Dual-amplitude weighted transition dispersion entropy and its application in feature extraction of ship-radiated noise

Abstract

Link dispersion entropy and its improved methods can effectively quantify the regularity and complexity of time series. However, they have two inherent limitations: (1) the patterns only focus on the amplitude information of time series, failing to take into account the differences between adjacent amplitudes simultaneously; (2) the state transition matrix is weighted in an equal-weight manner, ignoring the non-uniformity of weight allocation. To address these limitations, the dual-amplitude weighted transition dispersion entropy (DWTDE) is proposed in this paper. This method constructs a dual-amplitude coding pattern to simultaneously incorporate both amplitude information and adjacent differential information, and implements similarity-based weighting of the state transition matrix to enhance the rationality and pertinence of weight allocation. Furthermore, its multi-scale version, multi-scale DWTDE (MDWTDE), for characterizing the complexity of complex signals across different time scales. Simulation experiments demonstrate that DWTDE can accurately capture the dynamic changes of signals and exhibits superior robustness against noise. Two actual experiments based on ship-radiated noise signals (SRS) further verify that MDWTDE demonstrates superior feature extraction capability compared with the other four entropy-based methods.