical as well as for the examination of EEG entropy across brain zones in ASD.

Detection of Oculomotor Dysmetria From Mobile Phone Video of the Horizontal Saccades Task Using Signal Processing and Machine Learning Approaches

Eye movement assessments have the potential to help in diagnosis and tracking of neurological disorders. Cerebellar ataxias cause profound and characteristic abnormalities in smooth pursuit, saccades, and fixation. Oculomotor dysmetria (i.e., hypermetric and hypometric saccades) is a common finding in individuals with cerebellar ataxia. In this study, we evaluated a scalable approach for detecting and quantifying oculomotor dysmetria. Eye movement data were extracted from iPhone video recordings of the horizontal saccade task (a standard clinical task in ataxia) and combined with signal processing and machine learning approaches to quantify saccade abnormalities. Entropy-based measures of eye movements during saccades were significantly different in 72 individuals with ataxia with dysmetria compared with 80 ataxia and Parkinson's participants without dysmetria. A template matching-based analysis demonstrated that saccadic eye movements in patients without dysmetria were more similar to the ideal template of saccades. A support vector machine was then used to train and test the ability of multiple signal processing features in combination to distinguish individuals with and without oculomotor dysmetria. The model achieved 78% accuracy (sensitivity= 80% and specificity= 76%). These results show that the combination of signal processing and machine learning approaches applied to iPhone video of saccades, allow for extraction of information pertaining to oculomotor dysmetria in ataxia. Overall, this inexpensive and scalable approach for capturing important oculomotor information may be a useful component of a screening tool for ataxia and could allow frequent at-home assessments of oculomotor function in natural history studies and clinical trials.

Three-dimensional dispersion entropy for uterine fibroid texture quantification and post-embolization evaluation

BACKGROUND AND OBJECTIVE

Uterine fibroids are benign tumors that could lead to symptoms complicating a patient's daily life. Those fibroids can be treated using uterine fibroid embolization (UFE), an effective non-surgical procedure. However, objectively quantifying the benefits of such a procedure, and the patient's quality of life, is rather challenging.

METHODS

With a novel multiscale three-dimensional (3D) entropy-based texture analysis, the multiscale 3D dispersion entropy (MDispEn_3D), this work aims to objectively quantify the evolution -  after UFE  -  of patients' health in terms of quality of life, symptoms severity, and sexual function. For this purpose, clinical data and magnetic resonance imaging (MRI) scans of fibroids are analyzed before UFE (D0), ten days after (D10), and six months after (M6).

RESULTS

An inverse correlation is observed between MDispEn_3D entropy values and both size and volume of fibroids. An inverse correlation is also observed between MDispEn_3D at M6 and the scores of symptoms severity. Moreover, the patient age is found to be related to the relative difference of DispEn_3D and MDispEn_3D values, between D0 and M6, translating into an increasing entropy value. Furthermore, we show that history of fibroma plays a role in determining the obtained DispEn_3D values at D0. Finally, we observe that the lower MDispEn_3D values at D0, the larger the size of the fibroid at M6.

CONCLUSIONS

The proposed MDispEn_3D method - by quantifying fibroid texture - could assist the medical doctors in the prognosis of uterine fibroids and the patients' quality of life assessment post-UFE. It could therefore favor the choice of this treatment compared to other more invasive surgical treatments.

Enhancing classification of preterm-term birth using continuous wavelet transform and entropy-based methods of electrohysterogram signals

INTRODUCTION

Despite vast research, premature birth's electrophysiological mechanisms are not fully understood. Prediction of preterm birth contributes to child survival by providing timely and skilled care to both mother and child. Electrohysterography is an affordable, noninvasive technique that has been highly sensitive in diagnosing preterm labor. This study aimed to choose the more appropriate combination of characteristics, such as electrode channel and bandwidth, as well as those linear, time-frequency, and nonlinear features of the electrohysterogram (EHG) for predicting preterm birth using classifiers.

