Time-Frequency Analysis of Nonstationary Process Based on Multivariate Empirical Mode Decomposition

Currently, empirical mode decomposition (EMD) has become a popular data-driven time-frequency analysis method for nonstationary and nonlinear data. However, it is still limited to univariate data due to the number and/or scale misalignment for multivariate data. A newly developed multivariate EMD (MEMD) scheme decomposes multivariate data simultaneously and thus leads to mode alignment and minimizes mode mixing. In addition, an improved amplitude and frequency modulation (AM-FM) decomposition algorithm presented here provides an estimation of a more meaningful instantaneous amplitude and frequency than the widely used Hilbert transform (HT). Both of these facilitate development of a time-frequency analysis framework for multivariate nonstationary and nonlinear data analysis. In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectra and cospectra are proposed to characterize a multivariate nonstationary process. The scalogram and instantaneous frequency spectra capture spectral evolution of each component while the coscalogram and instantaneous frequency cospectra reveal embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectra and cospectra provide a more detailed portrait of multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is demonstrated by numerical examples of a thunderstorm downburst and an earthquake ground motion. Also, the results from the MEMD-based approach are compared with those based on a continuous wavelet transform, which further reinforces the effectiveness of the proposed framework.