Multiscale grayscale dispersion entropy: A new nonlinear dynamics metric for time series analysis

Link dispersion entropy (LDE), as an improvement of dispersion entropy (DE), focuses on transition states between adjacent dispersion patterns. However, the transition states of dispersion patterns at different intervals are ignored and parameters of LDE have a significant impact on entropy value. To address these problems, grayscale dispersion entropy (GDE) is proposed, which introduces transition step size considering the transition states between dispersion patterns at different intervals, reflecting the state transition information comprehensively and uses a grayscale matrix instead of a transition probability matrix to weaken the effect of parameter on entropy value. Moreover, multiscale grayscale dispersion entropy (MGDE) is proposed as a multiscale version of GDE, which reflects the complexity at various time scales. Simulation experiments have confirmed that GDE possesses the capability to precisely detect dynamic changes in signal and accurately represent signal complexity. For two types of publicly available ship radiated noise datasets and rolling bearing dataset, MGDE has better classification performance than other four complexity metrics.