Nonlinear Entropy Research Articles

Surface EMG data aggregation processing for intelligent prosthetic action recognition

In the current development and design of sports rehabilitation equipment or biomimetic prostheses, in addition to pay attention to the development and design of the structure, the more core is how to realize the accurate and effective control of the rehabilitation equipment or intelligent prosthesis, and the current research is based on data process and pattern recognition. This paper designs nine kinds of actions that can react effectively to the function of the hand and extracts the original EMG signals, which are based on the sEMG of the forearm muscles of human hand movement, and uses the 20-order comb filter and wavelet threshold to preprocess the signal, and uses the root-mean-square, wavelength and nonlinear characteristics sample entropy in time domain as three eigenvalues to construct the input feature vectors of the subsequent action classifier. Finally, the recognition of the hand movements is realized successfully through GRNN and SVM. The recognition rate is 98.64% in SVM classifier and 96.27% in GRNN classifier. Experimental results show that the SVM classifier is better than the GRNN classifier.

Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence

We develop first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates. Following an exact renormalization-group approach pioneered by Onsager, we demonstrate the existence of a "collisionless range" of scales (lengths and velocities) in 1-particle phase space where the ideal Vlasov-Maxwell equations are satisfied in a "coarse-grained sense". Entropy conservation may nevertheless be violated in that range by a "dissipative anomaly" due to nonlinear entropy cascade. We derive "4/5th-law" type expressions for the entropy flux, which allow us to characterize the singularities (structure-function scaling exponents) required for its non-vanishing. Conservation laws of mass, momentum and energy are not afflicted with anomalous transfers in the collisionless limit. In a subsequent limit of small gyroradii, however, anomalous contributions to inertial-range energy balance may appear due both to cascade of bulk energy and to turbulent redistribution of internal energy in phase space. In that same limit the "generalized Ohm's law" derived from the particle momentum balances reduces to an "ideal Ohm's law", but only in a coarse-grained sense that does not imply magnetic flux-freezing and that permits magnetic reconnection at all inertial-range scales. We compare our results with prior theory based on the gyrokinetic (high gyro-frequency) limit, with numerical simulations, and with spacecraft measurements of the solar wind and terrestrial magnetosphere.

Non-linear Entropy Analysis in EEG to Predict Treatment Response to Repetitive Transcranial Magnetic Stimulation in Depression.

Background: Biomarkers that predict clinical outcomes in depression are essential for increasing the precision of treatments and clinical outcomes. The electroencephalogram (EEG) is a non-invasive neurophysiological test that has promise as a biomarker sensitive to treatment effects. The aim of our study was to investigate a novel non-linear index of resting state EEG activity as a predictor of clinical outcome, and compare its predictive capacity to traditional frequency-based indices.Methods: EEG was recorded from 62 patients with treatment resistant depression (TRD) and 25 healthy comparison (HC) subjects. TRD patients were treated with excitatory repetitive transcranial magnetic stimulation (rTMS) to the dorsolateral prefrontal cortex (DLPFC) for 4 to 6 weeks. EEG signals were first decomposed using the empirical mode decomposition (EMD) method into band-limited intrinsic mode functions (IMFs). Subsequently, Permutation Entropy (PE) was computed from the obtained second IMF to yield an index named PEIMF2. Receiver Operator Characteristic (ROC) curve analysis and ANOVA test were used to evaluate the efficiency of this index (PEIMF2) and were compared to frequency-band based methods.Results: Responders (RP) to rTMS exhibited an increase in the PEIMF2 index compared to non-responders (NR) at F3, FCz and FC3 sites (p < 0.01). The area under the curve (AUC) for ROC analysis was 0.8 for PEIMF2 index for the FC3 electrode. The PEIMF2 index was superior to ordinary frequency band measures.Conclusion: Our data show that the PEIMF2 index, yields superior outcome prediction performance compared to traditional frequency band indices. Our findings warrant further investigation of EEG-based biomarkers in depression; specifically entropy indices applied in band-limited EEG components. Registration in ClinicalTrials.Gov; identifiers NCT02800226 and NCT01887782.

A Heartbeat Away From Consciousness: Heart Rate Variability Entropy Can Discriminate Disorders of Consciousness and Is Correlated With Resting-State fMRI Brain Connectivity of the Central Autonomic Network.

