平面近场声全息重建结果不准确性问题的研究

平面近场声全息作为一种有效的声场分析方法被广泛用于声场分析和振动体的振动模态及其辐射声场的研究。在介绍了平面近场声全息理论的基础上,指出了利用该方法进行声场重建时存在质点振动速度和声强重建不准确的问题,并从理论分析和模拟计算两个方面给予了证明,在此基础上进一步分析了该方法的应用局限性。     

Combined Helmholtz equation-least squares method for reconstructing acoustic radiation from arbitrarily shaped objects

A combined Helmholtz equation-least squares (CHELS) method is developed for reconstructing acoustic radiation from an arbitrary object. This method combines the advantages of both the HELS method and the Helmholtz integral theory based near-field acoustic holography (NAH). As such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements, thus significantly enhancing the reconstruction efficiency. The first step in the CHELS method is to establish the HELS formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration. Next enough field acoustic pressures are generated using the HELS formulations and taken as the input to the Helmholtz integral formulations implemented through the boundary element method (BEM). The acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition (SVD) and regularization techniques. Also presented are in-depth analyses of the advantages and limitations of the CHELS method. Examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated.     

Approximations of inverse boundary element methods with partial measurements of the pressure field

Boundary element methods (BEMs) based near-field acoustic holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby conformal surface. There are practical cases when measurements are available over a patch from the measurement surface in which conventional inverse BEM based NAH (IBEM) cannot be applied directly, but instead as an approximation. In this work two main approximations based on the indirect-implicit methods are considered: Patch IBEM and IBEM with Cauchy data. Patch IBEM can be applied with a continuation procedure, which as its predecessor patch NAH (a well known technique that can be used on separable geometries of the wave equation) continues the pressure field using an iterative procedure, or it can be applied by a direct procedure. On the other hand, IBEM with Cauchy data requires measurements over two conformal patches and it will be shown that this technique will be reliable regardless of the position of the source. The theory behind each method will be justified and validated using a cylindrical surface with numerical data generated by point sources, and using experimental data from a cylindrical fuselage excited by a point force.     

Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography

Nearfield acoustical holography (NAH) requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface, the latter generally coincident with a vibrator. Patch NAH provides a major simplification by eliminating the need for complete surface pressure scans-only a small area needs to be scanned to determine the normal velocity on the corresponding (small area) concentric patch on the vibrator. The theory of patch NAH is based on (1) an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and (2) a decomposition of the transfer function (pressure to velocity and/or pressure to pressure) between the two surfaces using the singular value decomposition (SVD) for general shapes and the fast Fourier transform (FFT) for planar surfaces. Inversion of the transfer function is stabilized using Tikhonov regularization and the Morozov discrepancy principle. Experimental results show that root mean square errors of the normal velocity reconstruction for a point-driven vibrator over 200-2700 Hz average less than 20% for two small, concentric patch surfaces 0.4 cm apart. Reconstruction of the active normal acoustic intensity was also successful, with less than 30% error over the frequency band.     

运动声源的边界元声全息识别方法研究

提出了一种可实现任意形状的运动结构噪声源识别的声全息方法。通过结合移动框架技术与边界元声全息技术两种算法的特点,提出利用移动框架技术将存在多普勒效应的时域数据转换成边界元声全息所需的双平面全息数据,然后由边界元法声全息公式重构任意结构表面的声学信息,实现运动结构噪声源定位。该方法既具有移动框架技术处理运动问题的快速简便,又具有边界元方法可处理任意形状问题的特点。最后在半消声水池中,对运动速度为9.96 cm/s的带帽圆柱壳体进行了试验验证,结果表明:在低速条件下,该方法能够准确反演得到该结构的表面有功声强以及声压等声场信息,从而实现噪声源定位。由于条件有限,高速验证需进一步验证。     

Measurement of structural intensity using boundary element method-based nearfield acoustical holography