METHODS

We analyzed two open-access datasets of 30 minutes of EHG obtained in regular checkups of women around 31 weeks of pregnancy who experienced premature labor (P) and term labor (T). The current approach filtered the raw EHGs in three relevant frequency subbands (0.3-1 Hz, 1-2 Hz, and 2-3Hz). The EHG time series were then segmented to create 120-second windows, from which individual characteristics were calculated. The linear, time-frequency, and nonlinear indices of EHG of each combination (channel-filter) were fed to different classifiers using feature selection techniques.

RESULTS

The best performance, i.e., 88.52% accuracy, 83.83% sensitivity, and 93.22% specificity, was obtained in the 2-3 Hz bands using Medium Frequency, Continuous Wavelet Transform (CWT), and entropy-based indices. Interestingly, CWT features were significantly different in all filter-channel combinations. The proposed study uses small samples of EHG signals to diagnose preterm birth accurately, showing their potential application in the clinical environment.

DISCUSSION

Our results suggest that CWT and novel entropy-based features of EHG could be suitable descriptors for analyzing and understanding the complex nature of preterm labor mechanisms.

Variational Embedding Multiscale Sample Entropy: A Tool for Complexity Analysis of Multichannel Systems

Entropy-based methods have received considerable attention in the quantification of structural complexity of real-world systems. Among numerous empirical entropy algorithms, conditional entropy-based methods such as sample entropy, which are associated with amplitude distance calculation, are quite intuitive to interpret but require excessive data lengths for meaningful evaluation at large scales. To address this issue, we propose the variational embedding multiscale sample entropy (veMSE) method and conclusively demonstrate its ability to operate robustly, even with several times shorter data than the existing conditional entropy-based methods. The analysis reveals that veMSE also exhibits other desirable properties, such as the robustness to the variation in embedding dimension and noise resilience. For rigor, unlike the existing multivariate methods, the proposed veMSE assigns a different embedding dimension to every data channel, which makes its operation independent of channel permutation. The veMSE is tested on both stimulated and real world signals, and its performance is evaluated against the existing multivariate multiscale sample entropy methods. The proposed veMSE is also shown to exhibit computational advantages over the existing amplitude distance-based entropy methods.

Double Feature Extraction Method of Ship-Radiated Noise Signal Based on Slope Entropy and Permutation Entropy

In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.

Spectrum Sensing Implemented with Improved Fluctuation-Based Dispersion Entropy and Machine Learning

Spectrum sensing is an important function in radio frequency spectrum management and cognitive radio networks. Spectrum sensing is used by one wireless system (e.g., a secondary user) to detect the presence of a wireless service with higher priority (e.g., a primary user) with which it has to coexist in the radio frequency spectrum. If the wireless signal is detected, the second user system releases the given frequency to maintain the principle of not interfering. This paper proposes a machine learning implementation of spectrum sensing using the entropy measure as a feature vector. In the training phase, the information about the activity of the wireless service with higher priority is gathered, and the model is formed. In the classification phase, the wireless system compares the current sensing report to the created model to calculate the posterior probability and classify the sensing report into either the presence or absence of wireless service with higher priority. This paper proposes the novel application of the Fluctuation Dispersion Entropy (FDE) measure recently introduced in the research community as a feature vector to build the model and implement the classification. An improved implementation of the FDE (IFDE) is used to enhance the robustness to noise. IFDE is further enhanced with an adaptive method (AIFDE) to automatically select the hyper-parameter introduced in IFDE. Then, this paper combines the machine learning approach with the entropy measure approach, which are both recent developments in spectrum sensing research. The approach is compared to similar approaches in literature and the classical energy detection method using a generated radar signal data set with different conditions of SNR(dB) and fading conditions. The results show that the proposed approach is able to outperform the approaches from literature based on other entropy measures or the Energy Detector (ED) in a consistent way across different levels of SNR and fading conditions.

