Data extrapolation method for boundary element method-based near-field acoustical holography

A new data extrapolation method for boundary element method (BEM)-based near-field acoustical holography (NAH) is proposed to reduce an error of the reconstructed result obtained from the pressure measured on an aperture small compared with the structure. The finiteness of the measurement aperture is a serious impediment to actual large-scale implementation of NAH, because NAH requires the measurement of the pressure field over a complete surface of structure. To eliminate the requirement, the wave number-space data extrapolation method for fast Fourier transform (FFT)-based NAH has been proposed. In this paper, the extension of this data extrapolation method to BEM-based NAH is presented. The effectiveness of this method is demonstrated by experiments. The experiment results confirm that the reconstruction error is sufficiently suppressed by the proposed method.     

Patch nearfield acoustic holography in a moving medium

To realize the accurate reconstruction of sound field in a moving medium under the condition of limited holographic aperture, a patch nearfield acoustic holography (NAH) in a moving medium is proposed. The proposed method not only reduces the influence caused by the limited aperture effects through sound field extrapolation, but also perfectly suits for sound field reconstruction in a moving medium by improving the shape of the modified Tikhonov regularization filter and the noise estimation method in accordance with flow effects. In the method, two cases that the flow direction is parallel to and perpendicular to the hologram surface are considered. Especially in the perpendicular case, the expression of the wavenumber component in the z direction is improved to make the proposed method suitable for the moving medium at a high Mach number. Simulations are investigated to examine the performance of the proposed method and show its advantages by comparing with NAH in a moving medium and the conventional patch NAH. It is found that, the proposed method is effective and robust at different flow velocities of the medium and different frequencies of the sound source.     

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.     

Reduction methods of the reconstruction error for large-scale implementation of near-field acoustical holography.

New extrapolation methods in real and wave number spaces are proposed to extend near-field acoustical holography (NAH) toward a more quantitative technique applicable to the vibration measurement of actual large-scale structures. The finiteness of the measurement aperture is a serious impediment to such large-scale implementation of NAH because the measurement aperture sufficiently larger than the vibrating structure of interest is usually needed. We should thus investigate how to reduce the reconstruction error when the measurement aperture is restricted to a fraction of the vibrating structure. The following practical suggestions are derived from simulations and underwater experiments: (1) A wave number-space extrapolation method can reduce the reconstruction error to about 25% for the measurement aperture corresponding to 1/16th of the vibrating structure when 10,000 iterations of the extrapolation process are applied. (2) A real-space extrapolation method can reduce the reconstruction error to negligible degree (10(-10)%) for the measurement aperture corresponding to four times as large as the vibration structure when ten iterations of the extrapolation process are applied. (3) The former method may be widely and safely applied, but many iterations are necessary; the latter method can reduce the reconstruction error very quickly, but a wider measurement aperture than that in the former is needed. Therefore, when the measurement aperture cannot be larger than the vibrating structure, the former method is recommended, while when the measurement aperture is larger than the structure, the latter method is recommended. Summing up, the accuracy of our proposed methods, which is attributed to the property of data extrapolation method that the data inside the measurement aperture is conserved after adequately extrapolating the data outside the aperture, will be relevant to a more quantitative measurement and analysis of real large-scale structures.     

平面近场声全息中正则化参数的确定

近场声全息的逆向重建过程属于线性病态逆问题,必须进行正则化处理。本文对三种基于Tikhonov正则化的参数选择方法,即离差原理法、广义交叉验证法、L曲线法,在不同全息距离、声源频率和信噪比的条件下进行了比较,结果表明,它们在远距离及低噪声环境下难以获得合适的正则化参数。采用等效噪声方差的方法,对其中较为稳定的离差原理进行了改进,使其在较远全息距离及低噪声环境下仍能获得合适的正则化参数。相应的仿真实验表明,改进后的离差原理法在很宽的信噪比(＞6 dB)和较远的全息距离(~10 cm)均能稳定地找到合适的正则化参数。此外,由于该方法无须对全息声压进行平滑处理,其有效重建孔径和全息孔径相等。      

Use of nonsingular boundary integral formulation for reducing errors due to near-field measurements in the boundary element method based near-field acoustic holography

In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular shaped boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff-Helmholtz integral equation has the singularity problem in the close near field of the source surface. This problem stems from the singular kernel of the Green function of the boundary integral equation (BIE) and the singularity can influence the reconstruction accuracy greatly. In this paper, the nonsingular BIE is introduced to the NAH calculation and the holographic BIE is reformulated. The effectiveness of nonsingular BEM has been investigated for the reduction of reconstruction error. Through interior and exterior examples, it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular BIE. Because the BEM-based NAH inevitably requires the field pressure measured in the close proximity to the source surface, the present approach is recommended for improving the resolution of the reconstructed source field.     

