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.     

Nearfield acoustic holography in a moving medium based on particle velocity input using nonsingular propagator

Nearfield acoustic holography in a moving medium is a technique which is typically suitable for sound sources identification in a flow.In the process of sound field reconstruction,sound pressure is usually used as the input,but it may contain considerable background noise due to the interactions between microphones and flow moving at a high velocity.To avoid this problem,particle velocity is an alternative input,which can be obtained by using laser Doppler velocimetry in a non-intrusive way.However,there is a singular problem in the conventional propagator relating the particle velocity to the pressure,and it could lead to significant errors or even false results.In view of this,in this paper,nonsingular propagators are deduced to realize accurate reconstruction in both cases that the hologram is parallel to and perpendicular to the flow direction.The advantages of the proposed method are analyzed,and simulations are conducted to verify the validation.The results show that the method can overcome the singular problem effectively,and the reconstruction errors are at a low level for different flow velocities,frequencies,and signal-to-noise ratios.     

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.     

基于支持向量回归的patch近场声全息研究

为了解决patch近场声全息中全息数据外推问题,提出一种基于支持向量回归的一步式patch近场声全息技术。该方法首先把初始全息面上的数据当成训练样本进行学习,构造出回归函数,然后利用回归函数实现全息数据外推,最后基于统计最优近场声全息进行重建。数值仿真和实验研究的结果表明:在各个分析频率下,该方法都可以实现小孔径全息面的近场外推。从近场声全息重建结果看,即使初始全息数据受到噪声干扰,该方法也是一种有效的patch近场声全息技术。      

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.     

基于统计最优和波叠加的联合局部近场声全息

提出了一种基于统计最优近场声全息和波叠加法的联合局部近场声全息技术。首先利用两次统计最优近场声全息的声源定位结果来指导配置等效源,其后利用波叠加法进行局部声场重构。该技术适合于中低频声场的局部重建,计算快速,重建精度高;可以在测量数据有缺失的情况下重建声场。进行了脉动球声源模型的数值仿真,并在半消声室内对电机噪声源进行了实验,仿真实验都准确地重构了声源所辐射的外部声场。该技术可以重建任意类球形声源辐射的声场。      

Planar nearfield acoustical holography in moving fluid medium at subsonic and uniform velocity

Nearfield acoustical holography (NAH) data measured by using a microphone array attached to a high-speed aircraft or ground vehicle include significant airflow effects. For the purpose of processing the measured NAH data, an improved nearfield acoustical holography procedure is introduced that includes the effects of a fluid medium moving at a subsonic and uniform velocity. The convective wave equation along with the convective Euler's equation is used to develop the proposed NAH procedure. A mapping function between static and moving fluid medium cases is derived from the convective wave equation. Then, a conventional wave number filter designed for static fluid media is modified to be applicable to the moving fluid cases by applying the mapping function to the static wave number filter. In order to validate the proposed NAH procedure, a monopole simulation at the airflow speed of Mach=-0.6 is conducted. The reconstructed acoustic fields obtained by applying the proposed NAH procedure to the simulation data agree well with directly-calculated acoustic fields. Through an experiment with two loudspeakers performed in a wind tunnel operating at Mach=-0.12, it is shown that the proposed NAH procedure can be also used to reconstruct the sound fields radiated from the two loudspeakers.     

Near-field acoustic holography analysis of modulated sound source

When conventional near-field acoustic holography(NAH) technique is applied to sound field induced by modulated signal,the modulating frequency can not be revealed by the reconstructed results.To solve the problem,a NAH analysis methodology for modulated sound source was proposed.Firstly,Hilbert transform was introduced to demodulate the signal,and then modulating component was reconstructed by NAH technique.Both numerical simulation and experiment results demonstrate that accurate reconstruction analysis can be obtained by the proposed method.     

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.     

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     

Research on the cyclostationary nearfield acoustic holography based on boundary element method

Cyclostationary sound field is a special kind of nonstationary sound field, in which the pressure signal is modulated seriously and sidebands exist in its spectrum. The reconstructed sound field can＇t figure the cyclostationary features in conventional Nearfield Acoustic Holography （NAH） procedure. On the basis of planar cyclostationary NAH, the cyclostationary NAH based on boundary element method is proposed which can be utilized to analyze radiators with complicated surface. Replacing the Fourier＇s transform with the second-order cyclic statistics, the Cyclic Spectral Density （CSD） functions is used as the reconstructed physical quantity in the proposed NAH technique, instead of the spectrum or power spectral density of pressure signal. By virtue of the demodulation ability of CSD function, the reconstructed CSD can effectively express the information of modulating and carrier wave respectively. The simulation and experiment illustrate that the validity and accuracy of this cyclostationary NAH technique satisfy the request of engineering.     

Approximate reconstruction of sound fields close to the source surface using spherical nearfield acoustical holography

This paper presents an investigation of the reconstruction of sound field parameters close to the surface of arbitrarily shaped sound sources. The field is reconstructed using nearfield acoustical holography (NAH) in spherical coordinates. Of particular interest are source shapes where the Rayleigh hypothesis is violated. To overcome the limitation of the minimal sphere given by the validity restriction of the Rayleigh hypothesis an algorithm is proposed for extracting local information from the nonconvergent NAH solution. For the assessment of the results an appropriate virtual test rig is developed employing the Kirchhoff-Helmholtz integral theorem.     

基于近场声全息的圆柱壳体内部声场重构效果的影响因素

在Neumann边界条件下基于近场声全息原理(NAH)重构了两端封闭的有限长圆柱壳体内部声场,计算出的结果与基于模态叠加法构建的内部声场进行比较,证明了重构方法的正确性,然后分别讨论了激励频率和全息面选择对NAH重构声场精度的影响以及重构面上不同位置的重构效果。     

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     

Improved Statistically Optimal Nearfield Acoustical Holography in subsonically moving fluid medium

Statistically Optimal Nearfield Acoustical Holography (SONAH) can be used to reconstruct three-dimensional sound fields by projecting two-dimensional data measured on a “small” aperture that partially covers a composite sound source in a “static” fluid medium. Here, an improved SONAH procedure is proposed that includes the mean flow effects of a moving fluid medium while the sound source and receivers are stationary. The backward projection performance of the proposed procedure is further improved by using a wavenumber filter to suppress subsonic noise components. Through numerical simulations at Mach 0.6, it is shown that the improved procedure can accurately reconstruct sound source locations and radiation patterns: e.g., the spatially averaged reconstruction errors of the conventional and improved SONAH procedures are 15.40 dB and 0.19 dB, respectively, for a monopole simulation and 21.60 dB and 0.19 dB for an infinite-size panel. The wavenumber filter further reduces spatial noise, e.g., decreasing the reconstruction error from 1.73 dB to 0.19 dB for the panel simulation. An existing data measured in a wind tunnel operating at Mach 0.12 is reused for the validation. The locations and radiation patterns of the two loudspeakers are successfully identified from the sound fields reconstructed by using the proposed SONAH procedure.     

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.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

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。