Background: Disorders of consciousness are challenging to diagnose, with inconsistent behavioral responses, motor and cognitive disabilities, leading to approximately 40% misdiagnoses. Heart rate variability (HRV) reflects the complexity of the heart-brain two-way dynamic interactions. HRV entropy analysis quantifies the unpredictability and complexity of the heart rate beats intervals. We here investigate the complexity index (CI), a score of HRV complexity by aggregating the non-linear multi-scale entropies over a range of time scales, and its discriminative power in chronic patients with unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS), and its relation to brain functional connectivity.Methods: We investigated the CI in short (CIs) and long (CIl) time scales in 14 UWS and 16 MCS sedated. CI for MCS and UWS groups were compared using a Mann-Whitney exact test. Spearman's correlation tests were conducted between the Coma Recovery Scale-revised (CRS-R) and both CI. Discriminative power of both CI was assessed with One-R machine learning model. Correlation between CI and brain connectivity (detected with functional magnetic resonance imagery using seed-based and hypothesis-free intrinsic connectivity) was investigated using a linear regression in a subgroup of 10 UWS and 11 MCS patients with sufficient image quality.Results: Higher CIs and CIl values were observed in MCS compared to UWS. Positive correlations were found between CRS-R and both CI. The One-R classifier selected CIl as the best discriminator between UWS and MCS with 90% accuracy, 7% false positive and 13% false negative rates after a 10-fold cross-validation test. Positive correlations were observed between both CI and the recovery of functional connectivity of brain areas belonging to the central autonomic networks (CAN).Conclusion: CI of MCS compared to UWS patients has high discriminative power and low false negative rate at one third of the estimated human assessors' misdiagnosis, providing an easy, inexpensive and non-invasive diagnostic tool. CI reflects functional connectivity changes in the CAN, suggesting that CI can provide an indirect way to screen and monitor connectivity changes in this neural system. Future studies should assess the extent of CI's predictive power in a larger cohort of patients and prognostic power in acute patients.

Estimation of Spectral Entropy of HRV Data and its Application to Depression and Thyroid Subjects to Predict Cardiac Risk

Heart Rate variability (HRV) analysis using nonlinear techniques is very much useful to estimate the status of Autonomic Nervous System (ANS) non invasively. In this paper ANS status is estimated using nonlinear Spectral Entropy (SE) technique for both Healthy, Depression and Thyroid subjects. HRV data of Thyroid , Depression and healthy subjects is derived from Power lab Instrument with sampling frequency of 500Hz.Three observations are made based on the estimated values of SE. First observation is that SE values of Thyroid and depression subjects is lower compared to Healthy subjects SE values. Second observation made is that among Thyroid and Depression subjects SE values are found to be the lowest for Thyroid subjects compared to Depression subjects. Third observation made is that the SE values of CHF and AF subjects is lower than Thyroid and depression subjects. From the three observations made lower values of SE indicates the existence of ANS dysfunction for AF,CHF, thyroid and depression subjects Further it indicates that these subjects are at higher risk of cardiac dysfunction as compared to CHF and AF subjects leading to mortality. From the results obtained it may be concluded that among the Thyroid and Depression subjects Thyroid subjects indicate higher ANS dysfunction indicating Thyroid subjects are at higher risk of cardiac dysfunction..These findings are in agreement with the medical findings available in the literature.

A Heartbeat Away From Consciousness: Heart Rate Variability Entropy can discriminate disorders of consciousness and is correlated with resting-state fMRI brain connectivity of the Central Autonomic Network

