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.

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.

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.

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.

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.

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.

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.

Characteristics Extraction of Vehicle State Information Based on Entropy Calculation

A method of extracting and detecting vehicle stability state characteristics based on entropy is proposed.The vehicle’s longitudinal and lateral dynamics models are established for complex driving and maneuver conditions.The corresponding state observer is designed by adopting the moving horizon estimation algorithm,which realizes the observation of the vehicle stability state considering the global state information.Meanwhile,the Shannon entropy is modified to approximate entropy,and the approximate entropy value of the observed vehicle state is calculated.Furthermore,the optimal controller is designed to further validate the reliability of the entropy value as the reference of control system.Simulation results demonstrate that this method can quickly detect the instability state of the system during the process of vehicle driving,which provides a reference for risk prediction and active control.

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.

Modified Multiple Scale/Segment Entropy （MMPE） Analysis of Heart Rate Variability of NHH, CHF ＆ AF Subjects

Nonlinear analysis of heart rate variability （HRV） has become important as heart behaves as a complex system. In this work, the approximate entropy （ApEn） has been used as a nonlinear measure. A new concept of estimating the ApEn in different segments of long length of the recorded data called modified multiple scale （segment） entropy （MMPE） is introduced. The idea of estimating the approximate entropy in different segments is useful to detect the nonlinear dynamics of the heart present in the entire length of data. The present work has been carried out for three cases namely the normal healthy heart （NHH） data, congestive heart failure （CHF） data and Atrial fibrillation （AF） data and the data are analyzed using MMPE techniques. It is observed that the mean value of ApEn for NHH data is much higher than the mean values for CHF data and AF data. The ApEn profiles of CHF, AF and NHH data for different segments obtained using MPE profiles measures the heart dynamism for the three different cases. Also the power spectral density is obtained using fast fourier transform （FFT） analysis and the ratio of LF/HF （low frequency/high frequency） power are computed on multiple scales/segments namely MPLH （multiple scale low frequency to high frequency） for the NHH data, CHF data and AF data and analyzed using MPLH techniques. The results are presented and discussed in the paper.

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.

Some nonlinear parameters of PP intervals of pulse main peaks

The PP intervals of pulse main peaks from healthy and unhealthy people(arrhythmia) have different nonlinear char-acteristics. In this paper,the extraction of PP intervals of pulse main peaks is achieved by picking up P peaks of pulse wave with wavelet transform. Furthermore,several nonlinear parameters(correlative dimensions,maximum Lyapunov exponents,com-plexity and approximate entropy) of the PP intervals of pulse main peaks extracted from normal and unhealthy pulse signals are calculated,with the results showing that these nonlinear parameters calculated from the main wave interval signals are helpful for analyzing human's health state and diagnosing heart diseases.

Structural Prediction of Membrane Protein:Application to Known Structures

Membrane proteins are embedded in the lipid bilayer,which creates a suitable environment for their actions. It is important to decide which tpye it belongs to because it is closely relevant to its biological function and its interaction process with other molecules in a biological system. Membrane proteins have different types. The function of a membrane protein is closely correlated with the type it belongs to. In this study,on the basis of the concept of pseudo amino acid (PseAA) composition originally introduced by Chou,the value of approximate entropy (ApEn) of the query membrane protein was used to integrate the complementary information. By fusing fifteen powerful individual fuzzy K-nearest neighbor ( FKNN) classifiers,an ensemble classifier was presented. Each basic classifier was trained in PseAA composition of membrane protein sequences with different parameters. The results of experiments demonstrate it is efficient for the structural prediction of membrane proteins.

A stall diagnosis method based on entropy feature identification in axial compressors

A stall diagnosis method based on the entropy feature extraction algorithm is developed in axial compressors.The reliability of the proposed method is determined and a parametric sensitivity analysis is experimentally conducted for two different types of compressor stall diagnoses.A collection of time‐resolved pressure sensors is mounted circumferentially and along the chord direction to measure the dynamic pressure on the casing.Results show that the stall and prestall precursor embedded in the dynamic pressures are identified through nonlinear feature perturbation extraction using the entropy feature extraction algorithm.Further analysis demonstrates that the prestall precursor with the peak entropy value is related to the unsteady tip leakage flow for the spike‐type stall diagnosis.The modal wave inception with increasing amplitude is identified by the considerable increase of the entropy value.The flow field in the tip region indicates that the modal wave corresponds to the flow separation in the suction side of the rotor blade.The warning time is 100–300 rotor revolutions for both types of stall diagnoses,which is beneficial for stall control in different axial compressors.Moreover,a parametric study of the embedding dimension m,similar tolerance n,similar radius r,and data length N in the fuzzy entropy method is conducted to determine the optimal parameter setting for stall diagnosis.The stall warning based on the entropy feature extraction algorithm provides a new stall diagnosis approach in the axial compressor with different stall types.This stall warning can also be adopted as an online stability monitoring index when using the concept of active stall control.

Dynamic multivariate multiscale entropy based analysis on brain death diagnosis

The recently introduced multivariate multiscale sample entropy(MMSE)well evaluates the long correlations in multiple channels,so that it can reveal the complexity of multivariate biological signals.The existing MMSE algorithm deals with short time series statically whereas long time series are common for real-time computation in practical use.As a solution,we novelly proposed our dynamic MMSE(DMMSE)as an extension of MMSE.This helps us gain greater insight into the complexity of each section of time series,producing multifaceted and more robust estimates than the standard MMSE.The simulation results illustrated the feasibility and well performance in the brain death diagnosis.