Adaptive generalized dispersive mode decomposition: A data-driven approach for nonlinear dispersive component extraction in mechanical systems

Dispersive signals are commonly encountered in mechanical systems and dispersion feature extraction is a critical task in various mechanical engineering applications such as fault diagnosis and nondestructive testing. However, traditional methods for decomposing dispersive signals, including generalized dispersive mode decomposition (GDMD) and nonlinear dispersive component decomposition, are heavily reliant on prior information such as initial group delay (GD), bandwidth parameters, and the number of modes. This reliance limits their adaptability in mechanical vibration signal analysis, particularly in extracting close dispersion features. To address these issues, this paper proposes a novel data-driven approach termed adaptive generalized dispersive mode decomposition (AGDMD). First, a frequency-varying low-pass filter based on dispersion compensation is constructed and then a fully data-driven GD estimation algorithm is proposed to determine effective initial GD. Subsequently, an adaptive bandwidth estimation strategy guided by initial GDs is devised to initialize and refine bandwidth parameters of the optimal dispersion compensation algorithm. Finally, according to the initial GDs and bandwidth parameters, the AGDMD adopts a recursive framework to sequentially extract nonlinear dispersive modes from the original signal. Simulated examples and real-life applications to railway fault diagnosis and Lamb wave analysis demonstrate that the proposed AGDMD has both high adaptability and good noise robustness, and can accurately extract close dispersive modes without excessive prior information.