Background: Disorders of consciousness are challenging to diagnose, with inconsistent behavioral responses, motor and cognitive disabilities, leading to approximately 40% misdiagnoses. Heart rate variability (HRV) reflects the complexity of the heart-brain two-way dynamic interactions. HRV entropy analysis quantifies the unpredictability and complexity of the heart rate beats intervals. We here investigate the complexity index (CI), a score of HRV complexity by aggregating the non-linear multi-scale entropies over a range of time scales, and its discriminative power in chronic patients with unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS), and its relation to brain functional connectivity. Methods: We investigated the CI in short (CIs) and long (CIl) time scales in 14 UWS and 16 MCS sedated. CI for MCS and UWS groups were compared using a Mann-Whitney exact test. Spearman's correlation tests were conducted between the Coma Recovery Scale-revised (CRS-R) and both CI. Discriminative power of both CI was assessed with One-R machine learning model. Correlation between CI and brain connectivity (detected with functional magnetic resonance imagery using seed-based and hypothesis-free intrinsic connectivity) was investigated using a linear regression in a subgroup of 10 UWS and 11 MCS patients with sufficient image quality. Results: Higher CIs and CIl values were observed in MCS compared to UWS. Positive correlations were found between CRS-R and both CI. The One-R classifier selected CIl as the best discriminator between UWS and MCS with 90% accuracy, 7% false positive and 13% false negative rates after a 10-fold cross-validation test. Positive correlations were observed between both CI and the recovery of functional connectivity of brain areas belonging to the central autonomic networks (CAN). Conclusion: CI of MCS compared to UWS patients has high discriminative power and low false negative rate at one third of the estimated human assessors' misdiagnosis, providing an easy, inexpensive and non-invasive diagnostic tool. CI reflects functional connectivity changes in the CAN, suggesting that CI can provide an indirect way to screen and monitor connectivity changes in this neural system. Future studies should assess the extent of CI's predictive power in a larger cohort of patients and prognostic power in acute patients.

Improved binary dragonfly optimization algorithm and wavelet packet based non-linear features for infant cry classification

Background and objectiveInfant cry signal carries several levels of information about the reason for crying (hunger, pain, sleepiness and discomfort) or the pathological status (asphyxia, deaf, jaundice, premature condition and autism, etc.) of an infant and therefore suited for early diagnosis. In this work, combination of wavelet packet based features and Improved Binary Dragonfly Optimization based feature selection method was proposed to classify the different types of infant cry signals. MethodsCry signals from 2 different databases were utilized. First database contains 507 cry samples of normal (N), 340 cry samples of asphyxia (A), 879 cry samples of deaf (D), 350 cry samples of hungry (H) and 192 cry samples of pain (P). Second database contains 513 cry samples of jaundice (J), 531 samples of premature (Prem) and 45 samples of normal (N). Wavelet packet transform based energy and non-linear entropies (496 features), Linear Predictive Coding (LPC) based cepstral features (56 features), Mel-frequency Cepstral Coefficients (MFCCs) were extracted (16 features). The combined feature set consists of 568 features. To overcome the curse of dimensionality issue, improved binary dragonfly optimization algorithm (IBDFO) was proposed to select the most salient attributes or features. Finally, Extreme Learning Machine (ELM) kernel classifier was used to classify the different types of infant cry signals using all the features and highly informative features as well. ResultsSeveral experiments of two-class and multi-class classification of cry signals were conducted. In binary or two-class experiments, maximum accuracy of 90.18% for H Vs P, 100% for A Vs N, 100% for D Vs N and 97.61% J Vs Prem was achieved using the features selected (only 204 features out of 568) by IBDFO. For the classification of multiple cry signals (multi-class problem), the selected features could differentiate between three classes (N, A & D) with the accuracy of 100% and seven classes with the accuracy of 97.62%. ConclusionThe experimental results indicated that the proposed combination of feature extraction and selection method offers suitable classification accuracy and may be employed to detect the subtle changes in the cry signals.

APPLICATION OF ENTROPIES FOR AUTOMATED DIAGNOSIS OF ABNORMALITIES IN ULTRASOUND IMAGES: A REVIEW

Automation of diagnosis process in medical imaging using various computer-aided techniques is a leading topic of research. Among many computer-aided methods, nonlinear entropies are widely applied in the development of automated algorithms to diagnose abnormalities present in medical images. The use of entropy features in development of Computer-Aided Diagnosis (CAD) may enhance the accuracy of the system. Entropy features depict the nonlinearity of images and thereby the presence of complexity in the images. Various types of entropies have been employed in medical image analysis for automated diagnosis of abnormalities present in the images. This paper focuses on the diverse types of entropies employed in the development of CAD systems for the diagnosis of abnormalities in the medical images. In addition to the diagnosis, these entropies can be used to differentiate the images based on the severity of the abnormalities and for other biomedical applications.

