Near-field Acoustic Holography Technology Based On Green’s Function

As the characteristic function reflecting the reverse transmission of the sound field in thesound field inverse problem, Green’s function played an important role in the developmentprocess of the near-field acoustic holography (NAH) technology, which is the ideal functionfor establishing the inversion model from the sound field to the sound source. As the morepopular noise source identification technology in recent years, NAH technology caneffectively reconstruct the sound source and forecast the relevant characteristics of the soundfield according to the distribution information of the known sound field, and has a goodoperability and engineering achievability in the practical engineering application. The paperconsidered Green’s function as the basic of the research, gave Green’s functions which wasapplicable for different types of the sound field reconstruction, and toke the problems of thenow NAH technology in depth study by optimizing Green’s function algorithms.Firstly, the paper systematically summarized and derived the basic theory of NAHtechnology in moving fluid medium, established and discussed the inherent relationship of thewave equation, Helmholtz-Kirchhoff integral equation, and space transformation sound fieldin the moving fluid medium.This paper gave the Green’s functions (Dirichlet and Neumann)and the wave number filter for reconstructing the sound field at the two typical boundaryconditons in a moving fluid medium, and compared the space distribution of the two Green’sfunction in moving and static medium through the numerical simulation which explained theaffection of the moving medium on the wave number space of the sound field, especially itcan not be ignored when the Mach number is large. Through the simulation verified theeffectiveness and feasibility of the use of these two typical boundary Green’s function forreconstructing the sound field,and gave the dynamic range for the future engineeringapplication through discussing and analyzing the calculation parameters like samplingpoints(or sampling interval), measurement distances, reconstructive distances and Machnumber.For the velocity measured Green’s function’s singularity at the radiation circumference inNeumann boundary, this article gave two different finite discretization algorithms for Green’sfunction: K-space integral Green’s function and real-space integral Green’s function, whichare different from K-space sampling Green’s function. Analyze the distribution characteristicsof three Green’s function algorithms in wave number space and real space through thesimulations, discuss the affection of different calculation parameters on the distributions of the two optimized Green’s function, and give the change of the two optimized Green’sfunction from the K-space sampling Green’s function’s singularity at the radiationcircumference. Reconstructing different types of sound sources by using these three finitediscretization algorithms, examined the contribution of the two optimized Green’s function forthe reconstructive accuracy and resolution.According to the two problems in the cylindrical NAH technology at the present, thepaper gave the formula derivation and simulation operations for these problems. Ons is usedfor cylindrical NAH in Neumann boundary condition, the other is for separating andreconstructing the aim source based on two measurements when there existed coherent sourcein cylindrical sound field measurement. Firstly, through the calculation based on themathematical physics theorem received the progressive expression of the Green’s functionsbased on the normal velocity measurement and the pressure measurement in Neumannboundary condition, verified the formula’s correctness and compared the advantages anddisadvantages of these two measurement method through the simulations. Secondly, the papergave the study for the sound field separation technology of cylindrical NAH. Through thesingle hologram method based on sound pressure-velocity measurement and the doubleholograms method based on sound pressure and velocity measurement simulated the affectionof different intensities of interference source on the reconstructive accuracy of the aim source,and compared the advantages and disadvantages of these two measurement method when thecoherent sources are located at completely symmetrical, not completely symmetrical andabsolutely asymmetrical position.For the transient sound field existing in the acoustic field, this article gave thetime-domain NAH technology (TDNAH) based on three Green’s function algorithms.Through analyzing the space distribution characteristics of these three Green’s functions, gavethe factors which may have impacts on the reconstructive accuracy in the reconstructionprocess, calculated the running time of every Green’s function according to their calculationcharacteristics and analyzed their affection on the reconstructive efficiency. As an example ofthe monopole source accompanied by a slowly varying radiation, reconstructed its transientfield by these three Green’s functions, modulated its space complex envelope by calculationsand discussed the affection of calculation parameters on the reconstructive accuracy by thesethree Green’s functions. Through analyzing the characteristics of sound field reconstructionbased on the three Green’s functions, taken the K-space Green’s function based on FFTtransformation into reconstructing the transient sound field produced by an infinite rigidbaffled piston and analyzed the affections of the calculated parameters on the sound field reconstruction accuracy.Finally, this article carried out the experimental study for the under-water noise sourceby using planar NAH technology, explored the feasibility and accuracy of planar NAHtechnology based on this paper algorithms, and examined the affections of the methods basedon the sound pressure measurement and the velocity measurement on the reconstructionaccuracy, as well as different algorithms based on the two measurement methods. The resultsof theoretical analysis and experimental data processing results are basically the consistency,which provided the experimental basis for the next practical engineering applications.