A denoising method for ship radiated noise based on Spearman variational mode decomposition, spatial-dependence recurrence sample entropy, improved wavelet threshold denoising, and Savitzky-Golay filter

Ship radiated noise denoising is the basis and premise of underwater acoustic signal processing. To obtain better denoising effect, a new denoising method for ship radiated noise based on Spearman variational mode decomposition (SVMD), spatial-dependence recurrence sample entropy (SdrSampEn), improved wavelet threshold denoising (IWTD) and Savitzky-Golay filter (SG) is proposed. Firstly, SVMD is proposed, ship radiated noise is decomposed a series of intrinsic mode functions (IMFs) by SVMD, and the SdrSampEn value of every IMF is counted. Then, according to the SdrSampEn value, these IMFs are divided into noise-dominated IMFs and real signal-dominated IMFs. Noise-dominated IMFs are denoised by IWTD, and real signal-dominated IMFs are denoised by SG. Finally, the processed IMFs are reconstructed, and the noise-reduced signal is acquired. The proposed method has three main advantages: (i) compared with empirical mode decomposition (EMD), variational mode decomposition (VMD) as a new non-recursive decomposition algorithm, overcomes the defect of mode mixing; (ii) the proposed SVMD method overcomes the problem that VMD needs to preset the number of decomposition levels K; (iii) real signal-dominated IMFs have also been denoised and the method improves signal-to-noise ratio (SNR) by 2 dB to 4 dB. The denoising experiments with the Lorenz signal and the Chen signal show that the proposed method can improve the SNR by 8 dB to 13 dB. Applying the proposed method to denoise ship radiated noise from the official website of National Park Administration (https://www.nps.gov/glba/learn/nature/soundclips.htm), the results show that the proposed method makes chaotic attractor phase waveform clearer and smoother, and can effective restrain marine environmental noise in ship radiated noise.