Linear and unconditionally energy stable schemes for the binary fluid–surfactant phase field model

In this paper, we consider the numerical solution of a binary fluid–surfactant phase field model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg–Landau double well potential, and a logarithmic Flory–Huggins potential. The resulting system consists of two nonlinearly coupled Cahn–Hilliard type equations. We develop a first and a second order time stepping schemes for this system using the “Invariant Energy Quadratization” approach; in particular, the system is transformed into an equivalent one by introducing appropriate auxiliary variables and all nonlinear terms are then treated semi-explicitly. Both schemes are linear and lead to symmetric positive definite systems in space at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable in the discrete sense. Various 2D and 3D numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

Metal-insulator (fermion-boson)-crossover origin of pseudogap phase of cuprates I: anomalous heat conductivity, insulator resistivity boundary, nonlinear entropy

Among all experimental observations of cuprate physics, the metal-insulator-crossover (MIC), seen in the pseudogap (PG) region of the temperature-doping phase diagram of copper-oxides under a strong magnetic field, when the superconductivity is suppressed, is most likely the most intriguing one. Since it was expected that the PG-normal state for these materials, as for conventional superconductors, is conducting. This MIC, revealed in such phenomena as heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy, resistivity temperature upturn, insulating ground state, nematicity- and stripe-phases and Fermi pockets, unambiguously indicates on the insulating normal state, from which the high-temperature superconductivity (HTS) appears. In the present work (article I), we discuss the MIC phenomena mentioned in the title of article. The second work (article II) will be devoted to discussion of other listed above MIC phenomena and also to interpretation of the recent observations in the hidden magnetic order and scanning tunneling microscopy (STM) experiments spin and charge fluctuations as the intra PG and HTS pair ones. We find that all these MIC (called in the literature as non-Fermi liquid) phenomena can be obtained within the Coulomb single boson and single fermion two liquid model, which we recently developed, and the MIC is a crossover of single fermions into those of single bosons. We show that this MIC originates from bosons of Coulomb two liquid model and fermions, whose origin is these bosons. At an increase of doping up to critical value or temperature up to PG boundary temperature, the boson system undegoes bosonic insulator - bosonic metal - fermionic metal transitions.

Normal state pair nematicity and hidden magnetic order and metal-insulator (fermionboson) crossover origin of pseudogap phase of cuprates II

In the present paper II, we will gain an understanding of the nematicity, insulating ground state (IGS), nematicity to stripe phase transition, Fermi pockets evolution, and resistivity temperature upturn, as to be metal - insulator (fermion-boson)- crossover (MIC) phenomena for the pseudogap (PG) region of cuprates. While in the paper I [1], we obtained an understanding of the observed heat conductivity downturn, anomalous Lorentz ratio, insulator resistivity boundary, nonlinear entropy as manifestations of the same MIC. The recently observed nematicity and hidden magnetic order are related to the PG pair intra charge and spin fluctuations. We will try to obtain an answer on the question: why ground state of YBCO is Fermi liquid oscillating and of Bi-2212 is insulating? We will also clarify the physics of the recently observed MIC results of Lalibert\'e et al. [2] and explain the long-discussed transition of the electric charge density from doping to doping+1 dependence at the critical doping. We predict that at the upturns this density should have the temperature dependence $n\sim T^3n_2$ for $T\rightarrow 0$, where $n_2$ is density for dopings close to the critical value. We understood that the upturns before and after the first critical doping have the same nature. We will find understanding of all above mentioned phenomena within the PG pair physics.

Predictable component analysis of a system based on nonlinear error information entropy

Based on the theory of information entropy concerning nonlinear errors, the growth rules for the nonlinear errors of the Lorenz system and its predictable components are studied. The results show that the impact of the uncertainties, both in the initial error and in the system itself, needs to be considered in a quantitative estimation of the system predictability. The nonlinear error growth is related to the magnitude of the initial error, and to the spatial distribution of the initial error vectors. Even if these initial errors have the same magnitude but different directions, there are also differences in the nonlinear error growth. The predictability of nonlinear error growth is related to the error component, but not related to the ratio of these components. The component with the highest/lowest rate of contribution does not necessarily have the greatest/least predictability. The different components have different predictabilities, and in different time periods, the different predictable components also have different predictabilities.

