On the Phase Coupling of Two Components Mixing in Empirical Mode Decomposition

Abstract

This paper investigates frequency mixing effect of empirical mode decomposition (EMD) and explores whether it can be explained by simple phase coupling between components of the input signal. The input is assumed to be a linear combination of harmonic oscillators. The hypothesis was tested assuming that phases of input signals’ components would couple according to Kuramoto’s model. Using a Kuramoto’s model with as many oscillators as the number of intrinsic mode functions (result of EMD), the model’s parameters were adjusted by a particle swarm optimization (PSO) method. The results show that our hypothesis is plausible, however, a different coupling mechanism than the simple sine-coupling Kuramoto’s model are likely to give better results.

KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem

“…However, due to its empirical behaviour, it is difficult to understand the operation of the method and the consequences of choices made during the intermediate steps of the iterative decomposition process and their effects on the resulting components. Given increasing interest in understanding the complex oscillatory phenomena, there is a great need for the development of techniques aimed at general anharmonic oscillations analysis that share the flexibility of data-driven techniques such as EMD, yet are proposed within a more principled mathematical framework, thus enabling their better understanding and analysis [Sharpley and Vatchev, 2006;Chu et al, 2013;Laszuk et al, 2016].…”