Hierarchical Refined Composite Multi-Scale Fractal Dimension and Its Application in Feature Extraction of Ship-Radiated Noise

The fractal dimension (FD) is a classical nonlinear dynamic index that can effectively reflect the dynamic transformation of a signal. However, FD can only reflect signal information of a single scale in the whole frequency band. To solve this problem, we combine refined composite multi-scale processing with FD and propose the refined composite multi-scale FD (RCMFD), which can reflect the information of signals at a multi-scale. Furthermore, hierarchical RCMFD (HRCMFD) is proposed by introducing hierarchical analysis, which successfully represents the multi-scale information of signals in each sub-frequency band. Moreover, two ship-radiated noise (SRN) multi-feature extraction methods based on RCMFD and HRCMFD are proposed. The simulation results indicate that RCMFD and HRCMFD can effectively discriminate different simulated signals. The experimental results show that the proposed two-feature extraction methods are more effective for distinguishing six types of SRN than other feature-extraction methods. The HRCMFD-based multi-feature extraction method has the best performance, and the recognition rate reaches 99.7% under the combination of five features.