Variable-step multiscale generalized link dispersion entropy for feature extraction of underwater acoustic signal

Link dispersion entropy (LDE) is a novel nonlinear dynamic metric grounded in Markov chain theory, that accurately quantifies the complexity of time series. However, LDE ignores the transition probability between non-adjacent dispersion patterns. To address this issue, the step-size parameter is introduced and the generalized LDE (GLDE) is proposed to characterize the correlation of dispersion patterns under different intervals, which can more comprehensively describe the complexity of time series. Furthermore, we extend GLDE to the variable-step multiscale GLDE (VSMGLDE) to analyze the complexity of time series from multiple time scales. The results of the simulated signals analysis show that GLDE is most sensitive to the amplitude and frequency changes of the signals, can better reflect the consistency with the dynamic properties of the chaotic system, and has the strongest ability to detect changes in the dynamic complexity and higher computational efficiency. In addition, the proposed VSMGLDE outperforms other nonlinear dynamic metrics for feature extraction of underwater acoustic signals from two different datasets.