Bearing Fault Diagnosis Using Refined Composite Generalized Multiscale Dispersion Entropy-Based Skewness and Variance and Multiclass FCM-ANFIS

Bearing vibration signals typically have nonlinear components due to their interaction and coupling effects, friction, damping, and nonlinear stiffness. Bearing faults affect the signal complexity at various scales. Hence, measuring signal complexity at different scales is helpful to diagnosis of bearing faults. Numerous studies have investigated multiscale algorithms; nevertheless, multiscale algorithms using the first moment lose important complexity data. Accordingly, generalized multiscale algorithms have been recently introduced. The present research examined the use of refined composite generalized multiscale dispersion entropy (RCGMDispEn) based on the second moment (variance) and third moment (skewness) along with refined composite multiscale dispersion entropy (RCMDispEn) in bearing fault diagnosis. Moreover, multiclass FCM-ANFIS, which is a combination of adaptive network-based fuzzy inference systems (ANFIS), was developed to improve the efficiency of rotating machinery fault classification. According to the results, it is recommended that generalized multiscale algorithms based on variance and skewness be examined for diagnosis, along with multiscale algorithms, and be used to achieve an improvement in the results. The simultaneous usage of the multiscale algorithm and generalized multiscale algorithms improved the results in all three real datasets used in this study.

EntropyHub: An open-source toolkit for entropic time series analysis

An increasing number of studies across many research fields from biomedical engineering to finance are employing measures of entropy to quantify the regularity, variability or randomness of time series and image data. Entropy, as it relates to information theory and dynamical systems theory, can be estimated in many ways, with newly developed methods being continuously introduced in the scientific literature. Despite the growing interest in entropic time series and image analysis, there is a shortage of validated, open-source software tools that enable researchers to apply these methods. To date, packages for performing entropy analysis are often run using graphical user interfaces, lack the necessary supporting documentation, or do not include functions for more advanced entropy methods, such as cross-entropy, multiscale cross-entropy or bidimensional entropy. In light of this, this paper introduces EntropyHub, an open-source toolkit for performing entropic time series analysis in MATLAB, Python and Julia. EntropyHub (version 0.1) provides an extensive range of more than forty functions for estimating cross-, multiscale, multiscale cross-, and bidimensional entropy, each including a number of keyword arguments that allows the user to specify multiple parameters in the entropy calculation. Instructions for installation, descriptions of function syntax, and examples of use are fully detailed in the supporting documentation, available on the EntropyHub website- www.EntropyHub.xyz. Compatible with Windows, Mac and Linux operating systems, EntropyHub is hosted on GitHub, as well as the native package repository for MATLAB, Python and Julia, respectively. The goal of EntropyHub is to integrate the many established entropy methods into one complete resource, providing tools that make advanced entropic time series analysis straightforward and reproducible.

A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice.

Enhancement of capability for motor imagery using vestibular imbalance stimulation during brain computer interface

Objective.Motor imagery (MI), based on the theory of mirror neurons and neuroplasticity, can promote motor cortical activation in neurorehabilitation. The strategy of MI based on brain-computer interface (BCI) has been used in rehabilitation training and daily assistance for patients with hemiplegia in recent years. However, it is difficult to maintain the consistency and timeliness of receiving external stimulation to neural activation in most subjects owing to the high variability of electroencephalogram (EEG) representation across trials/subjects. Moreover, in practical application, MI-BCI cannot highly activate the motor cortex and provide stable interaction owing to the weakness of the EEG feature and lack of an effective mode of activation.Approach.In this study, a novel hybrid BCI paradigm based on MI and vestibular stimulation motor imagery (VSMI) was proposed to enhance the capability of feature response for MI. Twelve subjects participated in a group of controlled experiments containing VSMI and MI. Three indicators, namely, activation degree, timeliness, and classification accuracy, were adopted to evaluate the performance of the task.Main results.Vestibular stimulation could significantly strengthen the suppression ofαandβbands of contralateral brain regions during MI, that is, enhance the activation degree of the motor cortex (p< 0.01). Compared with MI, the timeliness of EEG feature-response achieved obvious improvements in VSMI experiments. Moreover, the averaged classification accuracy of VSMI and MI was 80.56% and 69.38%, respectively.Significance.The experimental results indicate that specific vestibular activity contributes to the oscillations of the motor cortex and has a positive effect on spontaneous imagery, which provides a novel MI paradigm and enables the preliminary exploration of sensorimotor integration of MI.

