A Novel Nonlinear Feature Extraction Method of Ship Radiated Noise Based on Phase Space Reconstruction and Multiscale Improved Permutation Entropy*

The detection and feature extraction of underwater weak target signals are a challenging problem in underwater acoustic signal processing. Due to the complexity and variability of the ocean environment, the ship radiated noise is almost submerged in the ocean background noise completely. Therefore, traditional feature extraction methods based on time-frequency domain have been unable to achieve effective feature extraction under low Signal to Noise Ratio (SNR). To address this problem, a novel nonlinear feature extraction method for ship radiated noise is proposed, leveraging phase space reconstruction, Multiscale Improved Permutation Entropy (MIPE). Firstly, the phase space reconstruction is performed on ship radiated noise to achieve the mapping of time-domain data from low-dimensional to high-dimensional phase space. Secondly, combining coarse-grained theory and improved permutation entropy (IPE), MIPE algorithm is proposed. Compared with the traditional entropy algorithm, MIPE exhibits excellent separability to different signals and immunity to noise. Thirdly, a novel feature extraction model based on MIPE is designed. The separability of radiated noise from different ships is analyzed, and their nonlinear features are extracted. Finally, the extracted nonlinear features are input into Probabilistic neural network (PNN) classifier to quantify the classification performance and calculate the recognition rate. The simulation results demonstrate that the proposed nonlinear feature extraction method exhibits better separability and higher recognition rate for different types of ship radiated noise than traditional feature extraction methods.