Due to the non-linear and non-stationary characteristics of ship radiated noise (SR-N) signal, the traditional linear and frequency-domain denoising methods cannot be used for such signals. In this paper, an SR-N signal denoising method based on modified complete ensemble empirical mode decomposition (EMD) with adaptive noise (CEEMDAN), dispersion entropy (DE), and interval thresholding is proposed. The proposed denoising method has the following advantages: (1) as an improved version of CEEMDAN, modified CEEMDAN (MCEEMDAN) combines the advantages of EMD and CEEMDAN, and it is more reliable than CEEMDAN and has less consuming time; (2) as a fast complexity measurement technology, DE can effectively identify the type of intrinsic mode function (IMF); and (3) interval thresholding is used for SR-N signal denoising, which avoids loss of amplitude information compared with traditional denoising methods. Firstly, the original signal is decomposed into a series of IMFs using MCEEMDAN. According to the DE value of IMF, the modes are divided into three types: noise IMF, noise-dominated IMF and pure IMF. After noise IMFs are removed, the noise-dominated IMFs are denoised using interval thresholding. Finally, the pure IMF and the processed noise-dominated IMFs are reconstructed to obtain the final denoised signal. The denoising experiments with the Chen’s chaotic system show that the proposed method has a higher signal-to-noise ratio (SNR) than the other three methods. Applying the proposed method to denoise the real SR-N signal, the topological structure of chaotic attractor can be recovered clearly. It is proved that the proposed method can effectively suppress the high-frequency noise of SR-N signal.
Signal Denoising Method Combined With Variational Mode Decomposition, Machine Learning Online Optimization and the Interval Thresholding Technique