An EMD-based principal frequency analysis with applications to nonlinear mechanics

Abstract

Abstract There are time signals of general interest with periodic components in addition to trend and randomness. It is of great importance to identify their frequencies and amplitudes which may be varying with time. In the past, we have seen excellent works on time-frequency analysis of a signal such as short-time Fourier, wavelet, Hilbert and Hilbert-Huang transforms among others. Yet there are still critical and fundamental issues to be addressed. Notably all the previous analyses (tacitly) assume that the signal concerned is a linear superposition of its decomposed components with each of them being Fourier-analyzed its spectrum no matter whether a base set of functions or no base is employed. In this study, we propose to develop a principal frequency analysis (PFA) suitable for general summed linear (or single harmonic) signals and product signals (in the form of a beat or wave-packet). PFA is meant to extract the major frequencies from the phase of a complex signal as well as its amplitude (e.g., defined through Hilbert transform), in particular the product frequencies of a product signal or wave-packet. As an illustration, this approach of analysis, PFA for directly obtaining product frequencies is first applied to several basic examples, then to signals from nonlinear oscillators, and then to time-dependent lift and drag coefficients, related to vortex shedding behind a circular cylinder or a sphere in fluid mechanics.