TSMSlopRE: time-shifted multiscale slope Rényi entropy and its application in underwater radiated noise identification

Underwater radiated noise identification plays a critical role in marine monitoring and defense systems, yet remains challenging due to the limitations of existing feature extraction and classification methods. Its core lies in the construction of feature extraction and identification model. However, the existing slope entropy (SlopEn) suffers from insufficient dynamic feature characterization capability and limited multiscale analysis performance, while LSTSVM based on one-versus-one (OVO) or one-versus-all (OVA) strategies faces critical issues with class imbalance and local overfitting. Therefore, an underwater radiated noise identification method based on time-shifted multiscale slope Rényi entropy (TSMSlopRE) and directed acyclic graph LSTSVM (DAG LSTSVM) is proposed. Firstly, a time series measurement method called Slope Rényi Entropy (SlopRE) is constructed, which dynamically adjusts the sensitivity of SlopEn to probability distribution through an output method based on Rényi entropy, thereby improving the stability of entropy values. Secondly, we extend SlopRE to the multiscale domain by constructing time-shifted multiscale (TSM) coarse-grained and normalization processing strategies to ensure comprehensive and effective extraction of multiscale signal features. Then, we extend the LSTSVM to multiscale DAG LSTSVM by constructing DAG strategy, which significantly reduces the imbalance of model classification categories. Finally, we combine the proposed TSMSlopRE with the multi-classification strategy of DAG LSTSVM, and apply it to the research field of underwater radiated noise identification. Experiments have shown that the accuracy of underwater radiation noise recognition for ships and sea surface environments is as high as 97.40% and 100.00%, respectively, which has important research significance in actual marine environment investigations.