Characterization of surface EMG signals using improved approximate entropy

An improved approximate entropy (ApEn) is presented and applied to characterize surface electromyography (sEMG) signals. In most previous experiments using nonlinear dynamic analysis, this certain processing was often confronted with the problem of insufficient data points and noisy circumstances, which led to unsatisfactory results. Compared with fractal dimension as well as the standard ApEn, the improved ApEn can extract information underlying sEMG signals more efficiently and accu- rately. The method introduced here can also be applied to other medium-sized and noisy physiological signals.

Application of approximate entropy on dynamic characteristics of epileptic absence seizure

Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a good basis for further study on the prediction of seizures with nonlinear dynamics.

A wavelet-approximate entropy method for epileptic activity detection from EEG and its sub-bands

Epilepsy is a common brain disorder that about 1% of world's population suffers from this disorder. EEG signal is summation of brain electrical activities and has a lot of information about brain states and also used in several epilepsy detection methods. In this study, a wavelet-approximate entropy method is ap-plied for epilepsy detection from EEG signal. First wavelet analysis is applied for decomposing the EEG signal to delta, theta, alpha, beta and gamma sub- ands. Then approximate entropy that is a chaotic measure and can be used in estimation complexity of time series applied to EEG and its sub-bands. We used this method for separating 5 group EEG signals (healthy with opened eye, healthy with closed eye, interictal in none focal zone, interictal in focal zone and seizure onset signals). For evaluating separation ability of this method we used t-student statistical analysis. For all pair of groups we have 99.99% separation probability in at least 2 bands of these 6 bands (EEG and its 5 sub-bands). In comparing some groups we have over 99.98% for EEG and all its sub-bands.

Behavior and Approximate Entropy of Right-eye Lateralization During Predation in the Music Frog

Brain asymmetry for processing visual information is widespread in animals.However,it is still unknown how the complexity of the underlying neural network activities represents this asymmetrical pattern in the brain.In the present study,we investigated this complexity using the approximate entropy(ApEn)protocol for electroencephalogram(EEG)recordings from the forebrain and midbrain while the music frogs(Nidirana daunchina)attacked prey stimulus.The results showed that(1)more significant prey responses were evoked by the prey stimulus presented in the right visual field than that in the left visual field,consistent with the idea that right-eye preferences for predatory behaviors exist in animals including anurans;(2)in general,the ApEn value of the left hemisphere(especially the left mesencephalon)was greatest under various stimulus conditions,suggesting that visual lateralization could be reflected by the dynamics of underlying neural network activities and that the stable left-hemisphere dominance of EEG ApEn may play an important role in maintaining this brain asymmetry.

Approximate entropy and support vector machines for electroencephalogram signal classification

The automatic detection and identification of electroencephalogram waves play an important role in the prediction, diagnosis and treatment of epileptic seizures. In this study, a nonlinear dynamics index–approximate entropy and a support vector machine that has strong generalization ability were applied to classify electroencephalogram signals at epileptic interictal and ictal periods. Our aim was to verify whether approximate entropy waves can be effectively applied to the automatic real-time detection of epilepsy in the electroencephalogram, and to explore its generalization ability as a classifier trained using a nonlinear dynamics index. Four patients presenting with partial epileptic seizures were included in this study. They were all diagnosed with neocortex localized epilepsy and epileptic foci were clearly observed by electroencephalogram. The electroencephalogram data form the four involved patients were segmented and the characteristic values of each segment, that is, the approximate entropy, were extracted. The support vector machine classifier was constructed with the approximate entropy extracted from one epileptic case, and then electroencephalogram waves of the other three cases were classified, reaching a 93.33% accuracy rate. Our findings suggest that the use of approximate entropy allows the automatic real-time detection of electroencephalogram data in epileptic cases. The combination of approximate entropy and support vector machines shows good generalization ability for the classification of electroencephalogram signals for epilepsy.

Approximate entropy——a new statistic to quantify arc and welding process stability in short-circuiting gas metal arc welding

Based on the phase state reconstruction of welding current in short-circuiting gas metal arc welding using carbon dioxide as shielding gas, the approximate entropy of welding current as well as its standard deviation has been calculated and analysed to investigate their relation with the stability of electric arc and welding process. The extensive experimental and calculated results show that the approximate entropy of welding current is significantly and positively correlated with arc and welding process stability, whereas its standard deviation is correlated with them negatively. A larger approximate entropy and a smaller standard deviation imply a more stable arc and welding process, and vice versa. As a result, the approximate entropy of welding current promises well in assessing and quantifying the stability of electric arc and welding process in short-circuiting gas metal arc welding.

