Cumulative residual fuzzy dispersion entropy and its multiscale version: methodology, validation and application of feature extraction for ship target signals

• Cumulative residual fuzzy dispersion entropy was firstly proposed and applied to ship target signal feature extraction. • Propose a time-varying multiscale cumulative residual fuzzy dispersion entropy considering multiscale angles. • The proposed method shows the best differentiation ability for ship target features. When quantifying the complexity of ship target signal features, the existing entropy methods often encounter problems like low accuracy, insufficient robustness, and lack of reliability. In addressing the aforementioned challenges, this research puts forward a novel entropy index, namely the cumulative residual fuzzy dispersion entropy (CRFuzDisEn), along with its multiscale extension, the time-shift multiscale CRFuzDisEn (TMCRFuzDisEn). The aim is to overcome the limitations encountered by traditional entropy methods when analyzing non-stationary ship target signals with noise interference. By integrating cumulative residual probability, fuzzy membership functions, and multiscale analysis, CRFuzDisEn can effectively quantify the signal complexity while maintaining remarkable noise resistance. Verified by synthetic signals and measured ship target datasets, compared with dispersion entropy and fuzzy dispersion entropy, the classification accuracy of CRFuzDisEn is increased by 13.43%. And compared with other multiscale patterns, the classification accuracy of TMCRFuzDisEn is improved by 46.18%. Evidently, the method proposed in this research demonstrates outstanding performance in the area of ship target recognition.