Bicoherence Function Research Articles

Detecting dynamical states from noisy time series using bicoherence

Deriving meaningful information from observational data is often restricted by many limiting factors, the most important of which is the presence of noise. In this work, we present the use of the bicoherence function to extract information about the underlying nonlinearity from noisy time series. We show that a system evolving in the presence of noise which has its dynamical state concealed from quantifiers like the power spectrum and correlation dimension D2, can be revealed using the bicoherence function. We define an index called main peak bicoherence function as the bicoherence associated with the maximal power spectral peak. We show that this index is extremely useful while dealing with quasi-periodic data as it can distinguish strange non chaos from quasi periodicity even with added noise. We demonstrate this in a real world scenario, by taking the bicoherence of variable stars showing period doubling and strange non-chaotic behavior. Our results indicate that bicoherence analysis can also bypass the method of surrogate analysis using Fourier phase randomization, used to differentiate linear stochastic processes from non linear ones, in conventional methods involving measures like D2.

Detection of COPD’s auscultative symptoms using higher order statistics in the analysis of respiratory sounds

In this paper we present the method for determination of the specific auscultatory diagnostic signs in patients with chronic obstructive pulmonary disease (COPD), which is based upon the utilization of the polyspectral analysis and the calculation of higher order statistics. The main stages of the method are the calculation and construction of the bicoherence function of the lung sound signal in order to find its maximal value. The visual and numerical estimations of the obtained maximum allow us to conclude the presence or absence in this lung’s audio signal of the artifact, which indicates the pathology. For more accurate results one needs to determine asymmetry coefficient and to perform the estimation of bifrequency corresponding to the maximal value of the bicoherence coefficient. The calculation of skewness and kurtosis coefficients of cross-correlation functions of lung sound signals, which were recorded simultaneously in four channels, allows us to reduce the sensitivity of the method to noise components. Therefore, by analyzing all proposed calculated characteristics and parameters one can conclude the presence or absence of the pathology in this audio signal.

PHASE INTERACTION BETWEEN EEG RHYTHMS IN THE STUDY OF PROCESSES OF TIME PERCEPTION

The present study pursued to investigate the role of phase interactions between EEG rhythms in the process of the perception of time. The purpose of the study was to analyse the dependence of these interactions on the type and stage of the activity being performed, as well as on the individual characteristics of a human. For this purpose, 27 boys and 29 girls, all university students, were asked to reproduce and measure short intervals of time (200 and 800 ms), during which their EEG was recorded in frontal, central, parietal, temporal, and occipital lobes, according to the system 10–20%. While studying phase interactions between EEG rhythms, we used wavelet bispectral analysis and calculated the bicoherence function. As it follows from the conducted research, most often close phase interactions are observed between the gamma-rhythm and other rhythms of EEG or between different frequencies of the gamma-rhythm. It was established that the phase interactions under study were influenced by the factors of “sex”, “activity type”, and “activity stage”. The study showed correlations of phase interactions with the levels of intellect, extraversion, neuroticism, with the particularities of the lateral organisation of brain, and the accuracy of time perception.

Structural health monitoring of fixed offshore structures using the bicoherence function of ambient vibration measurements

This paper investigates the use of the bicoherence function of measured structural acceleration to provide automatic early detection of damage in an offshore structure. A detailed simulation model is developed, including realistic wave loading, and is used to assess the performance of the method. The method is shown through analytical and numerical analysis to be insensitive to typical operating parameter variations and to variations in wave excitation force. It is demonstrated that very small changes in stiffness of individual structural members are detectable from measurements of global structural motion.

Analysis on the interactions of harmonics in exhaust pipes of automotive engines

In exhaust pipes of automotive engines, the pulsating pressure waves are composed of fundamental frequency and high order harmonics. The nonlinearities in the exhaust pipe is caused by their interactions. The error between prediction and measurement is induced by the nonlinearities. We can not explain this phenomenon using linear acoustics theory. So power spectrum, which is used in linear theory, is not useful. This paper is concerned with the development of useful engineering techniques to detect and analyze nonlinearity in exhaust pipe of automotive engines. The study of higher order statistics has been dominated by work on the bispectrum. The bispectrum can be viewed as a decomposition of the third moment (skewness) of a signal over frequency and as such is blind to symmetric nonlinearities. The phenomenon of quadratic phase coupling (QPC) can be analyzed by the bicoherence function. Finally the application of these techniques to data from actual exhaust pipe systems is performed.