Effect of welding speed and electrode extension on the approximate entropy of welding current in short-circuiting GMAW

Based on the phase space reconstruction of welding current in short-circuiting transfer arc welding under carbon dioxide, the approximate entropy of welding current and its standard deviation have been calculated and analyzed at different welding speeds and different electrode extensions respectively. The experimental and calculated results show that at a certain arc voltage, wire feeding rate and gas flow rate, welding speed and electrode extension have significant effects not only on the approximate entropy of welding current, but also on the stability of welding process. Further analysis proves that when the welding speed and electrode extension are in an appropriate range respectively, the welding current approximate entropy attains maximum and its standard deviation minimum. Just under such circumstances, the welding process is in the most stable state.

Approximate entropy analysis of arc stability in VPPA-GMAW hybrid welding

Variable polarity plasma arc-gas metal arc welding(VPPA-GMAW)integrates the advantages of VPPA and GMAW,and it is particularly applied to weld thick-plates aluminum alloys.High-speed camera and data acquisition system were used to analyze the arc shape and the welding process electrical signal.According to the analysis of arc swing amplitude and the approximate entropy of arc voltage signal denoised by wavelet threshold method,the influence of VPPA frequency on the arc stability was studied.The results show that the approximate entropy of GMAW arc voltage decreases with the increase of VPPA frequency in a certain range,and the stability of the hybrid arc is significantly improved.The spectral analysis shows that the arc stability is reduced due to the resonance effect between the VPPA and the GMAW arc when the VPPA frequency closes to the GMAW arc pulse frequency.The results are helpful to understand hybrid welding mechanism and the selection of welding process parameters.

Measuring System Regularity Using Fuzzy Similarity-based Approximate Entropy

Approximate entropy (ApEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of ApEn. To overcome these problems, a modified ApEn based on fuzzy similarity (mApEn) was proposed. The performance on the MIX stochastic model, as well as those on the Logistic map and the Hennon map with noise, shows that the fuzzy similarity-based ApEn gets more satisfying results than the standard ApEn when characterizing systems with different regularities.

Effects of subject’s wakefulness state and health status on approximated entropy during eye opening and closure test of routine EEG examination

This study tested a novel method designed to provide useful information for medical diagnosis and treatment. We measured electroencephalography (EEG) during a test of eye opening and closing, a common test in routine EEG examination. This test is mainly used for measuring the degree of alpha blocking and sensitivity during eyes opening and closing. However, because these factors depend on the subject’s awareness, drowsiness can interfere with accurate diagnosis. We sought to determine the optimal EEG frequency band and optimal brain region for distinguishing healthy individuals from patients suffering from several neurophysiological diseases (including dementia, cerebrovascular disorder, schizophrenia, alcoholism, and epilepsy) while fully awake, and while in an early drowsy state. We tested four groups of subjects (awake healthy subjects, drowsy healthy subjects, awake patients and drowsy patients). The complexity of EEG band frequencies over five lobes in the human brain was analyzed using wavelet-based approximate entropy (ApEn). Two-way analysis of variance tested the effects of the two factors of interest (subjects’ health state, and subjects’ wakefulness state) on five different lobes of the brain during eyes opening and closing. The complexity of the theta and delta bands over frontal and central regions, respectively, was significantly greater in the healthy state during eyes opening. In contrast, patients exhibited increased complexity of gamma band activity over the temporal region only, during eyes-close. The early drowsy state and wakefulness state increased the complexity of theta band activity over the temporal region only during eyes-close and eyes-open states respectively, and this change was significantly greater in control subjects compared with patients. We propose that this method may be useful in routine EEG examination, to aid medical doctors and clinicians in distinguishing healthy individuals from patients, regardless of whether the subject is fully awake or in the early stages of drowsiness.

Approximate Entropy Analysis of Electroencephalogram

Based on the time-delayed embedding method of phase space reconstruction, a new method to compute the approximate entropy （ApEn） of electroencephalogram （EEG） is proposed. The computational results show that there are signiticant differences between epileptic： EEG and normal EEG in the approximate entropy with the variance of embedding dimension. This conclusion is helpful to analyze the dynamical behavior of difibrent EEGs by entropy.

Entropy generation analysis of tangent hyperbolic fluid in quadratic Boussinesq approximation using spectral quasi-linearization method

In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.

