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, complex ocean noise easily interferes with the propagation of SRN in water. To achieve a preferable denoising effect, a new denoising method for SRN is proposed. First, the SRN is decomposed by an improved variational mode decomposition (DVMD) by a dung beetle optimizer, and the complexity of each intrinsic mode function after decomposition is measured by the fractional order refined composite multiscale fluctuation dispersion entropy (FRCMFDE). Second, the entropy distribution characteristics are analyzed, and different adaptive division methods are used to determine the entropy distribution characteristics of different modes, i.e. it divides all modes into clean modes, mildly noisy modes, moderately noisy modes and highly noisy modes. Then, locally weighted scatterplot smoothing 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 groups of denoised modes and clean modes. The proposed denoising method is used to denoise Rossler, Chen and Lorenz signals, and the signal-to-noise ratio (SNR) is improved by 13.0785, 11.9390 and 12.3775 dB, respectively. Compared with DVMD-FRCMFDE, DVMD-FRCMFDE-wavelet soft threshold denoising ( WSTD) and DVMD-FRCMFDE-IDTCWT, the SNR 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 measured SRN. Based on these findings, the proposed denoising method enhances clarity and smoothness of the phase space attractor, and effectively suppresses marine environmental noise in SRN, which provides solid groundwork for subsequent processing of SRN.