A multi-index fusion array design method for sparse measurement of radiated sound field of large-aspect-ratio structures

To address the aggravated ill-conditioning of the transfer matrix and the resulting reduction in accuracy and stability of sound field prediction under limited measurement conditions for large-aspect-ratio structural sound sources, a Coherence-Condition Number-Energy Multi-index Method (CCEMM) is proposed for the Prolate Spheroidal Wave Function (PSWF) transfer matrix. The method employs average coherence, condition number, and row energy to characterize the column correlation, numerical stability, and measurement information acquisition capability of the transfer matrix, respectively. On this basis, an array design criterion matched to the Sparse Bayesian Learning (SBL) inversion process based on the PSWF expansion model is established, and the sparse array is constructed using deterministic initialization and a forward measurement-point addition strategy. Simulation results for a scaled underwater vehicle model show that at a sampling rate of 33.3%, the relative prediction error of CCEMM remains below 10% at most frequencies within the analyzed band. The airborne acoustic experimental results for the cylindrical shell exhibit error variation trends generally consistent with those obtained from the numerical simulations. Even at a sampling rate of only 28.6%, the prediction error curve remains in close agreement with the results obtained using all measurement points, and the relative prediction errors remain below 18%. These results demonstrate that CCEMM can substantially reduce the number of measurement points while maintaining sound field prediction accuracy and stability, thereby providing an effective array design method for sparse sound field measurements of large-aspect-ratio structural sound sources.