The time-frequency analysis of the acoustic signal produced in underwater discharges based on Variational Mode Decomposition and Hilbert–Huang Transform

The experiments of underwater discharges in an anechoic pool were carried out and analysis of the time-frequency characteristics of the acoustic signals was conducted based on Variational Mode Decomposition and Hilbert–Huang Transform (VMD-HHT). We propose a relative center frequency difference method to determine the decomposition numbers K which has to be given before the application of VMD and the result is satisfying. The HHT spectrum and marginal spectrum are obtained, then, some valuable conclusions are drawn. The high-frequency components of the acoustic signal are mainly attributed to the shock wave, and the low-frequency components mostly result from the bubble pulse. The frequency range of the acoustic signal is basically from 0 to 90kHz, and the ratio of energy in the low-frequency band(0–4kHz) to that of the total acoustic signal is up to 55.56%. Furthermore, this ratio versus gaps is also explored and it has the minimum at the gap of 1.5 mm which is the optimal gap for the peak pressure and radiated energy of the acoustic signal. Therefore, we can not obtain the maximum energy of the acoustic signal and the maximum ratio in the low-frequency band simultaneously.