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.

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.

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.

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.

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.

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.

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.

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.

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

基于VMD-LILGWO-LSSVM短期风电功率预测

目的为了减小风电功率并入国家电网时产生的频率波动,提高风电功率预测精度,方法提出一种结合变分模态分解(VMD)、改进灰狼算法(LILGWO)和最小二乘支持向量机(LSSVM)的风电功率短期预测方法。首先通过VMD方法将风电功率序列分解重构成3个复杂程度性不同的模态分量,降低风电功率的波动性;其次使用LSSVM挖掘各分量的特征信息,对各分量分别进行预测,针对LSSVM模型中重要参数的选取对预测精度影响较大问题,引入LILGWO对参数进行寻优;最后将各分量预测结果叠加重构,得到最终预测风电功率。结果以宁夏回族自治区某地区风电站实际数据为例,对未来三天分别进行预测取平均值,本文方法的预测平均绝对误差(mean absolute error,MAE)为2.7068 kW,均方根误差(root mean square error,RMSE)为2.0211,拟合程度决定系数(R-Square,R^(2))为0.9769,与对比方法3~6相比,RMSE分别降低了40.93%,25.21%,14.7%,6.24%;MAE分别降低了42.34%,28.04%,16.97%,7.77%;R^(2)分别提升了4.21%,1.78%,0.82%,0.28%。预测时长方面,BP和LSSVM平均训练时间分别是10,138 s,虽然LSSVM预测时间较长但效果最好,采用PSO、GWO、LILGWO对LSSVM进行寻优后训练时间分别平均缩短了39,44,58 s。结论仿真验证了所提方法在短期风电功率预测方面的有效性。

一测多评法测定法制半夏曲中11种成分含量及其GRA、EW-TOPSIS质量评价

目的采用一测多评(QAMS)法同时测定法制半夏曲中肌苷、鸟苷、腺苷等11种成分含量,并建立其灰色关联度分析(GRA)联合熵权逼近理想解排序分析法(EW-TOPSIS)综合质量评价方法。方法采用Shimadzu C 18色谱柱;乙腈-0.5%醋酸为流动相,梯度洗脱,流速1.0 mL·min-1;检测波长254和290 nm。以对甲氧基肉桂酸乙酯为内参比物质,计算其他10个成分的相对校正因子(RCF),测定各成分含量。采用GRA联合EW-TOPSIS模型对法制半夏曲进行综合质量评价。结果法制半夏曲中11种成分在一定浓度范围内线性关系良好,相关系数均>0.999;平均加样回收率96.94%~100.12%(RSD<2.0%,n=9);QAMS与外标法(ESM)实测值无明显差异。GRA模型相对关联度0.2903~0.6187,EW-TOPSIS模型相对接近度0.2114~0.6343;GRA和EW-TOPSIS模型综合评价结果基本一致。结论QAMS法便捷、准确,可用于法制半夏曲多指标成分定量控制,GRA联合EW-TOPSIS模型可用于法制半夏曲综合质量评价。

基于一维卷积神经网络与近似熵特征融合的水电机组故障诊断

针对水电机组振动信号存在非平稳和非线性,单一特征提取难以实现高精度故障诊断问题,提出了一种基于卷积神经网络和近似熵特征融合的故障诊断方法。利用卷积神经网络提取振动信号特征;EEMD与近似熵构建信号特征向量,将两种方法提取的状态特征融合构建融合特征向量;进一步,将融合特征作为输入、故障类别作为输出,训练BP神经网络得到水电机组故障识别器,识别水电机组运行状态,即正常或具体故障类型。结合转子实验台实验数据,验证了所提方法在挖掘信号特征方面的有效性及较高的故障诊断准确率。

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。

熵理论在轴承故障诊断中的应用

为了系统地总结熵理论在轴承故障诊断中演绎出的方法及成果,以时间为脉络对各种单尺度熵及其优化理论在处理轴承故障信号中的特性及优劣势进行了梳理和总结,比较了各种单尺度熵算法的常用参数及其影响因素。综述了近年来单尺度熵及其优化理论在轴承故障诊断领域的应用与改进,指出了各种熵算法的优缺点,对熵理论在轴承故障信号处理中的发展方向进行了展望。