Variable-step fine-grained multi-feature dispersion entropy with multi-domain extension and its application in underwater acoustic signal classification

Entropy-based nonlinear feature extraction plays an indispensable role in sonar detection, and the detection accuracy depends on whether the entropy feature has excellent separability for underwater acoustic signals. In this study, a novel variable-step fine-grained multi-feature dispersion entropy with multi-domain extension (VFMDEME) is proposed, which can achieve accurate resolution of underwater acoustic signals. Firstly, a new variable-step fine-grained multi-feature dispersion entropy (VFMDE) is proposed, which has excellent separability for noise, chaotic and ship signals. The variable-step fine-grained analysis not only reduces the amount of data processed but also retains more original and fine features of signals. The multi-feature analysis enables the extraction of key transient changes in frequency and amplitude that cannot be obtained by traditional multi-scale analysis, and effectively preserves the inherent features between different signals. Then, on the basis of VFMDE, its multi-domain extension version is proposed, and then VFMDEME can be obtained. VFMDEME analyzes the features of signals in both time and frequency domains, addressing the issue of traditional entropies that only extract features from the time domain while ignoring potential key features in the frequency domain. Final, a new underwater acoustic signal classification model based on CNN-BiLSTM-SA and VFMDEME is proposed, which can accurately classify different ship signals. For the time-domain-based VFMDEME, the classification accuracy exceeds 94.90%. In the frequency domain, the classification accuracy exceeds 93.67%. For the time-frequency domain-based VFMDEME, the classification accuracy can reach 96.57%. Compared with traditional entropy features, VFMDEME exhibits more stable entropy fluctuations and higher classification accuracy, with an improvement of more than 6%.