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.

Assessment of Dispersion and Bubble Entropy Measures for Enhancing Preterm Birth Prediction Based on Electrohysterographic Signals

One of the remaining challenges for the scientific-technical community is predicting preterm births, for which electrohysterography (EHG) has emerged as a highly sensitive prediction technique. Sample and fuzzy entropy have been used to characterize EHG signals, although they require optimizing many internal parameters. Both bubble entropy, which only requires one internal parameter, and dispersion entropy, which can detect any changes in frequency and amplitude, have been proposed to characterize biomedical signals. In this work, we attempted to determine the clinical value of these entropy measures for predicting preterm birth by analyzing their discriminatory capacity as an individual feature and their complementarity to other EHG characteristics by developing six prediction models using obstetrical data, linear and non-linear EHG features, and linear discriminant analysis using a genetic algorithm to select the features. Both dispersion and bubble entropy better discriminated between the preterm and term groups than sample, spectral, and fuzzy entropy. Entropy metrics provided complementary information to linear features, and indeed, the improvement in model performance by including other non-linear features was negligible. The best model performance obtained an F1-score of 90.1 ± 2% for testing the dataset. This model can easily be adapted to real-time applications, thereby contributing to the transferability of the EHG technique to clinical practice.

Intelligent Fault Diagnosis of Rolling-Element Bearings Using a Self-Adaptive Hierarchical Multiscale Fuzzy Entropy

The fuzzy-entropy-based complexity metric approach has achieved fruitful results in bearing fault diagnosis. However, traditional hierarchical fuzzy entropy (HFE) and multiscale fuzzy entropy (MFE) only excavate bearing fault information on different levels or scales, but do not consider bearing fault information on both multiple layers and multiple scales at the same time, thus easily resulting in incomplete fault information extraction and low-rise identification accuracy. Besides, the key parameters of most existing entropy-based complexity metric methods are selected based on specialist experience, which indicates that they lack self-adaptation. To address these problems, this paper proposes a new intelligent bearing fault diagnosis method based on self-adaptive hierarchical multiscale fuzzy entropy. On the one hand, by integrating the merits of HFE and MFE, a novel complexity metric method, named hierarchical multiscale fuzzy entropy (HMFE), is presented to extract a multidimensional feature matrix of the original bearing vibration signal, where the important parameters of HMFE are automatically determined by using the bird swarm algorithm (BSA). On the other hand, a nonlinear feature matrix classifier with strong robustness, known as support matrix machine (SMM), is introduced for learning the discriminant fault information directly from the extracted multidimensional feature matrix and automatically identifying different bearing health conditions. Two experimental results on bearing fault diagnosis show that the proposed method can obtain average identification accuracies of 99.92% and 99.83%, respectively, which are higher those of several representative entropies reported by this paper. Moreover, in the two experiments, the standard deviations of identification accuracy of the proposed method were, respectively, 0.1687 and 0.2705, which are also greater than those of the comparison methods mentioned in this paper. The effectiveness and superiority of the proposed method are verified by the experimental results.

TdP Incidence in Methoxamine-Sensitized Rabbit Model Is Reduced With Age but Not Influenced by Hypercholesterolemia

Metabolic syndrome is associated with hypercholesterolemia, cardiac remodeling, and increased susceptibility to ventricular arrhythmias. Effects of diet-induced hypercholesterolemia on susceptibility to torsades de pointes arrhythmias (TdP) together with potential indicators of arrhythmic risk were investigated in three experimental groups of Carlsson's rabbit model: (1) young rabbits (YC, young control, age 12-16 weeks), older rabbits (AC, adult control, age 20-24 weeks), and older age-matched cholesterol-fed rabbits (CH, cholesterol, age 20-24 weeks). TdP was induced by α-adrenergic stimulation by methoxamine and I_Kr block in 83% of YC rabbits, 18% of AC rabbits, and 21% of CH rabbits. High incidence of TdP was associated with high incidence of single (SEB) and multiple ectopic beats (MEB), but the QTc prolongation and short-term variability (STV) were similar in all three groups. In TdP-susceptible rabbits, STV was significantly higher compared with arrhythmia-free rabbits but not with rabbits with other than TdP arrhythmias (SEB, MEB). Amplitude-aware permutation entropy analysis of baseline ECG could identify arrhythmia-resistant animals with high sensitivity and specificity. The data indicate that the TdP susceptibility in methoxamine-sensitized rabbits is affected by the age of rabbits but probably not by hypercholesterolemia. Entropy analysis could potentially stratify the arrhythmic risk and identify the low-risk individuals.

