Low-Frequency noise prediction for underwater vehicles based on Bayesian-corrected sparse grids

The prediction of low-frequency hydrodynamic noise from underwater vehicles is of great significance for enhancing their acoustic stealth, supporting low-noise design optimisation, and ensuring the operational effectiveness of underwater equipment. To address the challenge of balancing computational accuracy and computational cost in the prediction of low-frequency hydrodynamic noise, a method for low-frequency noise prediction based on Bayesian-corrected sparse grids is proposed. As the mismatch between the mesh scale in a sparse-mesh finite element model and the spatial correlation scale of the analytical turbulent boundary layer fluctuating pressure can lead to distortion of the excitation forces, (1) a fluctuating pressure calculation model based on the Corcos auto-spectrum and the normalised cross-power spectral density function was developed, and virtual mesh refinement parameters were introduced to compensate for the spatial correlation characteristics of turbulent fluctuating pressure in the low-frequency range. (2) Taking into account the engineering characteristics and operating environment of the craft, a Bayesian network was established to characterise the key influencing factors of turbulent boundary layer fluctuating pressure. Empirical parameters and virtual refinement parameters were updated to posterior estimates using simulation data, thereby achieving correction of the excitation loads. The corrected spectral excitation is applied to the fluid-structure interaction model via a user-defined volume source, and radiated noise is predicted on a sparse grid. This method was validated against the analytical solution of the modal expansion for a simply supported plate, as well as through comparisons with the Discrete Sub-Element Method and circulating water tank tests, and was applied to a rotating body model. The results indicate that within the 40–500 Hz frequency band, the predicted spectrum agrees well with the reference results, with deviations of less than 3 dB. In the 60–360 Hz range at a flow velocity of 5 m/s, and in the 180–490 Hz range at a flow velocity of 7 m/s, the deviation from the discrete sub-element method is less than 1.5 dB, whilst the computational cost is significantly lower than that of finite element calculations on a fine mesh. This method is capable of effectively capturing trends in the low-frequency noise spectrum and provides an effective approach for the rapid prediction of low-frequency hydrodynamic noise from complex underwater vehicle structures under sparse-mesh conditions.