Conventional Near-field Acoustic Holography Research Articles

Sound field separation with cross measurement surfaces.

With conventional near-field acoustical holography, it is impossible to identify sound pressure when the coherent sound sources are located on the same side of the array. This paper proposes a solution, using cross measurement surfaces to separate the sources based on the equivalent source method. Each equivalent source surface is built in the center of the corresponding original source with a spherical surface. According to the different transfer matrices between equivalent sources and points on holographic surfaces, the weighting of each equivalent source from coherent sources can be obtained. Numerical and experimental studies have been performed to test the method. For the sound pressure including noise after separation in the experiment, the calculation accuracy can be improved by reconstructing the pressure with Tikhonov regularization and the L-curve method. On the whole, a single source can be effectively separated from coherent sources using cross measurement.

A patch near-field acoustical holography procedure based on a generalized discrete Fourier series

Planar near-field acoustical holography (NAH) can be used to reconstruct a three-dimensional sound field from sound pressure data measured by a planar microphone array. The conventional planar NAH makes use of the discrete Fourier transform (DFT) to process the measured data, yielding a low computational cost. However, if the measurement aperture does not fully cover the sound source extension, the spatial windowing will lead to severe reconstruction errors. Many patch NAH methods have been proposed to allow measurement apertures smaller than the source size, such as the statistically optimized NAH (SONAH), which is not based on the DFT. These methods have proven to outperform the conventional NAH for small measurement apertures, but with an increased computation time and more complex implementation. This paper introduces an alternative patch procedure for planar NAH that replaces the DFT with a so-called “generalized discrete Fourier series” (GDFS). Unlike the DFT, the periods of the two-dimensional GDFS and the number of Fourier coefficients are made larger than the measurement aperture and the number of microphones, respectively. Then, the Fourier coefficients are evaluated in the least-norm sense. This reduces the spectral leakage due to the spatial windowing, improving the NAH results. As a numerical example, a simply supported plate driven by a point force is considered, and patches of the plate normal velocity are estimated from simulations of the radiated sound pressure on a small microphone array. It is shown that the GDFS-based method might lead to reconstructed velocity fields as accurate as SONAH, or even more accurate. However, unlike SONAH, the proposed method presents a low computational cost and a straightforward implementation. Therefore, it is a worthy alternative to the currently available patch procedures for planar NAH.

Reconstruction of the sound field above a reflecting plane using the equivalent source method

In practical situations, vibrating objects are usually located above a reflecting plane instead of exposing to a free field. The conventional nearfield acoustic holography (NAH) sometimes fails to identify sound sources under such situations. This paper develops two kinds of equivalent source method (ESM)-based half-space NAH to reconstruct the sound field above a reflecting plane. In the first kind of method, the half-space Green's function is introduced into the ESM-based NAH, and the sound field is reconstructed based on the condition that the surface impedance of the reflecting plane is known a prior. The second kind of method regards the reflections as being radiated by equivalent sources placed under the reflecting plane, and the sound field is reconstructed by matching the pressure on the hologram surface with the equivalent sources distributed within the vibrating object and those substituting for reflections. Thus, this kind of method is independent of the surface impedance of the reflecting plane. Numerical simulations and experiments demonstrate the feasibility of these two kinds of methods for reconstructing the sound field above a reflecting plane.

Three‐dimensional application of improved equivalent source method for noise source identification

Near-field acoustical holography methods have bad resolution at medium-to-high frequencies. This is especially a problem for three-dimensional source identification, when the microphone array is not arranged around the source. To overcome this issue, an improved equivalent source method (IESM) with two mutually perpendicular sub-arrays is used. Similar to the equivalent source method, the equivalent source strengths of IESM can be evaluated by the steepest descend method on both sets of microphones. Using two perpendicular planar arrays surrounding the source, the spatial resolution of IESM can be improved in both directions. By introducing the steepest descend and threshold filtering method, IESM based on two mutually perpendicular planar arrays can suppress the ghost sources associated with the real sources. Hence, it can identify the main sources much more accurately at medium-to-high frequencies. The proposed method also is used on both synthetic and experimental data. The results also showed that IESM give source maps that are more interpretable than conventional near-field acoustical holography methods.

Direct extrapolation in near‐field acoustic holography

The size and shape of a reconstruction surface is the same as a holography surface in conventional near-field acoustic holography (NAH), which limits the size and shape of the measurement surface. To reduce the measurement points and use any shape of measurement array, the direct extrapolation in NAH based on wave superposition is proposed. According to the transitive relation of the acoustic signal in the sound field, the sound field information on a reconstruction surface could be directly extrapolated by the holography surface. A set of simulations are performed with an 18-channel wheel-type array to obtain more sound pressure data on a grid reconstruction surface. On comparing the reconstruction errors produced by different parameters, which are the source frequency, signal-to-noise ratio, reconstruction distance, point numbers, and grid spacing, the results show that the errors are all very low. Moreover, the experiment verifies the feasibility of the direct extrapolation method.