Brain Dynamics Altered by Photic Stimulation in Patients with Alzheimer's Disease and Mild Cognitive Impairment

Individuals with mild cognitive impairment (MCI) are at high risk of developing Alzheimer's disease (AD). Repetitive photic stimulation (PS) is commonly used in routine electroencephalogram (EEG) examinations for rapid assessment of perceptual functioning. This study aimed to evaluate neural oscillatory responses and nonlinear brain dynamics under the effects of PS in patients with mild AD, moderate AD, severe AD, and MCI, as well as healthy elderly controls (HC). EEG power ratios during PS were estimated as an index of oscillatory responses. Multiscale sample entropy (MSE) was estimated as an index of brain dynamics before, during, and after PS. During PS, EEG harmonic responses were lower and MSE values were higher in the AD subgroups than in HC and MCI groups. PS-induced changes in EEG complexity were less pronounced in the AD subgroups than in HC and MCI groups. Brain dynamics revealed a "transitional change" between MCI and Mild AD. Our findings suggest a deficiency in brain adaptability in AD patients, which hinders their ability to adapt to repetitive perceptual stimulation. This study highlights the importance of combining spectral and nonlinear dynamical analysis when seeking to unravel perceptual functioning and brain adaptability in the various stages of neurodegenerative diseases.

Gait Stability Measurement by Using Average Entropy

Gait stability has been measured by using many entropy-based methods. However, the relation between the entropy values and gait stability is worth further investigation. A research reported that average entropy (AE), a measure of disorder, could measure the static standing postural stability better than multiscale entropy and entropy of entropy (EoE), two measures of complexity. This study tested the validity of AE in gait stability measurement from the viewpoint of the disorder. For comparison, another five disorders, the EoE, and two traditional metrics methods were, respectively, used to measure the degrees of disorder and complexity of 10 step interval (SPI) and 79 stride interval (SI) time series, individually. As a result, every one of the 10 participants exhibited a relatively high AE value of the SPI when walking with eyes closed and a relatively low AE value when walking with eyes open. Most of the AE values of the SI of the 53 diseased subjects were greater than those of the 26 healthy subjects. A maximal overall accuracy of AE in differentiating the healthy from the diseased was 91.1%. Similar features also exists on those 5 disorder measurements but do not exist on the EoE values. Nevertheless, the EoE versus AE plot of the SI also exhibits an inverted U relation, consistent with the hypothesis for physiologic signals.

Assessment of Outliers and Detection of Artifactual Network Segments Using Univariate and Multivariate Dispersion Entropy on Physiological Signals

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research.

The Entropy Universe

About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy's strengths and of limitations is essential to ensure the proper improvement of this research field.

A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery

In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.

A New dispersion entropy and fuzzy logic system methodology for automated classification of dementia stages using electroencephalograms

A new EEG-based methodology is presented for differential diagnosis of the Alzheimer's disease (AD), Mild Cognitive Impairment (MCI), and healthy subjects employing the discrete wavelet transform (DWT), dispersion entropy index (DEI), a recently-proposed nonlinear measurement, and a fuzzy logic-based classification algorithm. The effectiveness and usefulness of the proposed methodology are evaluated by employing a database of measured EEG data acquired from 135 subjects, 45 MCI, 45 AD and 45 healthy subjects. The proposed methodology differentiates MCI and AD patients from HC subjects with an accuracy of 82.6-86.9%, sensitivity of 91 %, and specificity of 87 %.