Statistically optimized near field acoustic holography using an array of pressure-velocity probes

Statistically optimized near field acoustic holography (SONAH) differs from conventional near field acoustic holography (NAH) by avoiding spatial Fourier transforms; the processing is done directly in the spatial domain. The main advantage of SONAH compared with NAH is that the usual requirement of a measurement aperture that extends well beyond the source can be relaxed. Both NAH and SONAH are based on the assumption that all sources are on one side of the measurement plane whereas the other side is source free. An extension of the SONAH procedure based on measurement with a double layer array of pressure microphones has been suggested. The double layer technique makes it possible to distinguish between sources on the two sides of the array and thus suppress the influence of extraneous noise coming from the "wrong" side. It has also recently been demonstrated that there are significant advantages in NAH based on an array of acoustic particle velocity transducers (in a single layer) compared with NAH based on an array of pressure microphones. This investigation combines the two ideas and examines SONAH based on an array of pressure-velocity intensity probes through computer simulations as well as experimentally.     

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.     

Theoretical and experimental investigation of holographic reconstruction and prediction of multi-source hybrid acoustic field

Recently, NAH has been developed as an efficient tool for noise identification, noise localization and acoustic field visualization. Compared with the traditional acoustic ra-diation calculation problem, the solving problem in the NAH is an inverse acoustic problem. By measuring partial acoustic field information, such as complex pressures or particle velocities on the hologram surface, but not the surface normal velocities of the vibrating body, the surface information can be reconstructed,…     

A one-step patch near-field acoustical holography procedure

When performing holography measurements over a limited area of a source, the hologram pressure typically remains finite at the edge of the measurement aperture. Patch near-field acoustical holography (NAH) has been developed specifically to mitigate the effects related to that windowing. In iterative patch NAH, the source distribution is reconstructed in two steps: first, the partially measured sound field is extended iteratively, and then the extended pressure is projected onto the source surface by using conventional NAH procedures. In the present work, a one-step procedure for performing that combined task is described. In this approach, the acoustical property to be reconstructed on a surface of interest is related to the partially measured pressure on the hologram surface in terms of sampling and bandlimiting matrices, and the reconstructed result is obtained by finding the regularized least squares solution of the latter relation; a procedure for determining the cutoff wave number of the bandlimiting matrix without a priori knowledge of the signal bandwidth is suggested. The proposed procedure was validated by using a synthetic sound field created by a point-driven, simply supported plated.     

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.     

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.     

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     

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].     

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.]     

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.     

Regularization methods for near-field acoustical holography.

The reconstruction of the pressure and normal surface velocity provided by near-field acoustical holography (NAH) from pressure measurements made near a vibrating structure is a linear, ill-posed inverse problem due to the existence of strongly decaying, evanescentlike waves. Regularization provides a technique of overcoming the ill-posedness and generates a solution to the linear problem in an automated way. We present four robust methods for regularization; the standard Tikhonov procedure along with a novel improved version, Landweber iteration, and the conjugate gradient approach. Each of these approaches can be applied to all forms of interior or exterior NAH problems; planar, cylindrical, spherical, and conformal. We also study two parameter selection procedures, the Morozov discrepancy principle and the generalized cross validation, which are crucial to any regularization theory. In particular, we concentrate here on planar and cylindrical holography. These forms of NAH which rely on the discrete Fourier transform are important due to their popularity and to their tremendous computational speed. In order to use regularization theory for the separable geometry problems we reformulate the equations of planar, cylindrical, and spherical NAH into an eigenvalue problem. The resulting eigenvalues and eigenvectors couple easily to regularization theory, which can be incorporated into the NAH software with little sacrifice in computational speed. The resulting complete automation of the NAH algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for NAH.     

用声场空间变换识别水下噪声源

本文提出利用声场空间变换技术进行噪声源的分离与识别。     

Diversion of energy flow near crack tips of a vibrating plate using the structural intensity technique

The structural intensity (SI) of a vibrating rectangular plate with a crack is computed using the finite element method. The overall behavior of power flow patterns of the cracked plate is investigated. The presence of the crack can be identified by the changes of the directions of SI vectors near the crack. The effects of orientation of the crack and crack length on the energy flow pattern are also investigated. The SI method is then used to explore the positioning of dampers in vibrating thin plates to divert the vibration energy flow away from crack tips. This approach is proposed as a temporary measure to prevent further propagation of the crack before repair of the crack can be done.