Variational generalized nonlinear mode decomposition: Algorithm and applications

Recently proposed variational signal decomposition methods like adaptive chirp mode decomposition (ACMD) and generalized dispersive mode decomposition (GDMD) have attracted much attention in various fields. However, these methods are difficult to simultaneously separate chirp components and dispersive components. This paper proposes a variational generalized nonlinear mode decomposition (VGNMD) framework to address this issue. The VGNMD first introduces an adaptive time–frequency fusion and clustering (ATFFC) scheme to improve noise robustness and resolution of time–frequency distribution (TFD) of signal in a noisy environment and to accurately obtain the TFD of each mode. Then, a mode-type discrimination criterion is established to categorize modes into chirp modes or dispersive modes based on their time–frequency (TF) ridges. Finally, with these TF ridges as initial instantaneous frequencies (IFs) or initial group delays (GDs), a variational optimization algorithm is applied to accurately reconstruct the modes and refine their IFs or GDs. Simulated examples and real-life applications to bat echolocation signal analysis and railway wheel/rail fault diagnosis are considered to show the effectiveness of the VGNMD. The results indicate that the proposed approach can accurately extract chirp modes and dispersive modes simultaneously, and is well-suitable for analyzing nonlinear signals with discontinuous TF patterns.