The ship-radiated noise (SN) is easily affected by other hydroacoustic objects or complex ocean noise when it spreads through water. In order to reduce the impact from the environment, a denoising method for SN based on optimized variational mode decomposition with snake optimization (SO-VMD) and dual-threshold criteria of correlation coefficient (CC) is proposed in this paper. The first step is to optimize the parameter combination, that is, decomposition number K and penalty factor α, of variational mode decomposition (VMD) by snake optimization (SO) with envelope entropy (EE). Then, the input signal using the optimized results is decomposed and the intrinsic mode functions (IMFs) are obtained. After that, the IMFs are classified into three classes with the dual-threshold criteria of CC, including signal components, signal-noise components, and noise components. Finally, all the signal components and the processed signal-noise components denoised by wavelet threshold (WT) are reconstructed together. Simulations performed in this paper demonstrate that SO is the more appropriate optimization for VMD and the proposed method has the more outstanding performance in denoising different kinds of test signals. In addition, experiments on measured SNs show that the proposed method is effective and accurate in denoising.

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Fuzzy dispersion entropy (FuzDE) is a newly proposed entropy metric, which combines the superior characteristics of fuzzy entropy (FE) and dispersion entropy (DE) in signal analysis. However, FuzDE only reflects the feature from the original signal, which ignores the hidden information on the time scale. To address this problem, we introduce variable-step multiscale processing in FuzDE and propose variable-step multiscale FuzDE (VSMFuzDE), which realizes the characterization of abundant scale information, and is not limited by the signal length like the traditional multiscale processing. The experimental results for both simulated signals show that VSMFuzDE is more robust, more sensitive to dynamic changes in the chirp signal, and has more separability for noise signals; in addition, the proposed VSMFuzDE displays the best classification performance in both real-world signal experiments compared to the other four entropy metrics, the highest recognition rates of the five gear signals and four ship-radiated noises reached 99.2% and 100%, respectively, which achieves the accurate identification of two different categories of signals.

In recent years, fuzzy dispersion entropy (FDE) has been proposed and used in the feature extraction of various types of signals. However, FDE can only analyze a signal from a single time scale during practical application and ignores some important information. In order to overcome this drawback, on the basis of FDE, this paper introduces the concept of multiscale process and proposes multiscale FDE (MFDE), based on which an MFDE-based feature extraction method for ship-radiated noise is proposed. The experimental results of the simulated signals show that MFDE can reflect the changes in signal complexity, frequency, and amplitude, which can be applied in signal feature extraction; in addition, the measured experimental results demonstrate that the MFDE-based feature extraction method has a better feature extraction effect on ship-radiated noise, and the highest recognition rate is 99.5%, which is an improvement of 31.9% compared to the recognition rate of a single time scale. All the results show that MFDE can be better applied to the feature extraction and identification classification of ship-radiated noise.