Surface decomposition method for near-field acoustic holography

Near-field acoustic holography reconstruction of the acoustic field at the surface of an arbitrarily shaped radiating structure from pressure measurements at a nearby conformal surface is obtained from the solution of a boundary integral equation. This integral equation is discretized using the equivalent source method and transformed into a matrix system that can be solved using iterative regularization methods that counteract the effect of noise on the measurements. This work considers the case when the resultant matrix system is so large that it cannot be explicitly formed and iterative methods of solution cannot be directly implemented. In this case the method of surface decomposition is proposed, where the measurement surface is divided into smaller nonoverlapping subsurfaces. Each subsurface is used to form a smaller matrix system that is solved and the result joined together to generate a global solution to the original matrix system. Numerically generated data are used to study the use of subsurface extensions to increase the continuity of the global solution, and investigate the size of the subsurfaces, as well as the distance between the measurement and the vibrating surface. Finally a vibrating ship hull structure is considered as a physical example to apply and validate the proposed methodology.     

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.     

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。     

Regularization for improving the deconvolution in real-time near-field acoustic holography

Near-field acoustic holography is a measuring process for locating and characterizing stationary sound sources from measurements made by a microphone array in the near-field of the acoustic source plane. A technique called real-time near-field acoustic holography (RT-NAH) has been introduced to extend this method in the case of nonstationary sources. This technique is based on a formulation which describes the propagation of time-dependent sound pressure signals on a forward plane using a convolution product with an impulse response in the time-wavenumber domain. Thus the backward propagation of the pressure field is obtained by deconvolution. Taking the evanescent waves into account in RT-NAH improves the spatial resolution of the solution but makes the deconvolution problem "ill-posed" and often yields inappropriate solutions. The purpose of this paper is to focus on solving this deconvolution problem. Two deconvolution methods are compared: one uses a singular value decomposition and a standard Tikhonov regularization and the other one is based on optimum Wiener filtering. A simulation involving monopoles driven by nonstationary signals demonstrates, by means of objective indicators, the accuracy of the time-dependent reconstructed sound field. The results highlight the advantage of using regularization and particularly in the presence of measurement noise.     

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     

Krylov subspace iterative methods for boundary element method based near-field acoustic holography

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.     

循环谱密度组合切片分析在近场声全息中的应用研究

为减小循环谱密度的计算量以及提高其特征提取的准确性,提出了组合切片法:取循环自相关切片的各峰值频率作循环频率分别计算循环谱密度切片,通过组合切片分析来确定声场信号的特征频率。然后采用循环谱密度取代功率谱密度作为平面近场声全息的重建物理量。实验结果表明,此方法可针对性的提取循环平稳声场的调制特性,全息重建的结果可准确反映噪声源的位置。     

振动体及其辐射场的近场声全息实验研究

本文介绍我们自行研制的空气中近场声全息成像实验系统。用这一系统对单个扬声器,双扬声器及振动圆板等声源及其辐射场进行了测量,获得一些有意义的结果.这些结果与理论分析和计算机模拟良好地符合,表明近场声全息可以作为研究振动及其辐射场关系的有效手段.     

Interior near-field acoustical holography in flight

In this paper boundary element methods (BEM) are mated with near-field acoustical holography (NAH) in order to determine the normal velocity over a large area of a fuselage of a turboprop airplane from a measurement of the pressure (hologram) on a concentric surface in the interior of the aircraft. This work represents the first time NAH has been applied in situ, in-flight. The normal fuselage velocity was successfully reconstructed at the blade passage frequency (BPF) of the propeller and its first two harmonics. This reconstructed velocity reveals structure-borne and airborne sound-transmission paths from the engine to the interior space.     

The conception of structure-borne-sound-based near-field holography

A procedure for the projection of structure-borne sound fields is introduced, following the basic idea behind Near-Field Acoustic Holography. It is shown that the bending wave field of an infinite plate subjected to point force excitation can be reconstructed by means of Fourier transform-based wave field extrapolation. All required information on the wave field is obtained by vibrational response measurement in the near-field of the excitation, using a circular geometry with a limited number of positions. The procedure is verified both numerically and experimentally, to very satisfying results. The experiments indicate that the reconstruction at the source becomes erratic when standoff distances greater than half of the minimum wavelength under consideration are used. Reconstruction of the far-field plate response is found to be less restrictive.     

近场声全息成像方法的研究

本文对近场声全息成像方法的基本理论及特点做了简单介绍。针对声源重建问题的不适定性,提出一种新的空间频率域滤波方法——带约束条件的最小二乘法,改善了重建结果的稳定性。运用近场声全息成像的数字方法,对圆板的振动及其辐射声场进行了计算机模拟研究并验证了滤波处理的效果。本文还用自制的32阵元线阵扫描实验系统,对一个在空气中辐射400赫声波的小型扬声器的振动及声场进行了近场声全息成像研究,给出初步实验结果。     

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。     

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.     

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.     

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.     

Scanning near-field acoustic microscopy

Scanning near-field acoustic microscopy (SNAM) is a new method for imaging the topography of nonconducting surfaces at a potential lateral resolution in the sub-micron range. The basic element of this method is a distance sensor consisting of a sharply pointed vibrating tip, which is part of a high-Q quartz resonator driven at its resonance frequency. The decrease of the resonance frequency or of the amplitude of vibration when an object comes into the proximity of the tip serves as the important signal. The dependence of this signal on pressure and composition of the coupling gas shows that the hydrodynamic forces in the gas are responsible for the coupling between object and tip. The sensor is incorporated into a scanning device. Well-resolved line scans of a grating of 8 m periodicity, a lateral resolution of 3 m and a vertical resolution of 5nm have been achieved in our first experiments.     

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.     

A fault diagnosis scheme of rolling element bearing based on near-field acoustic holography and gray level co-occurrence matrix

Vibration signal analysis is the most widely used technique in condition monitoring or fault diagnosis, whereas in some cases vibration-based diagnosis is restrained because of its contact measurement. Acoustic-based diagnosis (ABD) with non-contact measurement has received little attention, although sound field may contain abundant information related to fault pattern. A new scheme of ABD for rolling element bearing fault diagnosis based on near-field acoustic holography (NAH) and gray level co-occurrence matrix (GLCM) is presented in this paper. It focuses on applying the distribution information of sound field to bearing fault diagnosis. A series of rolling element bearings with different types of fault are experimentally studied. Sound fields and corresponding acoustic images in different bearing conditions are obtained by fast Fourier transform (FFT) based NAH. GLCM features are extracted for capturing fault pattern information underlying sound fields. The optimal feature subset selected by improved F-score is fed into multi-class support vector machine (SVM) for fault pattern identification. The feasibility and effectiveness of our proposed scheme is demonstrated on the good experimental results and the comparison with the traditional ABD method. Considering test cost, the quantized level and the number of GLCM features for each characteristic frequency is suggested to be 4 and 32, respectively, with the satisfactory accuracy rate 97.5%.     

Fabrication of high-spatial-frequency gratings through computer-generated near-field holography

We demonstrate an innovative method for fabrication of high-spatial-frequency grating structures. This technique makes use of the near-field diffraction patterns from computer-generated phase holograms for lithographic fabrication of grating structures with periods that are one half that of the phase hologram mask. Linear, rectilinear, and circular gratings were fabricated with this technique. Experimental results from gratings with periods to 0.5 mum and feature sizes to ~0.2 mum are presented.     

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.