A family of fourth-order entropy stable nonoscillatory spectral collocation schemes for the 1-D Navier–Stokes equations

High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO) finite volume or weak-form finite element methods. Herein, a new family of fourth-order WENO spectral collocation schemes is developed, that are nonlinearly entropy stable for the one-dimensional compressible Navier–Stokes equations. Individual spectral elements are coupled using penalty type interface conditions. The resulting entropy stable WENO spectral collocation scheme achieves design order accuracy, maintains the WENO stencil biasing properties across element interfaces, and satisfies the summation-by-parts (SBP) operator convention, thereby ensuring nonlinear entropy stability in a diagonal norm. Numerical results demonstrating accuracy and nonoscillatory properties of the new scheme are presented for the one-dimensional Euler and Navier–Stokes equations for both continuous and discontinuous compressible flows.

Classification of cardiac arrhythmias based on alphabet entropy of heart rate variability time series

Abstract Background Symbolic dynamics’ methods provide a description of time series variability that allows inference of new predictive markers. Classification of disorders using symbolic dynamics is accomplished through the use of nonlinear entropies, measured upon encoded series. Method This work applies a recently developed symbolic dynamics method, alphabet entropy (AlphEn) to heart rate variability (HRV) analysis in order to improve automatic classification of cardiac arrhythmias. Experiments are conducted on PhysioNet MIT-BIH Arrhythmia Database. The approach is experimentally compared with other HRV linear and nonlinear feature combinations established in literature. AlphEn is experimentally compared with other common nonlinear entropies: Shannon’s entropy, approximate entropy, sample entropy, etc. Feature selection using symmetrical uncertainty is used for discovering relevant AlphEn features and random forest algorithm is used for arrhythmia classification. Results The best classification result obtained for six heart rhythms on 20 s segments is achieved for AlphEn no-change threshold θ = 100 ms. AlphEn features improved mean sensitivity of other feature combinations by 2% on average, with the best results achieved: SENS: 91.2%, SPEC: 97.1%, AUC: 99.0%. AlphEn may be used efficiently by adding top 10 ranking features, obtained with symmetrical uncertainty, to other established combinations. AlphEn provides the best incremental result to linear feature combination with respect to the inspected entropies. Conclusions AlphEn improves the results of established HRV feature combinations on the problem of automatic cardiac arrhythmia classification. The method enables the extraction of a number of potentially significant, domain-oriented features. It can be used as an accurate first-hand screening for arrhythmia problems.

Accelerometer-based determination of gait variability in older adults with knee osteoarthritis

Knee osteoarthritis (KOA) can affect the spatiotemporal (ST) aspects of gait as well as the variability of select ST parameters based on standard linear measures of variability (e.g., standard deviation (SD) and coefficient of variation). Non-linear measures (e.g., fractal scaling index (FSI) and sample entropy) can be more sensitive to changes in gait variability, and have been used to quantify differences in the stride patterns of patients with Parkinson’s disease and the motion of ACL-deficient knees. However, the effect of KOA on the dynamic complexity of the stride pattern has not been investigated. Therefore, the purpose of this study was to investigate the effect of KOA on gait variability (linear and non-linear measures) in a group of older adults, and to compare these results to a healthy control group. Participants walked for 10min with a tri-axial accelerometer placed at the lower back. Mean and SDs of stride time and step time as well as the FSI for the entire series of stride times were calculated for each participant. Participants with KOA had significantly greater mean stride time (p=0.031) and step time (p=0.024) than control group participants. While stride and step time variability (SD) were greater in the KOA group, the differences were not significant, nor was the difference in the FSI. Low statistical power (β=0.40 and 0.30 for stride and step time SD, respectively) combined with the confounding effects of walking speed and heterogeneous KOA severity likely prevented significant differences from being found.

