A novel complexity-based mode feature representation for feature extraction of ship-radiated noise using VMD and slope entropy

• Slope entropy is introduced in the feature extraction of ship signals. • Slope entropy can better distinguish ship signals than the several entropies. • Our approaches have good performance in feature extraction for ship signals. To extract more distinguishing features of ships, slope entropy (SloE) is introduced into underwater acoustic signal processing as a new feature to analyze ship-radiated noise signal (S-NS) complexity. SloE can solve the defect that permutation entropy (PE) ignores the amplitude information of time series, and has not been employed to the field of underwater acoustics. On this basis, combined with the variational mode decomposition (VMD) algorithm, a feature extraction method of S-NS based on VMD and SloE is proposed. Firstly, S-NSs are collected by high-precision sensor, and the S-NS are decomposed into a series of the intrinsic mode functions by VMD. Then, the SloE of IMFs are extracted, and the recognition rate is calculated by k-nearest neighbor (KNN) algorithm. Finally, the comparison experiments with permutation entropy (PE), dispersion entropy (DE), reverse dispersion entropy (RDE) and fluctuation dispersion entropy (FDE) are carried out. The experimental results show that under the condition of single feature, SloE has the highest recognition rate; under the condition of multiple features, the feature extraction method based on SloE can attain higher recognition rate under the same number of features, and can realize the effective recognition of S-NSs.