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.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。      

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     

Recovery of the free field in noisy environment by using the spherical wave superposition method

To remove the scattering effect of the disturbing sound on the target source when implementing nearfield acoustic holography in a non-free field, a free field recovery technique based on the spherical wave superposition method is proposed. In the method, the sound field separation technique based on the spherical wave superposition method is first used to separate the incoming and outgoing fields, and a further step for separating the radiated and scattered fields is performed by utilizing the surface admittance of the target source as the boundary condition. The technique makes it possible to correctly identify noise sources in a non-free sound field. The basic principle of the technique is described firstly, a method for choosing the optimal number of spherical wave expansion terms is given, and two numerical simulations are used to demonstrate the validity of this technique. It is shown that, for the lower frequency, the scattering effect can be neglected, and the radiated field of the target source can be obtained by the sound field separation technique, however, as the increasing of the frequency, the scattering effect cannot be neglected, and the free field recovery technique has to be used to obtain the radiated field of the target source.     

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.     

非自由声场中目标声场还原与重建的等效源方法

为消除在非自由声场中重建声场时干扰声源对重建效果的影响,提出一种采用单个测量面上的声压和质点振速作为输入、等效源法作为分离和重建算法的非自由声场中目标声场还原与重建方法。该方法首先利用单面声压-质点振速测量和基于等效源法的声场分离技术将测量的混合声场分离为来自目标声源的向外传播的声场和来自干扰声源的向内传播的声场,然后利用向内传播的声场和目标声源的边界条件计算出干扰声在目标声源表面产生的散射声场,并将其从向外传播的声场中去除,还原出目标声源在自由声场条件下的辐射声场,最后利用还原的声场实现目标声场重建。通过数值仿真和实验检验了该方法的有效性和必要性。仿真和实验的结果表明,该方法可以在非自由声场的测量条件下,有效地去除干扰声的影响,实现目标声场的准确重建。      

An equivalent source method for recovering and reconstructing the target sound field in a non-free field

In a non-free field,the existence of disturbing sources would destroy the free-field condition required by near-field acoustic holography,and confuse the identification of target source due to the scattering effect caused by disturbing sound falling on the target source.To totally remove the influence of disturbing source,a method for recovering and reconstructing the target sound field in a non-free field was proposed based on the equivalent source method and the pressure-velocity measurement.In the proposed method,the sound field separation technique was firstly used to separate the mixed sound field into the outgoing field coming from the target source and the incoming field coming from the disturbing source.Then the scattered component contained in the outgoing field was calculated by using the disturbing sound and the surface impedance of the target source.Finally,the sound field radiated by the target source in a free field was obtained by subtracting the scattered component from the outgoing field and was further used to reconstruct the sound field of the target source.The proposed method was numerically and experimentally testified and the results of both the simulation and the experiment demonstrated the validity of the proposed method.     

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.     

基于声压-振速测量的平面近场声全息实验研究

常规的近场声全息均是采用全息面声压或质点振速作为输入量求解,由于采用单一输入量无法分离来自全息面背向声波的干扰,因此要求所有声源均位于全息面的同一侧,即测量声场为自由声场,这种要求大大限制了近场声全息的实际应用.基于声压-速度测量的近场声全息以全息面上声压和质点振速同时作为输入量,通过建立和求解两侧声源在全息面上的声压和质点振速耦合关系,可以实现全息面两侧声波的分离,从而解决上述问题.文中在前期对声场分离技术研究的基础上,基于欧拉公式和有限差分近似,推导了新的基于声压-速度测量的平面近场声全息理论公式.随后通过实验检验了该方法在有背景源干扰情况下实现声场分离和重建的有效性.     

Geometrical interpretation of acoustic holography: Adaptation of the propagator and minimum quality guaranteed in the presence of errors

A large number of inverse problems in acoustics consist of a reverse propagation of the acoustic pressure measured with an array of microphones. The goal is usually to identify the acoustic source location and strength or the surface velocity of a vibrating structure. The quality of the results obtained depends on the propagation model, on the accuracy of the pressure measurements and, finally, on the inverse problem conditioning. How to quantify this quality is the issue addressed in this paper. For this purpose, a geometrical interpretation of the inverse acoustic problem is proposed. The main application will, eventually, be near-field acoustic holography (NAH), but it is expected that the proposed approach will also apply to other types of inverse acoustic problems. First, the geometrical representation of the inverse problem is proposed. The inverse problem is stated from a direct linear problem in the frequency domain. For each frequency, an overdetermined system of linear complex algebraic equations must be inverted. The concept of quality is discussed and a quality index is proposed based upon the residue of the inverse problem, solved in a mean square sense. Then, a simple one-dimensional (plane wave) acoustic example consisting of a source and two pressure measurements is used to illustrate the proposed geometrical representation of the inverse problem and the quality criterion inspired by it. In the simple example, the propagation model can be improved by searching for a reflection coefficient at the origin of the simulated hologram. This reflection coefficient is used to simulate the presence of a hidden source placed behind the source. An artificial attenuation is introduced to simulate the effect of geometrical attenuation present in real NAH problems. Again, using the geometrical representation, it is shown how, from an improved propagation model together with a given measurement noise level in the hologram, one can guarantee a certain quality level of the inverse procedure. Finally, numerical results show, in a preliminary way, how the identified source strength converges towards the exact velocity when the estimated propagation model tends to the exact propagation model.     