The regularization method for measurement of structural intensity (SI) using boundary element method (BEM)-based nearfield acoustical holography (NAH) is proposed. Spatial derivatives of normal displacement are necessary to obtain the structural intensity. The derivative operations amplify high-wavenumber component of measurement noise and contaminate the measurement result of SI. To overcome this difficulty, regularization method for measurement of SI using fast Fourier transform-based NAH has been introduced. In this paper, this regularization method is modified for the BEM-based NAH. The BEM-based NAH avoids the aperture replication problem; therefore, measurement aperture for BEM-based NAH can be set smaller than that for FFT-based NAH. The effectiveness of the proposed method is demonstrated by experiments.     

Underwater hybrid near-field acoustical holography based on the measurement of vector hydrophone array

Hybrid near-field acoustical holography(NAH) is developed for reconstructing acoustic radiation from a cylindrical source in a complex underwater environment. In hybrid NAH,we combine statistically optimized near-field acoustical holography(SONAH) and broadband acoustical holography from intensity measurements(BAHIM) to reconstruct the underwater cylindrical source field. First,the BAHIM is utilized to regenerate as much acoustic pressures on the hologram surface as necessary,and then the acoustic pressures are taken as input to the formulation implemented numerically by SONAH. The main advantages of this technology are that the complex pressure on the hologram surface can be reconstructed without reference signal,and the measurement array can be smaller than the source,thus the practicability and efficiency of this technology are greatly enhanced. Numerical examples of a cylindrical source are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than conventional NAH. Then,an experiment has been carried out with a vector hydrophone array. The experimental results show the advantage of hybrid NAH in the reconstruction of an acoustic field and the feasibility of using a vector hydrophone array in an underwater NAH measurement,as well as the identification and localization of noise sources.     

Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography

In this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half-space by using hybrid near-field acoustic holography (NAH) and modified Helmholtz equation least squares (HELS) formulations. In hybrid NAH, we combine modified HELS with an inverse boundary element method (IBEM) to reconstruct a vibroacoustic field. The main advantage of this approach is that the majority of the input data can be regenerated but not measured, thus the efficiency is greatly enhanced. In modified HELS, we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed-form solution to the measured acoustic pressure. Here the system of equations is ill conditioned and Tikhonov regularization is implemented through singular value decomposition (SVD) and the generalized cross-validation (GCV) method. Numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than does a modified HELS, but a modified HELS is more efficient than is hybrid NAH [Work supported by NSF].     

Study of the comparison of the methods of equivalent sources and boundary element methods for near-field acoustic holography

Boundary element methods (BEM) based near-field acoustic holography (NAH) has been used successfully in order to reconstruct the normal velocity on an arbitrarily shaped structure surface from measurements of the pressure field on a nearby conformal surface. An alternative approach for this reconstruction on a general structure utilizes the equivalent sources method (ESM). In ESM the acoustic field is represented by a set of point sources located over a surface that is close to the structure surface. This approach is attractive mainly for its simplicity of implementation and speed. In this work ESM as an approximation of BEM based NAH is studied and the necessary conditions for the successful application of this approach in NAH is discussed. A cylindrical fuselage surface excited by a point force as an example to validate the results is used.     

Planar near-field acoustical holography in a moving medium

Near-field acoustical holography (NAH) is a well-established method to study acoustic radiation near a stationary sound source in a homogeneous, stationary medium. However, the current theory of NAH is not applicable to moving sound sources, such as automobiles and trains. In this paper, the inclusion of a moving medium (i.e., moving source and receiver) is introduced in the wave equation and a new set of equations for plannar NAH is developed. Equations are developed for the acoustic pressure, particle velocity, and intensity when mean flow is either parallel or perpendicular to the hologram plane. If the source and the measurement plane are moving at the same speed, the frequency Doppler effect is absent, but a wave number Doppler effect exists. This leads to errors when reconstructing the acoustic field both towards and away from the source using static NAH. To investigate these errors, a point source is studied analytically using planar NAH with flow in one direction. The effect of the medium moving parallel to the hologram plane is noted by a shift of the radiation circle in wave number space (k-space). A k-space Green's function and a k-space filter are developed that include the effects of the moving medium.     