Nearfield acoustic holography in noisy environment based on the measurement using an acoustic mask with microphone array

Nearfield acoustic holography (NAH) has been widely used for identifying acoustic noise sources. However, conventional NAH is theoretically available only in the free field; therefore, the NAH may meet difficulties in many application in-situ environments. An NAH based on the measurement using an acoustic mask with microphone array is proposed in this presentation to reconstruct sound pressure and velocity of target sources in the environment with reflections and disturbing acoustic noise sources. The microphone array is flush-mounted at the bottom plane of an open rectangular mask. Four side surfaces are designed to acquire sound pressure in Neumann’s boundary condition. In an actual measurement, the mask faces to near field of a target source. Although the sound wave from disturbing sources may propagate into the mask by passing through the gap between the mask and source surface, the disturbing waves can be decomposed by the proposed NAH using inverse patch transfer functions. Numerical simulations and experiments indicate that this novel NAH using mask with microphone array is valid for reconstructing sound source in noisy environment. The influence of different distances between the source surface and the mask is also investigated.

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.

Sound field separation with sound pressure and particle velocity measurements

In conventional near-field acoustic holography (NAH) it is not possible to distinguish between sound from the two sides of the array, thus, it is a requirement that all the sources are confined to only one side and radiate into a free field. When this requirement cannot be fulfilled, sound field separation techniques make it possible to distinguish between outgoing and incoming waves from the two sides, and thus NAH can be applied. In this paper, a separation method based on the measurement of the particle velocity in two layers and another method based on the measurement of the pressure and the velocity in a single layer are proposed. The two methods use an equivalent source formulation with separate transfer matrices for the outgoing and incoming waves, so that the sound from the two sides of the array can be modeled independently. A weighting scheme is proposed to account for the distance between the equivalent sources and measurement surfaces and for the difference in magnitude between pressure and velocity. Experimental and numerical studies have been conducted to examine the methods. The double layer velocity method seems to be more robust to noise and flanking sound than the combined pressure-velocity method, although it requires an additional measurement surface. On the whole, the separation methods can be useful when the disturbance of the incoming field is significant. Otherwise the direct reconstruction is more accurate and straightforward.

Optimal two-layer directive microphone array with application in near-field acoustical holography

Conventional near-field acoustical holography (NAH) is generally based on the free-field assumption, which can cause errors when interfering sources are present in practical environments. To cope with this problem, previous research suggested a combined pressure-velocity approach for NAH that provides certain advantages to rejection of interferences. This paper revisits this idea in a broader context of optimal array design and examines the feasibility of using unidirectional microphones in each channel of the array such that the robustness of inverse reconstruction is enhanced against interfering sources. As indicated in the simulation, the numerical noise in finite difference estimation of particle velocity can nullify the advantage of the well-conditioned velocity-based reconstruction. In the proposed approach, the characteristics of each array channel consisting of two microphones are tailored by taking into account not only the directivity, but also the robustness against self-noise. An objective function based on directivity index and white noise gain is exploited in a linear quadratic optimization of a two-element end-fire array. The proposed optimal array is validated in conjunction with the equivalent source model (ESM) -based NAH through numerical simulations, with an interfering source positioned behind the array. The results have shown the directive optimal array has yielded improved quality of images in comparison with conventional approaches in the presence of an interfering source and sensor noise.

Near-field acoustic holography of acoustic radiation from structures

There are some difficulties for conventional Near-field Acoustic Holography (NAH) to analyze acoustic radiation from a large scale structure. To solve the problem, a method for NAH of large scale structures was presented. In the method, the normal velocities or sound pressure at a few points on the surface of the structure are measured by transducers, and that at other position on the surface of the structure are calculated by means of the radiation mode theory, then the radiated acoustic field may be analyzed by NAH. Since complex coupling terms no longer appear in the radiation modes, and only a few orders of modes are required to describe the acoustic field at low-to-mid frequencies, the accuracy of NAH analysis may be ensured. Moreover, according to the nesting property of radiation modes, the radiation modes at other frequencies can be replaced by that at maximum frequency, consequently the calculating procedure may be simplified and the calculating speed quicken. Finally, NAH analysis of acoustic radiation from large scale structures was illustrated using a 1m×1m simply supported steel plate. The results show that the radiated acoustic field can be reconstructed accurately under the circumstances of a few measurement points.

