Measured acoustic energy and neural network models for low-speed water entry by steel spheres

This paper investigates the acoustic radiation produced by water entry of objects. While current research predominantly focuses on the fluid dynamic characteristics of object submersion, studies on acoustic radiation are limited. Most existing studies derive conclusions from open-water or laboratory measurements of sound pressure, which are highly susceptible to experimental conditions such as measurement distance, water depth, and medium. This study focuses on solid steel balls and uses total sound energy to characterize the acoustic properties of underwater objects. Different methods are employed in near-field and far-field areas to measure water entry sound, and an optimized segmented calculation method suitable for the total sound energy of water entry sounds is proposed. This method reduces the impact of echo signals from the initial impact sound on bubble pulsation sounds in near-field measurements and avoids the influence of the cutoff frequency of the reverberation tank in far-field measurements. Additionally, the calculation results are integrated with a neural network-based data fitting method to establish a small-scale predictive model for the total sound energy of water entry sound. The measurement-calculation-modeling approach proposed in this study provides a theoretical foundation for engineering applications such as extracting acoustic characteristics of underwater targets in shallow marine environments and acoustically locating water entry events.