基于格林函数的近场声全息技术
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摘要
格林函数作为声场逆问题中反映声场逆向传递的特征函数，在近场声全息技术发展过程中扮演着重要角色，是建立从声场到声源反演模型的理想函数。近场声全息技术作为近些年来比较热门的噪声源识别技术，能够根据已知的声场分布信息，有效地重建声源和预报其声场的相关特性，并在实际工程应用中具有较好可操作性和工程实现性。本文以格林函数为研究基础，给出了适用于不同类型声场重建的格林函数，并通过优化格林函数算法的方法对现有近场声全息技术中存在的问题进行了系统、深入的研究。
本文首先系统的总结和推导了运动流体介质下平面近场声全息技术的基本理论，建立和讨论了运动流体介质中波动方程、Helmholtz-Kirchhoff积分方程、空间声场变换之间的内在关系。给出了运动流体介质下适用于两种典型边界条件声场重建的格林函数（Dirichlet边界条件、Neumann边界条件）及波数域滤波器，并通过数值仿真对比分析了运动和静止介质下两种格林函数的空间分布特点，说明了运动介质对声场波数空间的影响。通过仿真计算验证了利用这两个典型边界条件下格林函数对声场重建的有效性和可行性，并通过对采样点数（或采样间隔）、测量距离、重建距离以及马赫数的计算参数的讨论分析，给出一些有利于今后工程应用值得参考的测量范围。
针对静止介质中Neumann边界条件下基于振速测量的格林函数辐射圆周存在的奇异性，给出了两种与K-空间抽样格林函数不同的格林函数有限离散化算法：K-空间积分格林函数法和实空间积分格林函数法。通过数值仿真分析了三种格林函数算法分别在波数空间和实空间的分布特点，讨论不同的计算参数对这两种格林函数分布的影响，给出了两种格林函数优化算法相对于K-空间抽样格林函数辐射圆周上奇异性作出的改进。利用这三种格林函数有限离散化方法对不同类型声源的声场进行重建，以考查作为优化算法的两种格林函数对该条件下改善重建精度以及重建分辨率的贡献。
根据柱面近场声全息技术现阶段存在的两个问题，给出了相应的公式推导和仿真运算。一个是针对Neumann边界条件下的声场应用柱面近场声全息技术，另一个针对的是基于柱面声场测量时，声场存在相干声源时，如何应用两种测量方法分离目标声源并对其进行声场重建。首先，利用数学物理方法中的相关定理计算得到Neumann边界条件下基于法向质点振速测量和基于声压测量格林函数的渐进表达式，通过仿真计算验证该表达式的正确性，并通过仿真分析对比了这两种测量方法的优劣性。其次，研究了柱面相干声源的分离技术。通过基于声压联合振速测量的单全息面方法和基于声压、振速测量的双全息面方法，仿真计算了相干声源分别在完全对称、不完全对称以及完全不对称的条件下，干扰源不同强度对目标声源重建精度的影响，对比了两种测量方法的优劣性。
针对声场中存在的瞬态声场，给出了基于三种格林函数算法的时域近场声全息技术。通过对这三种格林函数空间分布特点的分析，给出了这三种格林函数可能在重建过程中对重建精度产生影响的因素，并根据这三种格林函数的计算特点，计算了每个格林函数在一定参数条件下的运行时间，分析了其对声场重建效率的影响。以单极子源伴随缓慢变化的空间复包络振荡和整体波动的辐射声场为例，利用这三种格林函数对该声场进行重建，并通过计算给出了对空间复包络进行调制的方法，通过计算参数对三种算法下的重建精度进行讨论。通过对三种格林函数声场重建特点的分析，采用基于FFT变换算法的K-空间格林函对无限大刚性障板上圆形活塞产生的瞬态声场进行重建，分析各个计算参数对声场重建精度的影响。
最后，开展针对水下噪声源利用平面近场声全息技术的实验研究，探讨基于本文算法的近场声全息技术的可行性和准确性，考查基于声压测量和基于振速测量方法对声场重建精度的影响，以及两种测量方法下不同算法对重建精度的影响。理论分析结果和实验数据处理结果基本一致，为其下一步的实际工程应用提供了实验基础。
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.