Bispectral Analysis of Gravity Capillary Waves

We perform a laboratory study of the nonlinear phase relation between short gravity waves with wavelengths of the order of 10 cm and their higher harmonics including “spurious” capillary ripple. The presence of higher harmonics of the basic low-frequency component in the spectrum of gravity capillary waves (GCWs) is confirmed on the basis of the methods of bispectral analysis. To determine the quantitative relations between the contributions of free and forced components in the GCW spectrum, we use the normalized bicoherence function. We show that it is correctly defined for both broadband random processes and polyharmonic random signals. The quantitative relation between the contributions from free and forced waves in the GCW spectrum at the frequency of the second harmonic is obtained.

Investigation of nonlinear interactions in ocean swell waves using the reduced bispectrum

In this paper, a two-dimensional (2-D) reduced bicoherence function which can be calculated via the reduced bispectrum is introduced. The statistical and computational aspects of the 2-D reduced bicoherence function are compared with those of the conventional bicoherence function. It is shown that the proposed technique is less noise-sensitive than the conventional bicoherence estimate. The use of the 2-D reduced bicoherence function to investigate nonlinear interactions in ocean swell waves is also demonstrated. As the 2-D reduced bicoherence can be efficiently calculated, it is proposed to use this novel technique in oceanographic field experiments that require real-time data processing and interpretation.

Bispectral analysis of complex patterns of sympathetic nerve discharge.

Bispectral analysis was used to demonstrate quadratic nonlinear coupling (i.e., phase locking) of different frequency components in inferior cardiac sympathetic nerve discharge (SND) of urethan-anesthetized rats. The complex patterns of SND analyzed included mixtures of 1) the cardiac-related and 10-Hz rhythms, 2) the 10-Hz rhythm and irregular 2-to 6-Hz oscillations, and 3) the 10-Hz rhythm and a lower frequency non-cardiac-related rhythm near 4 Hz. In some cases, the bicoherence function (normalized bispectrum) showed no phase locking of these frequency components. Cases of nil bicoherence are equated with linear superposition of frequency components, which implies the existence of multiple and noninteractive central circuits. Increased complexity of SND was observed in other cases, as evidenced by significant phase locking of different frequency components with or without frequency locking. Frequency locking (higher frequency rhythm is a multiple of lower) was confirmed by constructing Lissajous orbital plots showing covariation of voltages in selectively filtered bands of SND. We equate frequency locking with nonlinear coupling of the central generators of different sympathetic nerve rhythms and phase locking without frequency locking possibly with nonlinearities arising at levels below noncoupled central rhythm generators.

Etudes d'interactions acoustiques non-linéaires dans les jets confinés, par la fonction de bicohérence

Self-sustained tones are encountered when a flow passes two orifice plates, sufficiently close together, inside a duct. The upstream orifice plate creates a confined jet which impinges on the edge of the downstream orifice plate. The shear layer oscillations (coherent structures) of the confined jet in the presence of a resonant acoustic field (pipe mode), constitute the main features of cavity tones. The tones are synchronized by the pipe modes. When the flow velocity is varied for a fixed geometry, frequency jumps from one mode to another are observed. Pressure spectra showing intense acoustic energy localised in narrow bands near pipe mode frequencies are measured. We emphasize the existence of transition flow regimes during which quadratic non-linear coupling between spontaneously excited modes can take place. A digital bispectral analysis (bicoherence function) is used to quantify the degree of nonlinear interactions of acoustic waves of finite amplitude in the so-called transition region

An empirical bispectrum model for sea surface scattering

The properties of a surface bispectrum are found by generating a skewed surface on a digital computer and then evaluating its correlation function, bicoherence function, power spectrum, and bispectrum. The bispectrum is defined to be the Fourier transform of the bicoherence function. It is found that the surface bicoherence function and its first and second derivatives must all vanish at the origin. In general, the surface bispectrum is a complex function. Its real part is centrosymmetric, just like the surface spectrum, and its imaginary part is antisymmetric. A function with the above-stated properties is introduced to represent the imaginary part of the sea surface bispectrum. The unknown parameter in this function is calibrated using a data set from the FASINEX experiment. The sea surface backscattering model is based on an integral equation model which accounts for frequency, polarization, incident angle, azimuthal angle, and wind speed. It is found that the proposed bispectrum can be used to account for the up/down wind asymmetry. >