A hybrid nearfield acoustic holography based on the mapping relationship and boundary element method

Abstract

The nearfield acoustic holography (NAH) based on mapping relationship (MRS) had been developed. However, it is superior to the reconstructions on regular shapes by using the MRS-based NAH with spherical fundamental solutions (FS). In contrast, the boundary element method (BEM) based NAH is capable of handling complex shapes but requires relatively more measurement points. In this work, a hybrid method is developed by combing the MRS with spherical FS and the BEM. To circumvent the non-unique problems associated with the conventional BEM, the Burton-Miller formulation is adopted into the BEM based NAH. The merit of easy measurement setup, such as the determination of positions and number of microphones in the array is preserved in the hybrid method. Furthermore, it is possible to recast the reconstruction operation by the BEM-based NAH with sufficient measurements data on an artificial hologram that are implicitly interpolated by the MRS-based NAH. In conjunction with regularization techniques, results with improved accuracy are clearly observed in the velocity reconstructions for irregular shapes by the hybrid NAH. It is validated by numerical examples especially for an irregular box that the hybrid NAH is capable of producing reconstructions with significant improvement of accuracy even with small signal-to-noise ratio (SNR) as compared with the MRS-based NAH. An experiment is setup to further demonstrate the potential of the hybrid NAH for practical reconstruction of an irregular radiator. More robust and accurate reconstructions are achieved in contrast with the MRS-based NAH, which clearly illustrated advantages of the hybrid NAH.