Significance testing for wavelet bicoherence and its application in analyzing nonlinearity in turbulent shear flows

Abstract

Wavelet-based bispectral analysis has been applied in various physical and engineering fields in recent years, but discussion of its significance testing, which distinguishes statistically meaningful results from those due to random noise, has been scarce and incomplete in the literature. Previously derived significance levels for wavelet bicoherence were either preliminary or based on numerical simulations of a limited sample size. The present study reviewed relevant previous works analytically identified the sampling distribution of the estimated wavelet bicoherence and derived expressions for its significance levels for any given probability value. Its application in analyzing a turbulent shear flow around a bluff body was demonstrated in detail. The significance testing developed here helped to identify significant quadratic couplings among a triad of scales in a separated turbulent shear layer over very short time intervals. The results obtained here can be applied to a wide variety of research topics for detecting nonlinearity in physical systems.

Significance Testing for Cross Correlation: A Critical Examination of Correlations between ENSO and GRACE-Derived Terrestrial Water Storage Variabilities

“…Significance testing is necessary to draw statistical inferences from correlation analyses, which is essential for interpreting experimental results. In many cases, significance testing helps assess whether the obtained results have statistical or physical meaning (Ge, 2010). Particularly when dealing with red noise, even a large peak does not necessarily mean a significant correlation.…”

Wavelet Transform Based Methodology for Detection and Characterization of Multiple Oscillations in Nonstationary Variables

“…All of the proposed methodologies are based on comparing the estimated wavelet bicoherence with the one that could be estimated from Gaussian noise due to numerical issues. Ge has mathematically derived the probability distribution function (PDF) of the wavelet bicoherence estimated from white Gaussian noise as where where d is the allowable correlation between wavelet coefficients. The significance at the level of α ( D α ) can be obtained as Squared bicoherence significantly different from 0 is a sign of non-Gaussian distributed variable.…”

“…All of the proposed methodologies are based on comparing the estimated wavelet bicoherence with the one that could be estimated from Gaussian noise due to numerical issues. Ge 27 has mathematically derived the probability distribution function (PDF) of the wavelet bicoherence estimated from white Gaussian noise as…”

Experimental observation of resonance manifold shrinking under zonal flow shear

“…As we are interested in the extent of the manifold in k-space, the spectrum is averaged over all frequencies where the bicoherence is above the significance level, i.e. greater than 1/ √ N [33,34], leading to the reduced bicoherence spectrum b 2 (k 1 , k 2 , τ ).In Fig. 3 a common representation of such a spectrum for a single time point is shown schematically.…”