Abstract
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.
Highlights
As a part of underwater acoustic signal processing, research on denoising and feature extraction of ship play a very important role in the modern sea battlefield
In research [11], feature extraction algorithm of ship-radiated noise (SN) has been proven to be more efficient than traditional feature extraction algorithms, which extracts the features of SN using variational mode decomposition (VMD) and multi-scale PE (MPE)
VMD as a new self-adaptive signal processing algorithm is more robust to sampling and noise, and can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD)
Summary
As a part of underwater acoustic signal processing, research on denoising and feature extraction of ship play a very important role in the modern sea battlefield. Compared with the EMD and EEMD algorithms, VMD has a solid theoretical foundation and good robustness to noise It has been applied in the fields of biomedical sciences [8,9], mechanical diagnosis [10] and underwater acoustic signal processing [11]. The denoising algorithm using wavelet analysis has been widely used in different kinds of fields, and achieved good results [16,17] It is limited by the selection of wavelet basis function and the decomposition level [18]. Considering the better performance of VMD and NPE for SN signal, a new denoising algorithm and feature extraction algorithm are presented. Feature extraction algorithm is presented in Section 3; the denoising algorithm and feature extraction algorithm are, respectively, applied to SN signal in Sections 4 and 5; Section 6 concludes this paper
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