Prediction of Underwater Structural Acoustic Radiation via Compressed Modal Equivalent Source Method with Generalized Minimax-Concave Penalty

Accurate characterization of acoustic radiation from submerged structures is crucial for underwater noise assessment and vibro-acoustic analysis. In practical engineering, acoustic measurements are often confined to limited near-field regions and contaminated by noise, rendering sound field reconstruction an ill-posed inverse problem. The conventional Equivalent Source Method (ESM), employing Tikhonov regularization, typically yields over-smoothed solutions prone to spurious artifacts. In contrast, compressive sensing approaches using [Formula: see text]-norm regularization often suffer from amplitude bias in source strength estimation. To address these limitations, this study proposes a physically consistent reconstruction framework for underwater structural acoustic radiation. The non-convex Generalized Minimax-Concave (GMC) penalty is utilized to promote sparsity while mitigating the amplitude bias inherent in convex regularization. To overcome the inherent non-sparsity of submerged elastic structures in the spatial domain, acoustic radiation modes are employed. This transformation maps the dense source distribution into a sparse modal domain, inducing the requisite sparsity. The resulting optimization problem is solved within the framework of the Alternating Direction Method of Multipliers (ADMM). Numerical investigations on a complex cone-cylinder-sphere assembly demonstrate that the proposed method yields superior reconstruction accuracy and robustness compared to conventional techniques. The method suppresses spatial aliasing artifacts, especially in sparse measurement scenarios. Furthermore, a sparsity analysis is conducted to validate the effectiveness of the proposed sparse representation strategy.