A fast equivalent source method for underwater broadband sound prediction based on dynamic mode decomposition parameter extrapolation

• This work proposes the application of Dynamic Mode Decomposition (DMD) to the Equivalent Source Method (ESM) and accelerates broadband sound field computation through frequency-domain parameter extrapolation. • The proposed DMD-ESM method predicts broadband sound fields using only a limited number of frequency samples. • The proposed DMD-ESM maintains accuracy while significantly outperforming the conventional frequency-sweeping technique in computational efficiency. Efficient broadband sound field computation is vital for ocean engineering applications like seabed exploration and underwater target detection. While the Equivalent Source Method (ESM) is effective for underwater sound field prediction, its broadband efficiency is limited by the frequency-sweeping approach, where computation time increases linearly with bandwidth. This paper proposes the DMD-ESM for rapid broadband prediction. The method: (1) solves equivalent source strength distributions using sound field data at sparse frequencies within the target band; (2) applies Dynamic Mode Decomposition (DMD) to these distributions to build an empirical modal model, enabling source strength extrapolation to any frequency in the band; (3) calculates the sound field at target frequencies using the extrapolated source strengths. By requiring only a limited number of frequency samples, DMD-ESM achieves high efficiency. Numerical results show over 80% higher computational efficiency than conventional frequency-sweeping while maintaining equivalent accuracy. Key parameters affecting precision are analyzed, with empirical application ranges provided. The upper extrapolation frequency f max is bounded by d ≤ c w /(2 f max ) to ensure the equivalent source spacing remains between 1/5 and 1/2 wavelength, thereby preventing spatial undersampling. Finally, sea trial validation confirms effectiveness and engineering practicality: predicted versus measured sound field correlation averages over 0.75, power spectrum results errors average below 4 dB, and computation time is reduced by over 70%.