Bicoherence Index Research Articles

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

Bicoherence Analysis of Oxygen Ion Cyclotron Harmonic Waves Observed by Van Allen Probes

AbstractBicoherence analysis is statistically performed for the oxygen ion cyclotron harmonic (OCH) waves observed by Van Allen Probes. While OCH waves and so‐called electromagnetic ion cyclotron harmonics have indistinguishable spectral characteristics in observation, they are believed to be excited by different mechanisms with the latter being suggested to arise from nonlinear wave‐wave coupling. Our result reveals that most of the OCH wave events have small bicoherence indices, so they are unlikely excited by wave‐wave coupling. The result is not much affected by the parameter choice in the bicoherence analysis, although increasing the subinterval length and/or reducing the subinterval overlap increases the chance of getting large bicoherence index values. Furthermore, the examination of two special events with large bicoherence indices shows that the observed phase relationship among different wave components does not align with the expectation from wave‐wave coupling. The events cannot be convincingly confirmed to be generated through wave‐wave coupling.

Evidence of wave–wave coupling between frequency harmonic bands of magnetosonic waves

Previous studies demonstrated that frequency harmonic structures of fast magnetosonic (MS) waves are usually excited by the hot proton instability. Here, we present an unusual event of MS waves with more than six harmonics wavebands (n = 1–6) in which their high harmonic bands are highly phase-coupled with their fundamental waveband. While calculations of the wave growth rates indicate that the local instability of the hot protons can excite the fundamental waveband (n = 1) as well as only a part of wave branches in the second and third wavebands (n = 2, 3), the bicoherence index adopted to analyze the phase coupling between different wavebands provides evidence that the wave–wave coupling between the low-frequency parts of MS waves can contribute to the generation of their higher harmonics (n > 1). Such wave–wave coupling processes have the potential to additionally redistribute the energy of MS waves and then broaden the frequency range of wave–particle interactions, which has important implications for a better understanding of the generation, distribution, and consequence of space plasma waves.

On the Observation of Electrostatic Harmonics Associated With EMIC Waves

AbstractIn this study, we report two events of electrostatic harmonics associated with electromagnetic ion cyclotron (EMIC) waves recorded by the Van Allen Probes. Based on the wave and plasma measurements, the wave features are investigated and the possible generation mechanism is discussed. The frequencies of these electrostatic emissions are at the integer and fractional frequencies of the fundamental EMIC waves, which can be across and above the local proton gyrofrequencies. When the frequencies increase, the electric power spectral densities of the electrostatic waves decrease, and their durations become shorter. Considering the bidirectional propagation of the fundamental EMIC waves, we propose that wave‐wave resonance probably accounts for the generation of the observed electrostatic emissions. The calculation of cross bicoherence index supports this scenario. This study analyzes a type of electrostatic harmonic wave associated with EMIC waves, essentially different from the electromagnetic harmonics reported before, and provides new insight into the evolution of EMIC waves.

BISPECTRAL ANALYSIS OF SCALP ELECTROENCEPHALOGRAMS: QUADRATIC PHASECOUPLING PHENOMENON IN DETECTING BRAIN TUMOR

Since the power spectral analysis of a non-Gaussian process generated by a nonlinear mechanism e.g., EEG, does not provide much information on the underlying nonlinear dynamics due to the lack of phase information, the higher-order statistics such as the bispectra are used to better understand the underlying nonlinear dynamics e.g., the quadratic phase coupling phenomena. The quadratic phase couplings have been observed in the EEG by the researchers over a decade for many diagnostic applications such as epilepsy, sleep, mental states. This study discusses the use of bispectral analysis of the EEG recorded from the posterior region of the head of the brain tumor patient in quantifying the quadratic phase couplings to indicate the presence of the tumor. The Bicoherence Index (BCI) or simply the Bicoherence (BIC) has been used for the purpose. Self-couplings (around 27-52%) in the [8-13] Hz (alpha) band and phase couplings (around 23-42%) in the [1-8] Hz (delta-theta) band have been observed for the normal subjects while only self-couplings (around <6.5% and around 40-53%) have been seen in both bands for the brain tumor patients. Significant lowering of coupling strengths (from 38.15% (±12.76%) to 3.51% (±3.28%)) in the alpha band and mild increase of them (from 32.76% (±18.73%) to 45.49% (±17.49%)) in the delta band have been observed for the brain tumor patients. The Power Ratio Index (PRI) based on the power spectrum is only statistically inferior (p>0.05) to the BIC in discriminating the brain tumor case from the normal one.

