Fourier Transform-source Simulation Technique Application In Sound Pressure Reconstruction Of Nearfield Acoustic Holography

The holographic transform algorithm research on the nearfield acoustic holography(NAH) has been carried out in this dissertation supported by the Guangxi Natural ScienceFoundation"Acoustic Holography Fast Algorithm based on Multiple Virtual DomainsWave Superposition Approach". Based on source simulation technique and2-D discreteFourier transform, a new nearfield acoustic holography based on Fourier transform-sourcesimulation technique has been proposed. The NAH not only has the characteristics ofspatial Fourier transform-based NAH easy to implement and fast calculation, from limitedaperture limit, but also has characteristics of equivalent source method-based NAH. Thatis suitable for any shape of the sound source to avoid the problem of the complexity of theinterpolation operation, the processing of singular integral and non-uniqueness of thesolution of the characteristic wave number processing. Finally, through a large number ofsimulation experiments with the models of point source, vibrating spheres sound source,simply supported plate sound source, the result shows that this method is feasible andeffective. The specific contents are as follows.(1) Derivation of NAH reconstruction formula based on Fourier transform-sourcesimulation technique. Continuous simple source(monopole) is arranged in a rectangularvirtual source configuration surface (virtual source plane)，and the source function is takenas the3-D space Green’s function. The unknown source density is expanded into the2-DFourier series. So the sound pressure expression of the form of2-D discrete Fouriertransform has been derived, which is used to calculation of sound radiation, meanwhilecombining with the program of FFT and IFFT to accelerate the speed of calculation. Onthis basis, the sound pressure expression of each measuring point on the hologram plane isdeduced, and is organized into non-homogeneous linear equations which consist ofunknown terms of Fourier’s series expansion coefficients and constant terms of the soundpressures. Otherwise, the sound pressures are measured by the holographic measuringarray (ie, holographic data). Then the coefficients matrix could be solved by generalizedinverse matrix, and is substituted into the reconstruction formula. Finally, the soundpressure expression at any field point in the radiation field has been established, and it canbe used to the sound field reconstruction and prediction of entire space. The above is theNAH based on Fourier transform-source simulation technique, and is proved correctly bytwo examples.(2) Research of the transfer matrix condition number and its optimization. NAH is anacoustic inverse problem, and the ill-condition of transfer matrix affects the accuracy ofthe reconstruction results. In order to reduce the impact of the ill-condition of transfermatrix, this article has studied the influencing factors of the transfer matrix conditionnumber and its optimization, and got some guidance conclusions.(3) Research of regularization methods. Because the holographic data has errors inevitably, in order to reduce the impact of the errors on the reconstruction results,Regularization must be done. This paper has made a comparison of the directregularization methods (ie, TSVD and Tikhonov regularization), meanwhile theregularization parameter is selected by signal-to-noise ratio (SNR) and L-curve criterionrespectively. Finally, it has been found out the regularization method is suitable for thisNAH by simulation analysis.(4) Research of the factors that affect the reconstruction accuracy. In order to applythis NAH in practical engineering, this paper has analyzed the impact factors that affectthe accuracy of the reconstruction. This article has done some simulation analysis, mainlyin the arrangement position of the virtual source plane, the size of the virtual source plane,the size of the virtual source plane mesh and the distance of the holographic measurement.Finally, when the holographic data has errors, this paper has done research of thereconstruction robustness problem. These studies provide effective guidance for thepractical application of the reconstruction method mentioned in this article. By simulationanalysis, it has been found out some rules in error of the reconstruction method mentionedin this article.(5)Full-text summary and outlook. The article focuses on the research on the soundpressure reconstruction algorithm of nearfield acoustic holography, but NAH as anacoustic measurement system, there are many research contents. So systematicallysummarizes about the research have been done, and has been pointed out the direction ofthe sound pressure reconstruction method that needs further study.