基于EEMD与DSS-ApEn的脑电信号消噪方法

为了在消除信号中噪声的同时尽可能保留有效信息,提出了一种基于集合经验模态分解EEMD(Ensemble Empirical Mode Decomposition)和降噪源分离DSS(De-noising Source Separation)与近似熵Ap En(Approximate Entropy)相结合的脑电信号消噪方法。利用EEMD分解算法将含噪脑电信号分解为若干个内蕴模态函数IMF(Intrinsic Mode Functions)分量,滤除最高频分量后的IMF分量应用DSS分离出各独立源信号,再选择频谱近似熵最大的独立源信号作为去噪信号。仿真和真实脑电信号的消噪实验表明,与独立EEMD消噪方法以及基于EEMD与改进提升小波消噪方法相比,本文提出的方法消噪效果更好。

基于EMD和ApEn特征提取的心律失常分类研究

心律失常分类是心电图自动分析领域的重要研究内容,其中精准的特征提取在分类中起着至关重要的作用。提出一种基于经验模式分解(empirical mode decomposition,EMD)和近似熵(approximate entropy,ApEn)相结合的心电信号特征提取的新方法。首先利用EMD将心电信号分解为不同的本征模函数(intrinsic mode function,IMF),计算前6个IMF分量的近似熵作为特征向量。然后利用粒子群优化算法(particle swarm optimization,PSO)优化后的支持向量机(support vector machine,SVM)分类器进行分类。经过美国麻省理工MIT-BIH心律失常数据库进行验证,该方法能够对心律失常进行有效分类,其分类精度可达98.57%。

基于ApEn和EMD能量熵的电力变压器振动信号特征仿真研究

本文结合电力变压器振动信号的自身特性,提出了基于近似熵算法(ApEn)和经验模态分解-能量熵(EMD)的电力变压器振动信号特征提取方法并进行了仿真研究,最终的实验结果表明采用这两个参数的电力变压器振动信号特征提取方法在电力变压器故障诊断方面具有明显的可行性及优势。

Landslide displacement prediction based on the ICEEMDAN,ApEn and the CNN-LSTM models

Landslide deformation is affected by its geological conditions and many environmental factors.So it has the characteristics of dynamic,nonlinear and unstable,which makes the prediction of landslide displacement difficult.In view of the above problems,this paper proposes a dynamic prediction model of landslide displacement based on the improvement of complete ensemble empirical mode decomposition with adaptive noise(ICEEMDAN),approximate entropy(ApEn)and convolution long short-term memory(CNN-LSTM)neural network.Firstly,ICEEMDAN and Ap En are used to decompose the cumulative displacements into trend,periodic and random displacements.Then,the least square quintic polynomial function is used to fit the displacement of trend term,and the CNN-LSTM is used to predict the displacement of periodic term and random term.Finally,the displacement prediction results of trend term,periodic term and random term are superimposed to obtain the cumulative displacement prediction value.The proposed model has been verified in Bazimen landslide in the Three Gorges Reservoir area of China.The experimental results show that the model proposed in this paper can more effectively predict the displacement changes of landslides.As compared with long short-term memory(LSTM)neural network,gated recurrent unit(GRU)network model and back propagation(BP)neural network,CNN-LSTM neural network had higher prediction accuracy in predicting the periodic displacement,with the mean absolute percentage error(MAPE)reduced by 3.621%,6.893% and 15.886% respectively,and the root mean square error(RMSE)reduced by 3.834 mm,3.945 mm and 7.422mm respectively.Conclusively,this model not only has high prediction accuracy but also is more stable,which can provide a new insight for practical landslide prevention and control engineering.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part Ⅱ:Entropy Stability

In the hyperbolic research community,there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability.In the first part of the series[6],the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly.By applying this technique,the authors demonstrate that a pure continu-ous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way.In this work,we extend this investigation to the nonlinear case and focus on entropy conservation.By switching to entropy variables,we provide an estimation of the boundary operators also for nonlinear problems,that guarantee conservation.In numerical simulations,we verify our theoretical analysis.

基于IMF和MC-ApEn的含DG中压配电网故障测距研究

中压配电网的定位问题一直是电力系统的研究重点。由于发生单相接地故障后故障电流微弱,传统阻抗法和人工巡线法都存在缺点,DG的接入更加大了测距的难度。文章以行波理论为基础,提出一种基于IMF和MC-ApEn的含DG中压配电网测距方法。文章首先对含DG的配电网暂态电流特性进行分析,提出采用零模-线模传输时间差的测距原理。随后采用EMD分解法提取暂态信号最高频分量,获得行波波头的一次提取。借助表征信号复杂度的近似熵方法,提出MC-ApEn(滑动移除近似熵法)提取行波波头,从而实现故障测距。EMTP/ATP仿真验证了该方法的可行性。

Multiscale Entropy under the Inverse Gaussian Distribution： Analytical Results

The multiscale entropy （MSE） reveals the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. However, most research results are pure experimental search. Recently, Costa et al. have made the first attempt to present the theoretical basis of MSE, but it only supports the Gaussian distribution [Phys Rev. E 71 （2005） 021906]. We present the theoretical basis of MSE under the inverse Gaussian distribution, a typical model for physiological, physical and financial data sets. The analysis allows for uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, and then provides a reliable foundation for the potential applications of MSE to explore complev nhwical and Dhwical time series.