Detection of quadratic phase coupling from human EEG signals using higher order statistics and spectra

Interactions among neural signals in different frequency components have become a focus of strong interest in biomedical signal processing. The bispectrum is a method to detect the presence of quadratic phase coupling (QPC) between different frequency bands in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index (BCI), which is essentially a normalized bispectrum. The main disadvantage of the BCI is that the determination of significant QPC becomes compromised with noise. To mitigate this problem, a statistical approach that combines the bispectrum with an improved surrogate data method to determine the statistical significance of the phase coupling is introduced. The method was first tested on two simulation examples. It was then applied to the human EEG signal that has been recorded from the scalp using international 10–20 electrodes system. The frequency domain method, based on normalized spectrum and bispectrum, describes frequency interactions associated with nonlinearities occurring in the observed EEG.

Statistical Approach to Quantify the Presence of Phase Coupling Using the Bispectrum

The bispectrum is a method to detect the presence of phase coupling between different components in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index, which is essentially a normalized bispectrum. The major drawback of the bicoherence index (BCI) is that determination of significant phase coupling becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach that combines the bispectrum with a surrogate data method to determine the statistical significance of the phase coupling is introduced. Our method does not rely on the use of the BCI, where the normalization procedure of the BCI is the major culprit in its poor specificity. We demonstrate the accuracy of the proposed approach using simulation examples that are designed to test its robustness against noise contamination as well as varying levels of phase coupling. Our results show that the proposed approach outperforms the bicoherence index in both sensitivity and specificity and provides an unbiased and statistical approach to determining the presence of quadratic phase coupling. Application of this new method to renal hemodynamic data was applied to renal stop flow pressure data obtained from normotensive (N = 7) and hypertensive (N = 7) rats. We found significant nonlinear interactions in both strains of rats with a greater magnitude of coupling and smaller number of interaction peaks in normotensive rats than hypertensive rats.

Surface EMG analysis on normal subjects based on isometric voluntary contraction

The objective of this study was to compute reference SEMG values for normal subjects of 13 parameters extracted in the time, frequency and bispectrum domain, from the Biceps Brachii (BB) muscle generated under isometric voluntary contraction (IVC). SEMG signals were recorded from 94 subjects for 5 s at 10, 30, 50, 70 and 100% of maximum voluntary contraction (MVC). The Wilcoxon signed rank test was applied to detect significant differences or not at p < 0.05 between force levels for each of the 13 parameters. The main findings of this study can be summarized as follows: (i) The time domain parameters turns per second and number of zero crossings per second increase significantly with force level. (ii) The power spectrum median frequency parameter decreases significantly with force level, whereas maximum power and total power increase significantly with force level. (iii) The bispectrum parameter, maximum amplitude, increases significantly with force level with the exception the transition from 30% to 50% MVC. Although, the tests for Gaussianity and linearity show no significant difference with force level, the SEMG signal exhibits a more Gaussian distribution with increase of force up to 70% MVC. The SEMG linearity test, which is a measure of how constant the bicoherence index is in the bi-frequency domain, shows that the signal’s bicoherence index is less constant (hence, the signal is less linear) at 70% of MVC compared to 10, 30, 50 and 100% MVC. (iv) The time domain parameters have good correlation between them as well as, between each one of them and maximum and total power. The median frequency has a good (negative) correlation with the bispectrum peak amplitude. (v) No significant differences exist between values based on gender or age. The findings of this study can further be used for the assessment of subjects suffering with neuromuscular disorders, or in the rehabilitation laboratory for monitoring the elderly or the disabled, or in the occupational medicine laboratory.

Discrimination of cerebral ischemic states using bispectrum analysis of EEG and artificial neural network

No doubt a noninvasive technique for detection of cerebral ischemic extent, before the formation of the focus, is extremely valuable. This paper presents a new approach to early evaluate the degree of ischemic injury by combining bispectrum estimation of electroencephalograms (EEGs) with artificial neural network (ANN). The graded ischemic injuries in 24 Sprague–Dawley (SD) rats were induced for different periods of 8, 18, 30 min by infusing physiological saline along the left blood stream, based on the model for rat ischemic cerebral injury described in this paper. Four channels of EEG were collected in each rat at scheduled time of ischemia. The maximum bicoherence index and the weighted center of bispectrum (WCOB) were extracted from the EEGs and were used as input feature vector of a four-layer (12-7-2-1) ANN for prediction. Training and testing the ANN used the ‘leave one out’ strategy. The levels of ischemic injury were verified and classified by observing the ischemic area by conventional hematoxylin and eosin (HE) staining and the heat shock protein (HSP70) test. The proposed method was able to correctly detect ischemic extent in average accuracy of 91.67% of the cases. The results show that this scheme can be expected to diagnose ischemic cerebral injury in its earlier phases.

