Owing to the complexity of the ocean background noise, underwater acoustic signal denoising is one of the hotspot problems in the field of underwater acoustic signal processing. In this paper, we propose a new technique for underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), mutual information (MI), permutation entropy (PE), and wavelet threshold denoising. CEEMDAN is an improved algorithm of empirical mode decomposition (EMD) and ensemble EMD (EEMD). First, CEEMDAN is employed to decompose noisy signals into many intrinsic mode functions (IMFs). IMFs can be divided into three parts: noise IMFs, noise-dominant IMFs, and real IMFs. Then, the noise IMFs can be identified on the basis of MIs of adjacent IMFs; the other two parts of IMFs can be distinguished based on the values of PE. Finally, noise IMFs were removed, and wavelet threshold denoising is applied to noise-dominant IMFs; we can obtain the final denoised signal by combining real IMFs and denoised noise-dominant IMFs. Simulation experiments were conducted by using simulated data, chaotic signals, and real underwater acoustic signals; the proposed denoising technique performs better than other existing denoising techniques, which is beneficial to the feature extraction of underwater acoustic signal.

Noise reduction of underwater acoustic signals is of great significance in the fields of military and ocean exploration. Based on the adaptive decomposition characteristic of uniform phase empirical mode decomposition (UPEMD), a noise reduction method for underwater acoustic signals is proposed, which combines amplitude-aware permutation entropy (AAPE) and Pearson correlation coefficient (PCC). UPEMD is a recently proposed improved empirical mode decomposition (EMD) algorithm that alleviates the mode splitting and residual noise effects of EMD. AAPE is a tool to quantify the information content of nonlinear time series. Unlike permutation entropy (PE), AAPE can reflect the amplitude information on time series. Firstly, the original signal is decomposed into a series of intrinsic mode functions (IMFs) by UPEMD. The AAPE of each IMF is calculated. The modes are separated into high-frequency IMFs and low-frequency IMFs, and all low-frequency IMFs are determined as useful IMFs (UIMFs). Then, the PCC between the high-frequency IMF with the smallest AAPE and the original signal is calculated. If PCC is greater than the threshold, the IMF is also determined as a UIMF. Finally, all UIMFs are reconstructed and the denoised signal is obtained. Chaotic signals with different signal-to-noise ratios (SNRs) are used for denoising experiments. Compared with EMD and extreme-point symmetric mode decomposition (ESMD), the proposed method has higher SNR and smaller root mean square error (RMSE). The proposed method is applied to noise reduction of real underwater acoustic signals. The results show that the method can further eliminate noise and the chaotic attractors are smoother and clearer.

In recent years, the rapid development of marine science has put forward higher and higher requirements for the processing of ship-radiated noise signal. Ship-radiated noise is the noise signal generated by the vibration of various mechanical equipment or the movement of the hull and radiated into the sea when the ship is traveling. Ship-radiated noise signal contains a large number of time-varying, nonlinear and non-stationary components. The denoising processing of ship-radiated noise is the most critical part of underwater acoustic signal processing. In order to more effective reduce the noise of the ship-radiated noise signal, a new denoising method for underwater acoustic signal based on mutual information variational mode decomposition (MIVMD), multivariate multiscale dispersion entropy (mvMDE), and lift wavelet threshold (LWTD) and Savitzky Golay filter (S-G filter), named MIVMD-mvMDE-LWTD-SG, is proposed. Firstly, MIVMD is used to decompose the original signal into n sub-signals. Secondly, the mvMDE value of each sub-signal is calculated, and the n sub-signals are divided into high-frequency components and low-frequency components according to the threshold. Then, S-G filter and LWTD method are used to reduce the noise of low-frequency components and high-frequency components respectively. Finally, the low-frequency components and high-frequency components after the denoising processing are reconstructed to obtain the denoising signal. In order to verify the effectiveness of the proposed method, the proposed method is used to reduce the noise of chaotic signal under different signal-to-noise ratios (SNR), and compared with the EMD-mvMDE-LWTD and MIVMD-mvMDE-LWTD method. The results show that the proposed method can effective remove the noise in the chaotic signal, better distinguish the adjacent trajectories in the phase space, approximate the real chaotic attractor trajectory, and better retain the useful information in the chaotic signal. The proposed method is further applied to the actual ship-radiated noise signal, and the experimental analysis shows its effectiveness, which lays a solid foundation for further prediction and detection.

Aiming at the irregularity of nonlinear signal and its predicting difficulty, a deep learning prediction model based on extreme‐point symmetric mode decomposition (ESMD) and clustering analysis is proposed. Firstly, the original data is decomposed by ESMD to obtain the finite number of intrinsic mode functions (IMFs) and residuals. Secondly, the fuzzy c‐means is used to cluster the decomposed components, and then the deep belief network (DBN) is used to predict it. Finally, the reconstructed IMFs and residuals are the final prediction results. Six kinds of prediction models are compared, which are DBN prediction model, EMD‐DBN prediction model, EEMD‐DBN prediction model, CEEMD‐DBN prediction model, ESMD‐DBN prediction model, and the proposed model in this paper. The same sunspots time series are predicted with six kinds of prediction models. The experimental results show that the proposed model has better prediction accuracy and smaller error.

Owing to the problems that imperfect decomposition process of empirical mode decomposition (EMD) denoising algorithm and poor self-adaptability, it will be extremely difficult to reduce the noise of signal. In this paper, a noise reduction method of underwater acoustic signal denoising based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), effort-to-compress complexity (ETC), refined composite multiscale dispersion entropy (RCMDE) and wavelet threshold denoising is proposed. Firstly, the original signal is decomposed into several IMFs by CEEMDAN and noise IMFs can be identified according to the ETC of IMFs. Then, calculating the RCMDE of remaining IMFs, these IMFs are divided into three kinds of IMFs by RCMDE, namely noise-dominant IMFs, real signal-dominant IMFs, real IMFs. Finally, noise IMFs are removed, wavelet soft threshold denoising is applied to noise-dominant IMFs and real signal-dominant IMFs. The denoised signal can be obtained by combining the real IMFs with the denoised IMFs after wavelet soft threshold denoising. Chaotic signals with different signal-to-noise ratio (SNR) are used for denoising experiments by comparing with EMD_MSE_WSTD and EEMD_DE_WSTD, it shows that the proposed algorithm has higher SNR and smaller root mean square error (RMSE). In order to further verify the effectiveness of the proposed method, which is applied to noise reduction of real underwater acoustic signals. The results show that the denoised underwater acoustic signals not only eliminate noise interference also restore the topological structure of the chaotic attractors more clearly, which lays a foundation for the further processing of underwater acoustic signals.