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.

A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

In view of the problem that the features of ship-radiated noise are difficult to extract and inaccurate, a novel method based on variational mode decomposition (VMD), multi-scale permutation entropy (MPE) and a support vector machine (SVM) is proposed to extract the features of ship-radiated noise. In order to eliminate mode mixing and extract the complexity of the intrinsic mode function (IMF) accurately, VMD is employed to decompose the three types of ship-radiated noise instead of Empirical Mode Decomposition (EMD) and its extended methods. Considering the reason that the permutation entropy (PE) can quantify the complexity only in one scale, the MPE is used to extract features in different scales. In this study, three types of ship-radiated noise signals are decomposed into a set of band-limited IMFs by the VMD method, and the intensity of each IMF is calculated. Then, the IMFs with the highest energy are selected for the extraction of their MPE. By analyzing the separability of MPE at different scales, the optimal MPE of the IMF with the highest energy is regarded as the characteristic vector. Finally, the feature vectors are sent into the SVM classifier to classify and recognize different types of ships. The proposed method was applied in simulated signals and actual signals of ship-radiated noise. By comparing with the PE of the IMF with the highest energy by EMD, ensemble EMD (EEMD) and VMD, the results show that the proposed method can effectively extract the features of MPE and realize the classification and recognition for ships.

In order to solve the problem of feature extraction of underwater acoustic signals in complex ocean environment, a new method for feature extraction from ship-radiated noise is presented based on empirical mode decomposition theory and permutation entropy. It analyzes the separability for permutation entropies of the intrinsic mode functions of three types of ship-radiated noise signals, and discusses the permutation entropy of the intrinsic mode function with the highest energy. In this study, ship-radiated noise signals measured from three types of ships are decomposed into a set of intrinsic mode functions with empirical mode decomposition method. Then, the permutation entropies of all intrinsic mode functions are calculated with appropriate parameters. The permutation entropies are obviously different in the intrinsic mode functions with the highest energy, thus, the permutation entropy of the intrinsic mode function with the highest energy is regarded as a new characteristic parameter to extract the feature of ship-radiated noise. After that, the characteristic parameters—namely, the energy difference between high and low frequency, permutation entropy, and multi-scale permutation entropy—are compared with the permutation entropy of the intrinsic mode function with the highest energy. It is discovered that the four characteristic parameters are at the same level for similar ships, however, there are differences in the parameters for different types of ships. The results demonstrate that the permutation entropy of the intrinsic mode function with the highest energy is better in separability as the characteristic parameter than the other three parameters by comparing their fluctuation ranges and the average values of the four characteristic parameters. Hence, the feature of ship-radiated noise can be extracted efficiently with the method.

As the sound signal of ships obtained by sensors contains other many significant characteristics of ships and called ship-radiated noise (SN), research into a denoising algorithm and its application has obtained great significance. Using the advantage of variational mode decomposition (VMD) combined with the correlation coefficient for denoising, a hybrid secondary denoising algorithm is proposed using secondary VMD combined with a correlation coefficient (CC). First, different kinds of simulation signals are decomposed into several bandwidth-limited intrinsic mode functions (IMFs) using VMD, where the decomposition number by VMD is equal to the number by empirical mode decomposition (EMD); then, the CCs between the IMFs and the simulation signal are calculated respectively. The noise IMFs are identified by the CC threshold and the rest of the IMFs are reconstructed in order to realize the first denoising process. Finally, secondary denoising of the simulation signal can be accomplished by repeating the above steps of decomposition, screening and reconstruction. The final denoising result is determined according to the CC threshold. The denoising effect is compared under the different signal-to-noise ratio and the time of decomposition by VMD. Experimental results show the validity of the proposed denoising algorithm using secondary VMD (2VMD) combined with CC compared to EMD denoising, ensemble EMD (EEMD) denoising, VMD denoising and cubic VMD (3VMD) denoising, as well as two denoising algorithms presented recently. The proposed denoising algorithm is applied to feature extraction and classification for SN signals, which can effectively improve the recognition rate of different kinds of ships.

There are numerous studies showing that there is a constant increase in the ocean ambient noise level and the ever-growing demand for developing algorithms for detecting weak signals in ambient noise. In this study, we utilize dynamical and statistical complexity to detect the presence of weak ship noise embedded in ambient noise. The ambient noise and ship noise were recorded in the South China Sea. The multiscale entropy (MSE) method and the complexity-entropy causality plane (C-H plane) were used to quantify the dynamical and statistical complexity of the measured time series, respectively. We generated signals with varying signal-to-noise ratio (SNR) by varying the amplification of a ship signal. The simulation results indicate that the complexity is sensitive to change in the information in the ambient noise and the change in SNR, a finding that enables the detection of weak ship signals in strong background ambient noise. The simulation results also illustrate that complexity is better than the traditional spectrogram method, particularly effective for detecting low SNR signals in ambient noise. In addition, complexity-based MSE and C-H plane methods are simple, robust and do not assume any underlying dynamics in time series. Hence, complexity should be used in practical situations.