统计最优近场声全息重建精度和计算速度优化方法

分析了统计最优近场声全息(Statistically optimized nearfield acousticholography,简称SONAH)的重建过程发现采用SONAH重建噪声源表面法向振速时误差较大的原因在于正则化参数选取较小。在此基础上提出一种单元平面波优化选择方法,该方法保留了单元平面波中的全部传播波和部分倏逝波,去除了一些较高波数的倏逝波成分,保证了重建过程中正则化参数的准确选取。另外,采用单元平面波优化选择方法还可以降低SONAH中传递矩阵的阶数,从而解决SONAH的计算速度随着测量点数目的增加急剧变慢的问题。通过数值仿真和实验对所提出的单元平面波优化选择方法的有效性进行了验证,结果表明采用该方法后SONAH的计算速度和法向振速的重建精度都得到了较大提高。     

Near field acoustic holography with microphones on a rigid sphere (L)

Spherical near field acoustic holography (spherical NAH) is a technique that makes it possible to reconstruct the sound field inside and just outside a spherical surface on which the sound pressure is measured with an array of microphones. This is potentially very useful for source identification. The sphere can be acoustically transparent or it can be rigid. A rigid sphere is somewhat more practical than an open sphere. However, spherical NAH based on a rigid sphere is only valid if it can be assumed that the sphere has a negligible influence on the incident sound field, and this is not necessarily a good assumption when the sphere is very close to a radiating surface. This Letter examines the matter through simulations and experiments.     

统计最优平面近场声全息原理与声场分离技术

测量孔径尺寸的有限性，在基于空间傅里叶变换的平面近场声全息中会带来窗效应和卷绕误差. 为了克服窗效应和卷绕误差，引入了统计最优平面近场声全息技术. 运用声场叠加原理，证明了统计最优平面近场声全息的理论公式.通过在空间波数域限定kx,ky的取值范围，并离散其确定的空间波数面的途径，提出了一种确定波数矢量的方法.为了克服常规统计最优平面近场声全息技术的应用局限性——全息面一侧的声场必须为自由声场，提出了适用于统计最优平面近场声全息的、基于双全息面测量的空间声场分离技术. 通过实验和数值仿真对理论推导的正确性进行了验证. 关键词： 统计最优 平面近场声全息 波数矢量 声场分离     

Patch nearfield acoustic holography combined with sound field separation technique applied to a non-free field

The conventional nearfield acoustic holography(NAH) is usually based on the assumption of free-field conditions, and it also requires that the measurement aperture should be larger than the actual source. This paper is to focus on the problem that neither of the above-mentioned requirements can be met, and to examine the feasibility of reconstructing the sound field radiated by partial source, based on double-layer pressure measurements made in a non-free field by using patch NAH combined with sound field separation technique. And also, the sensitivity of the reconstructed result to the measurement error is analyzed in detail. Two experiments involving two speakers in an exterior space and one speaker inside a car cabin are presented. The experimental results demonstrate that the patch NAH based on single-layer pressure measurement cannot obtain a satisfied result due to the influences of disturbing sources and reflections, while the patch NAH based on double-layer pressure measurements can successfully remove these influences and reconstruct the patch sound field effectively.     

