ON THE RECONSTRUCTION OF THE VIBROACOUSTIC FIELD OVER THE SURFACE ENCLOSING AN INTERIOR SPACE USING THE BOUNDARY-ELEMENT METHOD

The vibrational velocity, sound pressure, and acoustic power on the vi brating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures. The si ngular value decomposition is used to obtain the inverse solution in t he least-square sense and to express the acoustic modal expansion betw een the measurement and source fields. In general, such an inverse ope ration has been considered an ill-posed problem having a divergence ph enomenon involved with extremely small measurement errors. The ill-con ditioned nature of the acoustic inverse problem is caused by the singu larity of the transfer matrix which produces nonradiating wave compone nts. In order to minimize the singularity and to also reduce the numbe r of measurement points, optimal measurement positions are determined by the effective independence method. Regularization methods are used to stabilize the reconstructed field by suppressing nonradiating compo nents resulting in the singular transfer matrix. In order to enhance t he resolution of the reconstructed field, the optimal regularization o rder for yielding the minimum mean-square error is estimated from the known measurement noise variance by virtue of the statistical analysis . A half-scaled automotive cabin is considered an example for validati ng and demonstrating the proposed reconstruction process. It is noted that the present method can improve the resolution of the reconstructe d field; thus vibro-acoustic parameters of the vibrating boundary can be estimated in reasonably good precision. (C) 1996 Acoustical Society of America.