In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular shaped boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff-Helmholtz integral equation has the singularity problem in the close near field of the source surface. This problem stems from the singular kernel of the Green function of the boundary integral equation (BIE) and the singularity can influence the reconstruction accuracy greatly. In this paper, the nonsingular BIE is introduced to the NAH calculation and the holographic BIE is reformulated. The effectiveness of nonsingular BEM has been investigated for the reduction of reconstruction error. Through interior and exterior examples, it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular BIE. Because the BEM-based NAH inevitably requires the field pressure measured in the close proximity to the source surface, the present approach is recommended for improving the resolution of the reconstructed source field.

In applying the conformal near-field acoustical holography (NAH) to actual source identification problems, it is often possible to determine the velocity at certain points of the source surface in advance. This partially known velocity data would reduce the problem size and permit better reconstruction accuracy. In this paper, the effectiveness of using partially measured source data in the conformal NAH is investigated, which uses the boundary element method. A vibro-acoustic transfer matrix and measured field pressure data, which is involved with the boundary integral equation, are reorganized in order to deal with the partially measured surface velocities. For a baffled vibrating panel, simulations were performed by varying the number of velocity-known nodes. In addition, the effect of measurement error is investigated for two extreme positioning methods of velocity-known nodes. Without regularization, the reconstructed error can be reduced considerably by employing some of the source data and this error can be further reduced by increasing those surface points. However, the velocity reconstruction error is not reduced substantially when the number of velocity-known nodes is less than 30%-40% of the total nodes. The reduction in the reconstruction error is not large if the regularization technique is applied to the restored field.

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In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff–Helmholtz integral equation has the singularity problem in the very-near field of the source surface: computation error increases very rapidly as approaching from the far field. This problem originated from the singular kernel of the fundamental solution of the BIE and can influence the reconstruction accuracy. In this paper, the holographic BIE is reformulated to remove the singularity by introducing an additional propagating plane wave. Reconstructed results by the conventional and the nonsingular BIE are compared for a simple radiator model. It is observed that the nonsingular formulation can yield accurate vibro-acoustic transfer matrix and thus improve the resolution of the reconstructed source field.

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.