The local properties of ocean surface waves by the phase‐Time method

Abstract

Traditionally, investigation of statistical properties of ocean waves has been limited largely to global quantities related to elevation and amplitude such as the power spectral and various probability density functions. Although these properties give valuable information about the wave field, the results cannot be related directly to any portion of the time data from which it was derived. We present a new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking. We apply the method here to ocean wave time series data and identify a new type of wave group (containing the large “rogue” waves), but the method also has the capability of broad applications in the analysis of time series data in general.

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

“…In the past, applications of the Hilbert transform have been limited to narrow band data; otherwise, the results are only approximately correct (Long et al 1993b). Even under such restrictions, the Hilbert transform has been used by Huang et al (1992) and Huang et al (1993) to examine the local properties of ocean waves with detail that no other method has ever achieved. Later, it was also used by Huang (1995) to study nonlinear wave evolution.…”

Detection of wave groups from the motion behaviour of a discus buoy

“…The phase-time method (PTM), based on the Hilbert transformation, was introduced by Huang et al (1992) to study the frequency modulation, structure of the wave group and wave breaking in the measured wave elevation time histories, which was later used by Griffin et al (1996) to study the local properties of the laboratory generated breaking waves. In PTM, an analytical function is derived from the time histories (x(t)), as following,…”

Features extraction of tool cutting AE signals based on Hilbert-Huang transformation

“…EMD [8][9] is a fully data-driven, adaptive technique for analyzing time series from nonlinear and non-stationary processes. The essence of this method is to empirically identify the intrinsic oscillatory modes by their characteristic time scale imbedded in a signal, and then decompose the signal into a collection of a finite and often small number of IMFs through sifting process.…”

“…To deal with non-stationary and non-linearity signals like this AE signal, time-frequency analysis techniques such as Short Time Fourier Transform (STFT) [4], Wavelet Transform (WT) [5][6][7][8][9][10] and Wigner-Vile distribution (WVD) [11][12] are widely used in signal processing and faults diagnosis. As a result, FFT cannot describe adequately the characteristics of the transient signal in the lower frequency.…”