A method for detection of Mode-Mixing problem

Classical Empirical Mode Decomposition (EMD) is a data-driven method used to analyze non-linear and non-stationary time series data. Besides being an adaptable method by its nature, EMD assumes that every data consists of oscillations of the intrinsic mode functions (IMF). EMD also requires the condition that IMFs which represent the characteristic structures in the data should show only a unique sub-characteristic of the data. However, in some cases, depending on the way the sub-characteristics which make up a sophisticated data coexist, the IMFs are able to be not unique. This is called the mode-mixing problem. Although there are many studies and successful methods (such as EEMD, CEEMDAN) for eliminating the mode-mixing problem, a limited number of studies exist on determining the presence of the aforementioned problem. In this study, a method for the determination of the mode-mixing problem is proposed. In the suggested method, the Itakura–Saito distance, which is a measurement of the similarity of stationary signals and based on Fourier spectrums, is modified by applying Kaiser filter onto short-time signals. The performance of the method is tested via various applications with simulated and real data, and the results show successful detection of the mode-mixing if it exists in time series.