Variational Holo-spectral analysis method of high-dimensional feature representation for underwater acoustic target recognition

The modulation spectrum reveals the structural features of the underwater target propeller. It is challenging to extract the propeller shaft frequency and blade frequency because the modulation characteristics in the radiated noise are nonlinear and non-stationary. To address this issue, a variational Holo-spectral analysis (VHSA) method is proposed. Following the decomposition strategy of Holo-Hilbert spectral analysis (HHSA), the Variational mode decomposition (VMD) is introduced to improve the description capability of the amplitude modulation, and the segmented Fourier transform is further developed to obtain a robust spectrogram representation for modulation frequency. The core idea is to unveil complex modulation patterns between nonlinear modulation components and non-stationary instantaneous frequency in a high-dimensional Holo-spectrum for propeller shaft frequency and blade frequency recognition. Simulations and experimental data analysis demonstrate that, compared to HHSA, LOFAR and DEMON, the VHSA method clearly displays nonlinear and non-stationary modulation patterns embedded in radiated noise using high-dimensional and Holo-spectral representation. In practical applications, the VHSA method can achieve more accurate and effective recognition of propeller shaft frequency and blade frequency.