本文首先系统的总结和推导了运动流体介质下平面近场声全息技术的基本理论，建立和讨论了运动流体介质中波动方程、Helmholtz-Kirchhoff积分方程、空间声场变换之间的内在关系。给出了运动流体介质下适用于两种典型边界条件声场重建的格林函数（Dirichlet边界条件、Neumann边界条件）及波数域滤波器，并通过数值仿真对比分析了运动和静止介质下两种格林函数的空间分布特点，说明了运动介质对声场波数空间的影响。通过仿真计算验证了利用这两个典型边界条件下格林函数对声场重建的有效性和可行性，并通过对采样点数（或采样间隔）、测量距离、重建距离以及马赫数的计算参数的讨论分析，给出一些有利于今后工程应用值得参考的测量范围。
针对静止介质中Neumann边界条件下基于振速测量的格林函数辐射圆周存在的奇异性，给出了两种与K-空间抽样格林函数不同的格林函数有限离散化算法：K-空间积分格林函数法和实空间积分格林函数法。通过数值仿真分析了三种格林函数算法分别在波数空间和实空间的分布特点，讨论不同的计算参数对这两种格林函数分布的影响，给出了两种格林函数优化算法相对于K-空间抽样格林函数辐射圆周上奇异性作出的改进。利用这三种格林函数有限离散化方法对不同类型声源的声场进行重建，以考查作为优化算法的两种格林函数对该条件下改善重建精度以及重建分辨率的贡献。
根据柱面近场声全息技术现阶段存在的两个问题，给出了相应的公式推导和仿真运算。一个是针对Neumann边界条件下的声场应用柱面近场声全息技术，另一个针对的是基于柱面声场测量时，声场存在相干声源时，如何应用两种测量方法分离目标声源并对其进行声场重建。首先，利用数学物理方法中的相关定理计算得到Neumann边界条件下基于法向质点振速测量和基于声压测量格林函数的渐进表达式，通过仿真计算验证该表达式的正确性，并通过仿真分析对比了这两种测量方法的优劣性。其次，研究了柱面相干声源的分离技术。通过基于声压联合振速测量的单全息面方法和基于声压、振速测量的双全息面方法，仿真计算了相干声源分别在完全对称、不完全对称以及完全不对称的条件下，干扰源不同强度对目标声源重建精度的影响，对比了两种测量方法的优劣性。
针对声场中存在的瞬态声场，给出了基于三种格林函数算法的时域近场声全息技术。通过对这三种格林函数空间分布特点的分析，给出了这三种格林函数可能在重建过程中对重建精度产生影响的因素，并根据这三种格林函数的计算特点，计算了每个格林函数在一定参数条件下的运行时间，分析了其对声场重建效率的影响。以单极子源伴随缓慢变化的空间复包络振荡和整体波动的辐射声场为例，利用这三种格林函数对该声场进行重建，并通过计算给出了对空间复包络进行调制的方法，通过计算参数对三种算法下的重建精度进行讨论。通过对三种格林函数声场重建特点的分析，采用基于FFT变换算法的K-空间格林函对无限大刚性障板上圆形活塞产生的瞬态声场进行重建，分析各个计算参数对声场重建精度的影响。
最后，开展针对水下噪声源利用平面近场声全息技术的实验研究，探讨基于本文算法的近场声全息技术的可行性和准确性，考查基于声压测量和基于振速测量方法对声场重建精度的影响，以及两种测量方法下不同算法对重建精度的影响。理论分析结果和实验数据处理结果基本一致，为其下一步的实际工程应用提供了实验基础。
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.
引文
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