文档介绍：First- and Higher-Order Correlation Detection Using Wavelet
Transforms
K. Gurley, ; T. Kijewski, ; and A. Kareem,
Abstract: In order to detect intermittent first- and higher-order correlation between a pair of signals in both time and frequency, a
wavelet-based coherence and bicoherence technique was developed. Due to the limited averaging in a time-frequency coherence estimate,
spurious correlated pockets were detected due to statistical variance. The introduction of multiresolution, localized integration windows
was shown to minimize this effect. A coarse ridge extraction scheme utilizing hard thresholding was then applied to extract meaningful
coherence. This thresholding scheme was further enhanced through the use of ‘‘smart’’ thresholding maps, which represent the likely
statistical noise between uncorrelated simulated signals bearing the same power spectral density and probability-density function as the
measured signals. It was demonstrated that the resulting filtered wavelet coherence and bicoherence maps were capable of capturing low
levels of first- and higher-order correlation over short time spans despite the presence of ubiquitous leakage and variance errors.
Immediate applications of these correlation detection analysis schemes can be found in the areas of bluff body aerodynamics, wave-
structure interactions, and seismic response of structures where intermittent correlation between linear and nonlinear processes is of
interest.
DOI: -9399͑2003͒129:2͑188͒
CE Database keywords: Correlation; Methodology.
Introduction the exception of the windward face, are not amenable to a func-
Though transients have long defined signature characteristics tional relationship with the ing wind field. Efforts to iden-
across the engineering spectrum, available analysis tools like Fou- tify significant linear correlation between wind and pressure fluc-
rier transforms have been ill equipped to represent this phenom-