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To promote the effect of variational mode decomposition (VMD) and further enhance the recognition performances of bearing fault signals, genetic algorithm (GA) is applied to optimize the combination of VMD parameters in this paper, and GA-VMD algorithm is put forward to improve the decomposition accuracy of VMD. In addition, combined with the center frequency, a feature extraction method based on GA-VMD and center frequency is proposed to ameliorate the difficulty of bearing fault feature extraction. Firstly, the bearing signal is decomposed into a series of intrinsic mode components (IMFs) by GA-VMD. Then, the Center Frequency of IMFs is extracted, and the recognition rate is calculated by k-nearest neighbor (KNN) algorithm. Simulation signal experiments state clearly that, compared with manual parameter setting-VMD algorithm and parameter optimization VMD algorithm based on particle swarm optimization (PSO), the decomposition result of GA-VMD has a smaller root mean square error and higher decomposition accuracy, which verifies the effectiveness of GA-VMD. The experimental results demonstrate that, by comparison with the feature extraction method based on envelope entropy, the feature extraction method based on center frequency has better inter class separability and higher mean recognition rate (the highest recognition rate of single feature is 94.5%, and in the case of multiple features, the recognition rate reaches 100% when four features are extracted) and can realize the accurate identification of different bearing fault signals.

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In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.