半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场.在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场.在边界...     

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.]     

Visualization of acoustic radiation from a vibrating bowling ball.

This paper presents visualization of acoustic radiation from a vibrating bowling ball using the Helmholtz equation least squares (HELS) method. In conducting the experiments, the ball is excited by a vibration shaker using stationary random signals. The radiated acoustic pressures are measured using two microphones and taken as input to the HELS formulations. The reconstructed acoustic pressures on the bowling ball surface are compared with those measured at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the bowling ball surface. Results demonstrate that the accuracy of reconstruction based on measurements over a conformal surface is much higher than that over a finite planar surface. This is because the latter often extends beyond the near-field region, making the accuracy of measurements inconsistent. Nevertheless, satisfactory reconstruction of acoustic pressure fields over the entire bowling ball surface can still be obtained based on the measurements taken over a finite planar surface on one side of the source. In a similar manner, the normal component of the surface velocity is reconstructed. Once these acoustic quantities are determined, the time-averaged acoustic intensity is calculated. Also presented are the formulations for estimating a priori the numbers of expansion functions and measurements required by the HELS method and the guidelines for determining the reconstruction error and optimum measurement locations, given the overall dimensions of the source and the highest frequency of interest in reconstruction.     

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.     

Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure

This paper presents experimental validations of the Helmholtz Equation Least Squares (HELS) method [Wang and Wu, J. Acoust. Soc. Am. 102, 2020-2032 (1997); Wu and Wang, U.S. Patent Number 5712805 (1998); Wu, J. Acoust. Soc. Am. 107, 2511-2522 (2000)] on reconstruction of the radiated acoustic pressures from a complex vibrating structure. The structure under consideration has geometry and dimensions similar to those of a real passenger vehicle front end. To simulate noise radiation from a vehicle, a high fidelity loudspeaker installed inside the structure at the location of the engine is employed to generate both random and harmonic acoustic excitations. The radiated acoustic pressures are measured over a finite planar surface above the structure by a microphone. The measured data are taken as input to the HELS formulation to reconstruct the acoustic pressures on the top surface of the structure as well as in the field. The reconstructed acoustic pressures are then compared with measured ones at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the surface. Results show that satisfactory reconstruction can be obtained on the top surface of the structure subject to both random and harmonic excitations. Moreover, the more measurements and the closer their distances to the source surface, the more accurate the reconstruction. The efficiency of the HELS method may decrease with increasing of the excitation frequency. This high frequency difficulty is inherent in all expansion theories.     

板结构的声辐射模态分析及其高分辨率法向振动速度重建

提出了一种基于声辐射模态的速度基向量构建方法,该速度基向量不受网格划分的影响,可用于高分辨率的板结构法向振动速度重建。首先对板表面稀疏网格的声辐射模态进行计算,再以声辐射模态和模态系数构建板法向振动速度分布的基向量,然后由声场测量声压求解基向量系数,最后由该系数和加密网格的速度基向量重建高分辨率的板法向振动速度分布。以简支板声源进行仿真计算,当测量声压信噪比为30 dB时,低频的法向振动速度重建误差最低可达3.7%;以固支板声源在消声室中进行实验验证,131.5 Hz振动频率下的重建误差低于7%。该方法实现了只需要少量声压测量点即可精确重建板声源更高分辨率的法向振动速度分布。      

利用源强密度声辐射模态重建声场

为了利用声场中少量测点声压数据精确重建复杂结构的辐射声场,提出了源强密度声辐射模态分析理论和声场重建公式.在结构表面定义的空间上,利用以源强密度分布函数为参量的结构辐射声功率泛函表达式定义了一个线性自伴正辐射算子,该算子的特征函数为结构的源强密度声辐射模态.然后通过对矩形平板和带有半球帽的圆柱体的源强密度声辐射模态的分析,证明了源强密度声辐射模态具有空间滤波特性,并利用该性质建立了声场重建公式.球体仿真和平板实验验证了所提出的声场重建方法的可行性和稳健性.基于源强密度声辐射模态的声场重建方法简单,利用较少测点数据就可以获得较高的声场重建精度,特别适合于复杂结构的低频声场重建.     

基于波叠加法的近场声全息空间分辨率增强方法

提出一种基于波叠加法的近场声全息空间分辨率增强方法. 该方法在波叠加法的基础上,利用全息面声压信号求得布置在全息面附近的虚源面上的简单源源强,再根据求得的简单源源强实现对全息面声压的插值,进而利用插值后的全息面声压数据进行重建. 该方法可以提高近场声全息重建图像的空间分辨率,减少测量工作量,简化测量过程. 通过仿真对影响插值结果的参数进行了分析,给出了合理的选取范围;通过仿真和实验研究验证了该方法的有效性. 关键词： 波叠加法 近场声全息 空间分辨率     

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.     

半自由声场的全息重建和预测实验研究

半自由声场环境下的声源重建和声场预测研究对声全息技术走向实际应用具有非常重要的意义.在提出基于分布源边界点法的半自由声场全息重建和预测方法的基础上，对此展开了实验研究.并将重建和预测的结果与常规方法重建和预测的结果进行了比较和讨论，说明了重建预测过程中反射声压的影响和考虑反射声压的必要性，证明了所提出方法在解决半自由声场环境下存在地面反射时的声源重建和声场预测时的有效性和准确性.还提出了采用奇异值截断滤波和Tikhonov正则化方法来削弱测量误差的影响，从而进一步优化了重建结果，提高了全息成像的可信度. 关键词： 声全息 半自由场 边界点 声辐射 反射声     

