The use of partially measured source data in near-field acoustical holography based on the BEM

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.