A New Underwater Acoustic Signal Denoising Technique Based on CEEMDAN, Mutual Information, Permutation Entropy, and Wavelet Threshold Denoising

Abstract

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 Hybrid Energy Feature Extraction Approach for Ship-Radiated Noise Based on CEEMDAN Combined with Energy Difference and Energy Entropy

“…In order to get the rest of IMFs c j (t) and the residual item R j (t), we can construct f new j−1 (t) and repeat step (6) and step (7). We can express f new j−1 (t) c j (t) and R j (t) as follows:…”

“…On the one hand, it is the improvement of EMD, in particular for mode mixing. Two of the revised EMD approaches are generally accepted to be effective, they are ensemble EMD (EEMD) [6] and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) [7]. In addition, CEEMDAN is an upgrade of EEMD, which can better suppress mode mixing than EEMD.…”

Feature Extraction of Ship-Radiated Noise Based on Regenerated Phase-Shifted Sinusoid-Assisted EMD, Mutual Information, and Differential Symbolic Entropy

“…Originating from the classic and profoundly influential work by Shannon, the MI between discrete random variables X and Y is defined as [30]:…”

Fault Diagnosis for Rail Vehicle Axle-Box Bearings Based on Energy Feature Reconstruction and Composite Multiscale Permutation Entropy

“…In order to overcome the drawbacks of EMD, such as the boundary effect, mode mixing, and under-and over-shoot problems, improved methods, including ensemble EMD (EEMD) [10], complementary EEMD (CEEMD) [11], and complete EEMD with adaptive noise (CEEMDAN) [12] have been proposed. In [13][14][15], the CEEMDAN and VMD methods have been applied for feature extraction and denoising of underwater acoustic signals.EMD and its derivative methods, LMD, and VMD methods can decompose complicated signals self-adaptively; however, the signal frequency bands cannot be accurately divided, and the IMF decomposition results are related to the original signal characteristics, which cannot form a uniform frequency distribution. WPT can decompose a signal with multiple scales and high resolution based on the frequency distribution with more uniform frequency feature extraction results, which is beneficial to the unified feature extraction of different frequency bands of fault-impact signals and facilitates intelligent classification of multiple sets of signals.…”

“…In order to overcome the drawbacks of EMD, such as the boundary effect, mode mixing, and under-and over-shoot problems, improved methods, including ensemble EMD (EEMD) [10], complementary EEMD (CEEMD) [11], and complete EEMD with adaptive noise (CEEMDAN) [12] have been proposed. In [13][14][15], the CEEMDAN and VMD methods have been applied for feature extraction and denoising of underwater acoustic signals.…”