Hybrid near-field acoustic holography

Hybrid near-field acoustical holography (NAH) is developed for reconstructing acoustic radiation from an arbitrary object in a cost-effective manner. This hybrid NAH is derived from a modified Helmholtz equation least squares (HELS) formula that expands the acoustic pressure in terms of outgoing and incoming waves. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching the assumed-form solution to measured acoustic pressures through the least squares. Measurements are taken over a conformal surface around a source at close range so that the evanescent waves can be captured. Next, the modified HELS is utilized to regenerate as much acoustic pressures on the conformal surface as necessary and take them as input to the Helmholtz integral formulation implemented numerically by boundary element method (BEM). The acoustic pressures and normal velocities on the source surface are reconstructed by using a modified Tikhnov regularization (TR) with its regularization parameter determined by generalized cross validation (GCV) method. Results demonstrate that this hybrid NAH combines the advantages of HELS and inverse BEM. This is because a majority of the input data are regenerated but not measured, thus the efficiency of reconstruction is greatly enhanced. Meanwhile, the accuracy of reconstruction is ensured by the Helmholtz integral theory and modified TR together with GCV method, provided that HELS converges fast enough on the measurement surface. Numerical examples of reconstructing acoustic quantities on the surface of a simplified engine block are demonstrated. [Work supported by NSF.]     

On optimal retreat distance for the equivalent source method-based nearfield acoustical holography

As a basic form of the equivalent source method (ESM) that is used to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a "retreat distance" between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. In prior research, 1-2 times lattice spacing, or the inter-element distance of microphones, is generally recommended as retreat distance in using the ESM-based NAH. While this rule has shown to yield good results in many cases, the optimal choice is a complicated issue that depends on frequency, geometry of the physical source, content of evanescent waves, distribution of sensors and virtual sources, etc. This paper deals about attaining the best compromise between the reconstruction errors induced by the point source singularity; the reconstruction ill-posedness is an interesting problem in its own right. The paper revisits this issue, with the aid of an optimization algorithm based on the golden section search and parabolic interpolation. Numerical simulations were conducted for a baffled planar piston source and a spherically baffled piston source. The results revealed that the retreat distance appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Experiments carried out for a vibrating aluminum plate also revealed that the retreat distance with 0.5 times the spacing yielded better reconstructed velocity than those with 1/20 and 1 times the spacing.     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法     

分部优化正则化在近场声全息技术中的应用

在基于等效源法近场声全息技术的基础上,对稳定重建过程不适定性的正则化技术进行深入研究。为改善正则化效果,综合考虑Tikhonov正则化和截断奇异值法,提出一种新的分部优化正则化技术。该技术兼取了两种方法的优点,比Tikhonov正则化稳定,避免了过滤波等正则化失效的情况;比截断奇异值法精度高,包含了更多的细节信息。通过对简支板的数值仿真,分别和Tikhonov正则化和截断奇异值法进行了比较,说明了本文所提方法稳定性较好和精度较高的优点。最后通过实验研究进一步证明了本文方法的有效性和正确性。     

The application of regularization technique based on partial optimization in the nearfield acoustic holography

The regularization technique for stabilizing the reconstruction based on the nearfield acoustic holography(NAH) was investigated on the basis of the equivalent source method.In order to obtain higher regularization effect,a regularization method based on the idea of partial optimization was proposed,which inherits the advantages of the Tikhonov and another regularization method—truncated singular value decomposition(TSVD).Through the numerical simulation,it is proved that the proposed method is stabler than the Tikhonov,and more precise than the TSVD.Finally the validity and the feasibility of the proposed method are demonstrated by an experiment carried out in a semi-anechoic room with two speakers.     

联合波叠加法的全息理论与实验研究

当空间声场中同时存在多个相干声源时，运用常规近场声全息方法无法重建每个相干声源表面的声学信息，当然也无法预测每个声源单独产生的空间声场，相干声场的全息重建与预测已成为全息技术推广应用过程中亟待解决的问题.在提出联合波叠加法并将其应用于空间声场变换的基础上，对其进行了实验研究.通过对实际相干声场的全息重建与预测，验证了常规波叠加法在相干声场重建中的局限性、联合波叠加法在相干声场全息重建与预测过程的可行性和准确性，还研究了Tikhonov正则化方法在抑制声学逆问题的非适定性中的有效性和滤波系数的选择原则的可行性，以提高全息重建与预测的精度. 关键词： 近场声全息 联合波叠加 相干声场 Tikhonov正则化