Meanings of SVD and wave-vector filtering in the near-field acoustical holography using the inverse BEM

Abstract

In the conformal near-field acoustical holography (NAH), using the boundary element method (BEM), the vibroacoustic information on the source surface can be indirectly reconstructed by utilizing the measured field pressure and the inverse transfer matrix. The involved vibroacoustic transfer matrix is generally ill conditioned and the reconstruction process should include the singular value decomposition (SVD) in order to solve the problem in the inverse procedure. The accuracy of the reconstructed field is deteriorated substantially due to the ill conditioning of the transfer matrix and the inevitable measurement noise of field pressure related to the nonpropagating wave components. In this study, the computational processes of SVD and wave-vector filtering in the BEM-based NAH are discussed and their physical meanings are investigated through a simulation example. The vibroacoustic transfer matrix decomposed by SVD permits an effective regularization of the source field: This is possible because the involved information in the transfer matrix can be separated into the radiation efficiency and the wave modes at the source and surface fields. In particular, it is clearly shown that the restored source image can be improved dramatically by adopting the wave-vector filter that suppresses the nonpropagating wave components appropriately that cause the deterioration of the reconstruction accuracy.