A new denoising method of ship-radiated noise: Improved variational mode decomposition coupled with fractional order entropy double threshold criterion

Abstract Ship-radiated noise (SRN) contains abundant ship characteristic information. The detection and analysis of SRN is very important for ship target recognition, positioning and tracking. However, the propagation of SRN in water is easily interfered by complex ocean noise. To achieve preferable denoising effect, a new denoising method of ship-radiated noise is proposed. Firstly, the SRN is decomposed by improved variational mode decomposition by dung beetle optimizer (DVMD), and the complexity of each intrinsic mode functions after decomposition is measured by fractional order refined composite multiscale fluctuation dispersion entropy (FRCMFDE). Secondly, the entropy distribution characteristics are analyzed, and different adaptive division methods are used for the entropy distribution characteristics of different modes, it divides all modes into clean modes, mildly noisy modes, moderately noisy modes and highly noisy modes. Then, locally weighted scatterplot smoothing (LOWESS) and improved dual-tree complex wavelet transform (IDTCWT) are used to denoise the mildly noisy modes and moderately noisy modes respectively. Finally, the denoised SRN is obtained by reconstructing the two group of denoised modes and clean modes. The proposed denoising method is used to denoise Rossler signal, Chen signal and Lorenz signal, and the signal-to-noise ratio can be improved by 13.0785 dB, 11.9390 dB and 12.3775 dB respectively. Compared with DVMD-FRCMFDE, DVMD-FRCMFDE-WSTD and DVMD-FRCMFDE-IDTCWT, the signal-to-noise ratio of the proposed denoising method is increased by 48%, 45.93% and 38.76% respectively, and the root mean square error is increased by 46.55%, 42.76% and 30.04% respectively. The proposed denoising method is applied to four types of actually measured SRN. According to the findings, the proposed denoising method enhances clarity and smoothness of phase space attractor, and effectively suppresses marine environmental noise in SRN, which provides a solid groundwork for subsequent processing of SRN.