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The vibrational velocity, sound pressure, and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures. The singular value decomposition is used to obtain the inverse solution in the least-square sense and to express the acoustic modal expansion between the measurement and source fields. In general, such an inverse operation has been considered an ill-posed problem having a divergence phenomenon involved with extremely small measurement errors. The ill-conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components. In order to minimize the singularity and to also reduce the number 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 components resulting in the singular transfer matrix. In order to enhance the resolution of the reconstructed field, the optimal regularization order 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 validating and demonstrating the proposed reconstruction process. It is noted that the present method can improve the resolution of the reconstructed field; thus vibro-acoustic parameters of the vibrating boundary can be estimated in reasonably good precision.
Kim et al. (Fri,) studied this question.