Reconstruction of surface velocity field using wavelet transformation and boundary-element method

Abstract

This paper shows the application of discrete wavelet transformation (DWT) to inverse acoustics for reconstructing the surface velocity of a noise source. This approach uses the boundary-element analysis based on the measured sound pressure at a set of field points, the Helmholtz integral equations, and wavelet transformation to reconstruct the normal surface velocity field. The reconstructed velocity field can be diverged due to the small measurement errors in the case of nearfield acoustic holography using an inverse boundary-element method. In order to bypass the instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the order of an optimal truncation is difficult to determine. In this paper, a DWT is applied to reduce the computation time for inverse acoustics and to enhance the reconstructed surface velocity field. The computational speed-up is achieved, with solution time being reduced to 14.3 per cent.