Performance and limitations of the Hilbert–Huang transformation (HHT) with an application to irregular water waves

Abstract

This paper relates to the newly developed Hilbert–Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series.