Bicoherence Research Articles

A novel approach to damage localisation based on bispectral analysis and neural network

The normalised version of bispectrum, the so-called bicoherence, has often proved a reliable method of damage detection on engineering applications. Indeed, higher-order spectral analysis (HOSA) has the advantage of being able to detect non-linearity in the structural dynamic response while being insensitive to ambient vibrations. Skewness in the response may be easily spotted and related to damage conditions, as the majority of common faults and cracks shows bilinear effects. The present study tries to extend the application of HOSA to damage localisation, resorting to a neural network based classification algorithm. In order to validate the approach, a non-linear finite element model of a 4-meters-long cantilever beam has been built. This model could be seen as a first generic concept of more complex structural systems, such as aircraft wings, wind turbine blades, etc. The main aim of the study is to train a Neural Network (NN) able to classify different damage locations, when fed with bispectra. These are computed using the dynamic response of the FE nonlinear model to random noise excitation.

Gamma (30-80Hz) bicoherence distinguishes seizures in the human epileptic brain.

We have applied wavelet bicoherence (BIC) analysis to human iEEG data to characterize non-linear frequency interactions in the human epileptic brain. Bicoherence changes were most prominent in the gamma (30-80 Hz) frequency band, and allowed for the differentiation between seizure and non-seizure states in all patients studied (n=3). While gamma band BIC values increased during seizure activity, this trend was only observed in a select number of electrode(s) located on the implanted patient subdural grids. Several studies have suggested that fast frequencies may play a role in the process of seizure genesis. While the small patient numbers limit the significance of our study, our results highlight the bicoherence of the gamma frequency band (30-80 Hz) as an ictal identifier, and suggest an active role of this fast frequency during seizures.

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.

Analysis of time-variant quadratic phase couplings in the tracé alternant EEG by recursive estimation of 3rd-order time–frequency distributions

The quantification of transient quadratic phase couplings (QPC) by means of time-variant bispectral analysis is a useful approach to explain several interrelations between signal components. A generalized recursive estimation approach for 3rd-order time–frequency distributions (3rd-order TFD) is introduced. Based on 3rd-order TFD, time-variant estimations of biamplitude (BA), bicoherence (BC) and phase bicoherence (PBC) can be derived. Different smoothing windows and local moment functions for an optimization of the estimation properties are investigated and compared. The methods are applied to signal simulations and EEG signals, and it can be shown that the new time-variant bispectral analysis results in a reliable quantification of QPC in the tracé alternant EEG of healthy neonates.