Structure normal velocity reconstruction withsparse measurement points

To achieve normal velocity reconstruction of a vibrating surface with sparse measurement points, a reconstruction method is proposed by exploiting of acoustic radiation modes as expansion functions, which are capable of describing the geometric shape of a vibrating surface. Firstly, acoustic radiation modes of the vibrating surface are calculated and the relationship between normal velocity and acoustic radiation modes is built. Then actual measured normal velocity values are expressed by corresponding acoustic radiation modes and the expansion coefficients are calculated. Subsequently, all normal velocity values can be reconstructed by the obtained expansion coefficients. Experimental validations have been performed by a double-layer steel cylindrical shell with enclosed ends in.an anechoic water tank. Two cases with different wavenumber components distribution were designed by a vibration shaker and a rotor device respectively. Two experimental results both show that actual vibration distribution cannot be revealed exactly by the sparse measurement points, which corresponds to severe loss of vibration related wavenumber components. On the other hand, normal velocity and corresponding wavenumber components can be restored accurately in both two wavenumber components distribution cases according to the proposed method, which demonstrates obvious effectiveness of the proposed method.     

Extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem

An improvement of the Force Analysis Technique (FAT), an inverse method of vibration, is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate. This method is a significant progress since the usual techniques of measurements with flush-mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high. Moreover, the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate. This underlines the need to extract the acoustic part. In this work, numerical experiments are performed to solve both the direct and inverse problems of vibration. The excitation is a turbulent boundary layer and combines the pressure field of the Corcos model and a diffuse acoustic field. These pressures are obtained by a synthesis method based on the Cholesky decomposition of the cross-spectra matrices and are used to excite a plate. Thus, the application of the inverse problem FAT that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation. Indeed, the discretization of the inverse operator (motion equation of the plate) acts as a low-pass wavenumber filter. In addition, this method is simple to implement because it can be applied locally (no need to know the boundary conditions), and measurements can be carried out on the opposite side of the plate without affecting the flow. Finally, an improvement of FAT is proposed. It regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution. This optimized FAT, in the case of the turbulent flow, has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise.     

On the choice of expansion functions in the Helmholtz equation least-squares method

This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.     

Equivalent source method for identification of panel acoustic contribution in irregular enclosed sound field

For the interior sound field formed by the complex vibrating structure,an identification approach of panel acoustic contribution based on equivalent source method(ESM)was presented.The normal velocity on the surface of vibrating structure was first reconstructed by using interior nearfield acoustic holography based on ESM and the prediction of whole interior enclosed sound field was realized.Then the sound pressure produced by each panel at the interested field point was respectively replaced by the radiated pressure of the enclosed interior sound field which is formed by the equivalent virtual sources located near the surface of the cavity.Combining with the reconstructed normal surface velocity,the acoustic contribution of each panel to any position in the cavity was obtained by transforming the complex enclosed non-free field into the simple interior free field.Numerical simulations and experiments are conducted,and the influences of the number of the equivalent sources and the distance between them and the reconstructed surface have been investigated.The results show that the proposed method is easier to be implemented with the same accuracy than the traditional analysis method.     

复杂封闭声场面板声学贡献度识别的等效源法

针对由复杂结构振动形成的封闭空间声场,提出了一种基于等效源法的面板声学贡献度分析方法。该方法首先利用基于等效源法的内部声全息技术,重构出振动结构表面的法向振速并实现对整个内部封闭声场的预测。再将振动结构的每个面板在腔体内部场点产生的声压分别用位于空腔表面附近的等效源在该点产生的辐射声压代替,将复杂的封闭非自由声场问题转化为简单的内部自由场问题,结合重建出的结构表面法向振速进而识别出封闭振动结构各面板对腔体内任意位置的声学贡献度。通过对复杂结构内声场的数值仿真和验证实验,分析了等效源的数量及与重建面距离等参数对重建精度的影响,结果表明所提方法不仅能够达到传统数值分析方法的计算精度,而且具有更简单的求解过程。      

Efficient inverse radiation analysis of temperature distribution in participating medium based on backward Monte Carlo method

An efficient numerical inverse radiation analysis based on the backward Monte Carlo (BMC) method is presented to determine the three-dimensional (3-D) temperature distribution in a large rectangular enclosure containing the participating medium, using radiative intensities in the visible range received by charge-coupled device (CCD) cameras. For large radiative sources and small detectors, when the radiation onto a small spot and onto a small direction cone is desired, the BMC method is more efficient than the forward Monte Carlo (FMC) method. Because the temperature reconstruction from the measured radiative intensities is an ill-posed inverse problem, least-square QR decomposition (LSQR) method is introduced to determine the meaningful temperature distribution. In order to gain insight into the effects on the accuracy of temperature distribution reconstruction, the detailed analyses are made using numerical simulations. The results show that the temperature distribution can be reconstructed accurately for the exact and noisy data.     

Real-time near-field acoustic holography for continuously visualizing nonstationary acoustic fields

Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.     

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     

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,…     

单层传声器阵列重建相干声场的近场声全息方法研究

针对传声器阵列两侧存在相干声源的非自由声场重建问题,提出基于球面谐波函数扩展近场声全息理论的相干声场重建方法。该方法在已知测量面两侧声源几何位置时,使用单层传声器阵列获取测量面处的声压分布,通过最小二乘法获得与目标声源和干扰噪声源响应对应的最优球波函数扩展项数和最优系数向量,结合测点位置的空间坐标进行声波分解,并分别重建出各声源在测量面上的声压分布。为了验证方法的有效性,分别给出了相干噪声源为球形声源和非球形声源的仿真验证,并在全消声室内对双扬声器产生的相干声场的重建进行了实验验证。结果表明:该方法对球形声源和非球形声源干扰下的声场重建都具有较好的效果,球形声源干扰下的重建精度更高。