Nonlinear analyses applied in cerebral autoregulation and blood flow changes in patients with acute intracerebral hemorrhage

Abstract Cerebral autoregulation (CA) is an important mechanism for maintaining constant cerebral blood flow during changes in blood pressure. Although previous studies have shown that CA may be impaired in patients with intracerebral hemorrhage (ICH), the variability of cerebral blood flow (CBF) in response to changes in CA has not been investigated. In the present study, we recruited twelve patients presenting with acute subcortical ICH and seven non-stroke controls. The status of CA was determined by assessing Pearson’s moving correlation coefficient between arterial blood pressure and cerebral blood flow velocity (CBFV) of the middle cerebral artery (MCA). The variability of CBFV was calculated using nonlinear sample entropy analyses. The results indicated that ICH patients significantly showed poorer CA than controls, particularly localized to the MCA ipsilateral to the ICH (controls 0.17 ± 0.13 versus ICH side 0.41 ± 0.27 and non-ICH side 0.34 ± 0.26, p = 0.044 and 0.120, respectively). Moreover, the variability of CBFV in the hemisphere ipsilateral to the ICH was significantly increased in ICH patients when compared to controls (1.145 ± 0.26 versus 1.66 ± 0.193 and 1.595 ± 0.43, p

Effect of salt intake on beat-to-beat blood pressure nonlinear dynamics and entropy in salt-sensitive versus salt-protected rats

Blood pressure exhibits substantial short‐ and long‐term variability (BPV). We assessed the hypothesis that the complexity of beat‐to‐beat BPV will be differentially altered in salt‐sensitive hypertensive Dahl rats (SS) versus rats protected from salt‐induced hypertension (SSBN13) maintained on high‐salt versus low‐salt diet. Beat‐to‐beat systolic and diastolic BP series from nine SS and six SSBN13 rats (http://www.physionet.org) were analyzed following 9 weeks on low salt and repeated after 2 weeks on high salt. BP complexity was quantified by detrended fluctuation analysis (DFA), short‐ and long‐range scaling exponents (α S and α L), sample entropy (SampEn), and traditional standard deviation (SD) and coefficient of variation (CV(%)). Mean systolic and diastolic BP increased on high‐salt diet (P < 0.01) particularly for SS rats. SD and CV(%) were similar across groups irrespective of diet. Salt‐sensitive and ‐protected rats exhibited similar complexity indices on low‐salt diet. On high salt, (1) SS rats showed increased scaling exponents or smoother, systolic (P = 0.007 [α L]) and diastolic (P = 0.008 [α L]) BP series; (2) salt‐protected rats showed lower SampEn (less complex) systolic and diastolic BP (P = 0.046); and (3) compared to protected SSBN13 rats, SS showed higher α L for systolic (P = 0.01) and diastolic (P = 0.005) BP. Hypertensive SS rats are more susceptible to high salt with a greater rise in mean BP and reduced complexity. Comparable mean pressures in sensitive and protective rats when on low‐salt diet coupled with similar BPV dynamics suggest a protective role of low‐salt intake in hypertensive rats. This effect likely reflects better coupling of biologic oscillators.

A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure

We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code $\texttt{FLASH}$ (http://flash.uchicago.edu). The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in $\texttt{FLASH}$.

An Entropy-based Mathematical Formulation for Straight Assembly Line Balancing Problem

This paper focuses on formulating a typical simple assembly line balancing problem. A new objective function based on a nonlinear entropy function is considered for the simple assembly line balancing problem for the first time. This objective function force the stations to have more similar total task processing time, so that the workers of the stations will have similar work load. Using a bounded variable approach, the nonlinear objective function is converted to an approximated linear objective function. Finally, efficiency of the linearized formulation of the entropy-based assembly line balancing problem is tested by a numerical example.

Classifying Driving Fatigue Based on Combined Entropy Measure Using EEG Signals

Driving fatigue is a common occupational hazard for any long distance or professional driver, and fatigue detecting has major implications for transportation safety. Monitoring physiological signal while driving can provide the possibility to detect the fatigue and give the necessary warning. In this paper, fifty subjects participated in driving simulations experiment with their recorded EEG signals to induce two kinds of fatigue states: Alert and drowsy. Two nonlinear methods, approximate Entropy (AE) and Sample Entropy (SE), were used to characterize irregularity and complexity of EEG data. Subsequently Support Vector Machine (SVM) was applied to classify these two fatigue states. The experimental result shows that two complexity parameters are significantly decreased as the fatigue level increases. The result indicates that both of two nonlinear indicators can be used to characterize driver fatigue level. Furthermore, the combined measure feature results in higher classification accuracy, indicating the proposed classification method is more robust and effective, compared with single complexity measure.