A hybrid method for predicting the echo strength and statistical regularity of warships coupled with undulating sea surfaces

Abstract

The echo signatures of a warship can be tracked by an underwater weapon equipped with an active sonar system. However, the dynamics of undulating sea surfaces and the influence of sound reflection result in a lack of sufficiently detailed feature studies. A hybrid method is proposed to predict the acoustic scattering of warships under time-varying undulating sea surfaces, considering the multiple reflection effects of the sea surface. Specifically, the echo strength (ES) of warships is predicted under various wave spectra by coherently summing the echoes from different paths using the Four-Path method. This predictive process involves constructing a 3D warship model, acquiring the six degrees of freedom (DOFs) motion attitude, and determining the sea surface reflection coefficient under different sea state parameters. Furthermore, a statistical model is proposed for the ES of undulating interface targets. To validate the effectiveness of this hybrid method, an acoustic scattering echo experiment was conducted in a towing tank under wave-making conditions. The results demonstrate that the average error of ES between the prediction and experimentation is less than 2 dB within the detection frequency range of 120 kHz to 180 kHz. With the statistical model, the results also indicate that the ES over time conforms to the statistical regularity of the chi-square distribution. Additionally, the mean value of ES and the value of double degree of freedom k align well. In summary, this work represents a systematic effort to predict the ES of warships coupled with undulating sea surfaces using a new method.