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.     

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.     

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.     

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.     

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].     

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.     

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.     

双面声场反向神经网络声压外推分离

针对有限测量孔径造成的窗效应和离散传声器阵列带来的卷绕误差对双面声场分离技术的影响,提出了一种利用反向传播神经网络的全息面声压外推方法。该方法首先利用孔径内部测点平面坐标和相应声压值组成的学习样本训练神经网络,拟合出两者的函数关系。接着代入孔径外部测点坐标得到对应声压值,实现有限孔径外推。最后将已有测量值和外推测量值组成的虚拟大孔径导入双面声场分离处理。与传统外推方法相比,该方法不需要先验知识,操作简单,计算抗干扰能力强,结果准确性高。数值仿真和实验进一步验证了该方法在改善声场分离结果方面的可行性和有效性。      

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.     

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,…     

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。      

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.     

基于双色条纹投影的薄膜振动模式分析

结构光投影和条纹时间平均分析技术已被用于振动模式分析中,但由于投影单色正弦条纹时振动薄膜变形条纹傅里叶谱中零频涵盖范围较大,会限制滤波窗的选取范围,从而影响模式的最终重建结果。为提高振动模式重建的准确性,提出了一种利用π相移正弦条纹投影进行薄膜振动模式分析和振幅重建的方法,通过处理两个通道的条纹分量达到消除零频的目的。给出了该方法的理论分析,完成了相应的计算机模拟,分析了影响测量精度的因素。通过与投影单色正弦条纹的振动模式重建结果对比,表明该方法有较高的重建精度。不同激励频率下的实际薄膜振动实验结果也证明了该方法正确可行。     

两种多光谱高温计无源温区标定方法抗随机误差能力研究

两种多光谱高温计无源温区标定方法,即依据图形相似性原理的标定方法和依据高温计传递函数的标定方法。为验证两种方法的实用性,通过对黑体辐射出度加入不同大小的随机误差模拟不同测量精度的多光谱高温测量系统,对这两种方法的抗干扰能力进行了研究。实验结果证明,依据图形相似原理的标定方法具有强抗随机误差能力,适用于随机误差较大的测量系统。当随机误差很小时,其精度低于依据传递函数的标定方法,但当随机误差增加到一定范围,其精度远高于后者。基于高温计传递函数的标定方法虽在一定的随机误差范围内具有高的外推标定精度,但抗随机误差能力较弱,适用于随机误差小的测量系统。     

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.     

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.     

Approximations of inverse boundary element methods with partial measurements of the pressure field

Boundary element methods (BEMs) based near-field acoustic holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby conformal surface. There are practical cases when measurements are available over a patch from the measurement surface in which conventional inverse BEM based NAH (IBEM) cannot be applied directly, but instead as an approximation. In this work two main approximations based on the indirect-implicit methods are considered: Patch IBEM and IBEM with Cauchy data. Patch IBEM can be applied with a continuation procedure, which as its predecessor patch NAH (a well known technique that can be used on separable geometries of the wave equation) continues the pressure field using an iterative procedure, or it can be applied by a direct procedure. On the other hand, IBEM with Cauchy data requires measurements over two conformal patches and it will be shown that this technique will be reliable regardless of the position of the source. The theory behind each method will be justified and validated using a cylindrical surface with numerical data generated by point sources, and using experimental data from a cylindrical fuselage excited by a point force.     

A high precision phase reconstruction algorithm for multi-laser guide stars adaptive optics

Adaptive optics(AO) systems are widespread and considered as an essential part of any large aperture telescope for obtaining a high resolution imaging at present.To enlarge the imaging field of view(FOV),multi-laser guide stars(LGSs) are currently being investigated and used for the large aperture optical telescopes.LGS measurement is necessary and pivotal to obtain the cumulative phase distortion along a target in the multi-LGSs AO system.We propose a high precision phase reconstruction algorithm to estimate the phase for a target with an uncertain turbulence profile based on the interpolation.By comparing with the conventional average method,the proposed method reduces the root mean square(RMS) error from 130 nm to 85 nm with a 30% reduction for narrow FOV.We confirm that such phase reconstruction algorithm is validated for both narrow field AO and wide field AO.     

Low-frequency harmonic vibration analysis with temporal speckle pattern interferometry

In this paper, the time sequence phase method (TSPM) has been applied to measure the displacement caused by low-frequency vibration in temporal speckle pattern interferometry (TSPI). The principle is that by capturing the temporal speckle patterns related to the object vibration, the whole-field displacement responses (amplitude and phase) of the vibrating object can be calculated through scanning these fluctuations. Thus, quantitative measurement can be carried out using a conventional ESPI system without a camera synchronized to the object vibration or a phase shifting system. The elaboration on the method is given and experimental results are presented.