Research On Solving Algorithm Of Near-field Acoustical Holography Based On Equivalent Source Method

Near-field acoustical holography(NAH) is a technology based on field measurements performed by a microphone array, and has found wide applications in the automobile fields for sound source identification and spatial sound field visualization. NAH has a variety of holographic algorithms, one of which is the NAH based on equivalent source method(ESM-based NAH). ESM-based NAH can be adapted to any form of source and array shape. With higher reconstruction precision and computational efficiency, it has been widely studied and applied in recent years. The key of ESM-based NAH is to obtain the equivalent source intensity which has multiple solving algorithms, and different solving algorithms result in different sound field reconstruction performance. Tikhonov regularization ESM(TRESM), iterative weighted ESM(IWESM) and steepest descent iteration ESM(SDIESM) three kinds of solving algorithms were given in this paper. And the research route with the combination of theoretical derivation, mathematical modeling, numerical simulation and experimental verification was adopted to compare three algorithms. The aim of this study is to explore a new algorithm which can achieve better reconstruction performance in wide frequency band, at the same time, it is devoted to improving the performance of sound field reconstruction and sound source identification, and to expanding the application range of the ESM-based NAH.To improve the sound field reconstruction precision of TRESM, the modified Hald empirical formula method and Bayesian regularization criterion method with better performance were proposed to determine the regularization parameter. The correctness and superiority of the proposed methods are validated through the simulation analysis and sound radiation experiment with loudspeakers. Subsequently, to enhance the low-frequency reconstruction performance of ESM-based NAH, the IWESM algorithm was presented. The sound field reconstruction precision of the TRESM and IWESM algorithms was compared based on single/dual sources. And the correctness that IWESM has better low-frequency reconstruction performance is validated by the experiment. Further, to improve the high-frequency reconstruction performance of ESM-based NAH, the SDIESM algorithm was derived in detail, and its reconstruction performance was also presented. The comprehensive reconstruction performance of TRESM, IWESM and SDIESM were compared respectively at different holographic distances and signal-to-noise ratios(SNR). And their respective advantages and disadvantages are as follows: the reconstruction precision of TRESM is not good enough in the low-medium frequency and even poor in the high frequency; IWESM with higher precision and resolution in low frequency, is regrettably unstable in the medium-high frequency because of the sensitive holographic distance; SDIESM with higher precision in the medium-high frequency, is not good enough in the low frequency and the computational efficiency. Finally, to achieve better reconstruction performance in wide frequency band, a refined wideband acoustical holography(RWAH) based on ESM was proposed on the basis of the advantages and disadvantages of TRESM, IWESM and SDIESM algorithms. RWAH adopts IWESM below a transition frequency, and switches to the SDIESM whose principal components have been truncated above that transition frequency. The higher reconstruction precision and good computational efficiency of RWAH is validated under the single/dual sources, different holographic distances and SNR values. Besides, a sound radiation experiment was conducted by the single/dual loudspeakers, confirming that RWAH can achieve better reconstruction performance in wide frequency band.