Image-based lens geometric distortion correction using minimization of average bicoherence index

In this paper, a lens geometric distortion correction method for low-cost digital cameras is described. The lens distortion coefficient is estimated by the value minimizing average bicoherence index which denotes image-dependent higher-order correlations in the frequency domain. In order to formulate the minimization of the average bicoherence index in terms of the lens distortion coefficient alone, the feasibility of a square-pixel assumption and the effect of the image center bias on the image quality are shown experimentally. At the same time, a computationally efficient method for calculating the bicoherence index is proposed, which comprises an approximation of coordinate resampling and development of a relationship between the lens distortion coefficients of the original and its reduced image. Depending on the spatial distribution of image features, the performance of the proposed method can be made comparable to that of precision camera calibration.

MONITORING OF AN INDUSTRIAL DEAROMATISATION PROCESS

This paper is concerned with the statistical analysis of closed loop data for diagnosing the causes of poor control loop performance. Higher Order Statistical (HOS) techniques have been developed over the last two decades, but until now have not been applied to the area of process monitoring. The main contribution of this work is to utilize the higher order statistical tools such as cumulants and their frequency domain counterparts (bispectrum, bicoherence, trispectrum) to detect and quantify the non-Gaussianity and nonlinearity of regulated processes or control error variables which are sometimes the main contributors to the poor performance of many of the control loops. The bicoherence index together with the process and manipulated variable plots are used to diagnose the sources of system nonlinearities. Successful application of the proposed method is demonstrated on simulated as well as industrial data.

Higher-order statistics: a robust vehicle for diagnostic assessment and characterisation of lung sounds

The use of higher-order statistics for diagnostic assessment and characterisation of lung sounds is presented in this article. The parametric approach of bispectrum estimation, which is a third-order spectrum, based on a non-Gaussian white noise driven autoregressive (AR) model, reveals information about lung sounds that is not contained in the ordinary power spectrum, such as the degree of nonlinearity and deviations from normality. Characterisation of source and transmission of lung sounds is achieved using an AR model based on third-order statistics. Furthermore, harmonic analysis of lung sounds is combined with the bicoherence index in order to obtain information regarding possible quadratic phase coupling among harmonic components of musical lung sounds. Experiments have shown that higher-order statistics can offer reliable evaluation of lung sounds characteristics, since their general properties and robustness in noiseless or noisy environments (lung sounds contaminated with additive symmetrical noise, e.g., Gaussian) proved to have superior advantages in objective analysis of pulmonary dysfunction.

Surface mechanomyogram reflects muscle fibres twitches summation

The aim of this work is to define the pattern of summation of the muscle fibre twitches in the surface mechanomyogram (MMG) generation process. For this purpose, two groups of muscle fibres of the extensor digitorum communis (EDC) were stimulated using needle electrodes. To these two artificial (because made by different muscle fibre types) motor units (MU1 and MU2), we administered: (a) separate stimulations: 3 and 9 Hz (MU1), 8 and 20 Hz (MU2) for 5 s; (b) simultaneous stimulation: 3 Hz (MU1) + 8 Hz (MU2); 9 Hz (MU1) + 20 Hz (MU2) for 5 s. The mechanomyograms, recorded during separate stimulation of MU1 and MU2, were linearly summated for the generation of a mechanomyographic signal to be compared with the one detected during (b) stimulation procedure. The bispectrum and the bicoherence of the generated MMG (MMGg) and of the MMG recorded during simultaneous (MMGs) stimulation were calculated for the detection of the quadratic non-linearity in the system responses. It was found that the MMGg and MMGs presented difference in the bispectrum and bicoherence index only when the 9–20 Hz stimulation pair was considered. In conclusion, our data indicate that the MMG derives from the summation of the active muscle fibres twitches and that the latter is linear only for very low firing rates. This is to be carefully considered when studies on MMG modelling will be undertaken.