Calculation of acoustic scattering of a nonrigid surface using physical acoustic method

In this paper the physical acoustic method or the Kirchhoff approxima-tion is extended to treat the scattering of a nonrigid surface in order to estimatethe target strength of targets with absorbing coatings.By using the locally planewave approximation,the relationship between the sound pressure and its normalderivative on the surface can be represented by the plane wave reflectioncoefficient and the acoustic impedance of the surface.The resulting modifiedKirchhoff approximation involves the plane wave reflection coefficient.For aimpedance sphere,a comparison between the physical acoustic method and theexact solution shows that the physical acoustic method still is a good approxima-tion at higher κα values.     

适用于循环平稳声场的基于波叠加法的近场声全息技术

在原有的平面循环平稳近场声全息基础上,提出一种基于波叠加法的循环平稳近场声全息技术,可以对具有复杂表面的声源进行全息重建,重建的声源表面声压谱相关密度函数能反映出调制信号的信息.声源表面声压谱相关密度函数全息图形象地反映了调制信号在表面的强弱分布情况,可由此确定调制信号源的产生位置.仿真分析和实验验证表明,基于波叠加法的循环平稳近场声全息技术可以更准确地反映循环平稳声场的调制特性.该方法继承了波叠加法的优点,无需计算边界奇异积分,计算效率高、精度好. 关键词： 近场声全息 循环平稳信号 波叠加     

适用于循环平稳声场的基于波叠加法的近场声全息技术

在原有的平面循环平稳近场声全息基础上，提出一种基于波叠加法的循环平稳近场声全息技术，可以对具有复杂表面的声源进行全息重建，重建的声源表面声压谱相关密度函数能反映出调制信号的信息.声源表面声压谱相关密度函数全息图形象地反映了调制信号在表面的强弱分布情况，可由此确定调制信号源的产生位置.仿真分析和实验验证表明，基于波叠加法的循环平稳近场声全息技术可以更准确地反映循环平稳声场的调制特性.该方法继承了波叠加法的优点，无需计算边界奇异积分，计算效率高、精度好.     

Effect of sensor proximity over the non-conformal hologram plane in the near-field acoustical holography based on the inverse boundary element method

Near-field acoustical holography (NAH) is a useful tool for the identification and visualization of vibro-acoustic sources. In particular, NAH can be applied to many practical sources having irregular shape if the inverse boundary element method (BEM) is employed. Once the relation between the source and the radiated field is defined in the transfer matrix modeled by the BEM, the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface. The usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface, which can be a flat, cylindrical, or spherical shape, for the measurement ease. Then, the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill-posed than the conformal case. To investigate the effect of sensor proximity and distance variability on the reconstruction error, simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate. Flat, tilted, and randomized hologram surfaces were adopted in the test. It was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor. To improve the reconstruction accuracy, an investigation was conducted to find proper field points among a large number of overdetermined field points. The number of field data was reduced gradually under various reduction schemes using condition number, effective independence value, and sensor distance. It was demonstrated that the quality of reconstruction result given by the non-conformal measurement can be improved by removing some field points that contribute to the ill-conditioning of the inverse problem. A small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation. However, further reduction of the field points, becoming an underdetermined situation, yielded a drastic improvement of the reconstruction accuracy.     

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。      

循环平稳声场的声源定位研究

旋转机械产生的辐射声场具有循环平稳特性,传统的平面近场声全息技术无法准确反映其调制特性,往往在边频带上出现虚假的能量的分布.采用循环谱密度取代功率谱密度作为重建物理量,则可准确提取循环平稳声场的调制和载波信息.考虑到循环谱密度的计算量以及特征提取的准确性,提出了循环谱密度组合切片分析法,并分析了加性白噪声对重建的影响.仿真分析及实验结果表明,此方法有较强的噪声抑制能力,全息重建的结果可准确反映声源的位置.     

声场分离技术及其在近场声全息中的应用

提出空间声场分离技术，突破了近场声全息（NAH）的应用局限.它们的局限在于全息面一侧的声场必须是自由声场，即要求所有的声源必须位于另一侧.利用波数域内的波场外推理论及声压的标量叠加原理，建立起声场分离技术的双全息面实现方法，利用波数域内的Euler公式及粒子振速的矢量叠加原理，建立起该技术的单全息面实现方法.该技术的一个突出优点是在具有背景噪声的全息测量情况下, 可以消除背景噪声对全息变换结果的影响.理论的推导表明该技术方法的正确性，而仿真算例和实验则显示该技术的可行性和有效性. 关键词： 声全息 波数域 声场分离 背景噪声