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.

An experimental investigation of planar nearfield acoustic holography using pressure and particle velocity measurements

In the conventional nearfield acoustic holography （NAH）, only the pressure or particle velocity is used as the input quantity, and it cannot separate the waves from the two sides of the hologram surface. Therefore, all sources are assumed to be on one side of the hologram surface, i.e. the sound field is assumed to be free. This assumption limits the practical applications of NAH. In the NAH using pressure and particle velocity measurements, both pressure and particle velocity are used as the input quantities. By establishing and solving the coupling relationship on the hologram surface between the waves from the two sides of the hologram surface, the waves from the two sides can be separated. On the basis of the previous studies on sound field separation techniques and based on the Euler formula and the finite difference approximation technique, a new theoretical formula of NAH using pressure and particle velocity measurements is given, and then an experiment is performed to validate the method.

Scan-based near-field acoustical holography on partially correlated fields: Theory and numerical experiments.

Conventional near-field acoustical holography (NAH) requires a coherent field. For a coherent source, a scan-based approach can be used with one reference microphone to stitch the phase. For a noncoherent field, scan-based NAH can be performed if the virtual coherence technique is used. This technique uses multiple reference microphones to decompose the partial field into mutually uncorrelated partial fields, which are then processed by some NAH method. In particular, the statistically optimized near-field acoustical holography (SONAH) method is used with modified Tikhonov regularization. Numerical experiments are performed on a series of point sources with source strengths chosen to mimic the source characteristics of high-powered jets. The experiments are designed to aid in determining the proper number and location of reference microphones for doing NAH work on high-powered jet noise. [Work supported by Blue Ridge Research and Consulting and the Air Force Research Laboratory.]

The Application of Wave Superposition Algorithm to Identify Cyclostationary Sound Source

The cyclostationary characteristics can not be extracted clearly in reconstruction of the acoustic field radiated from the cyclostationary sources by the conventional near-field acoustic holography procedures. The cyclostationary near-field acoustic holography method uses the cyclic spectrum density function as the reconstruction variance instead of the spectrum or the power spectrum density, which decomposes the carrier wave and modulating wave in the appropriate cyclic frequency. The reconstructed CSD shows the distribution of the modulating wave of cyclostationary sources and supplies more cyclostationary acoustical information than the conventional NAH. In the present work, the theory of the cyclostationary NAH combined with the wave superposition is introduced, which can be used for the arbitrarily shaped cyclostationary sources. A numerical simulation and a speaker experiment are employed to validate this WSA-based cyclostationay NAH method. The results of the simulation show great agreement between the reconstruction and the analytical value. The distribution of the CSD of the cyclostationary acoustical source on the surface coincides with the speaker box accurately.

Nearfield acoustic holography based on wave superposition algorithm for cyclostationary sound filed

The seriously modulated radiation sound waves, as a kind of special nonstationary signal in the engineering, can be considered as cyclostationary. The modulating feature can not be understood clearly via the reconstructed sound field by conventional nearfield acoustic holography (NAH). A cyclostationary NAH (CYNAH) technique based on wave superposition algorithm (WSA) is suggested for reconstructing the cyclostationary sound field, which can be applied to the cyclostationary acoustic sources with complicated profiles. The information of modulating wave can be understood by the reconstructed hologram of cyclic spectrum density (CSD), in which the distribution of modulating wave is visualized and the location of modulating wave can be determined. The simulation and the experiment verified that the modulating characteristic can be understood by CYNAH based on WSA. The main advantages of WSA, including the high calculation accuracy and calculation efficiency due to the exclusion of uniqueness and singularity problems inherent in the boundary element method, are retained in the presented CYNAH procedure.

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.

Reconstruction and Separation in a Semi-Free Field by Using the Distributed Source Boundary Point Method-Based Nearfield Acoustic Holography

In a semi-free field, the acoustic field is composed of two components: the direct sound and the reflected sound. Because it is difficult to separate the direct sound from the acoustic field, conventional nearfield acoustic holography (NAH) methods cannot reconstruct an acoustic source and predict the acoustic field directly. Through utilization of the distributed source boundary point method (DSBPM)-based NAH, a treatment method for a semi-free field is proposed. In the method, the source in a semi-free field can be reconstructed correctly, and the acoustic field can be predicted and separated. An experiment on a speaker in a semi-anechoic chamber is carried out to verify the proposed method. By comparing the reconstructed and predicted results in DSBPM-based NAH with and without the proposed method, the proposed method is validated. The disadvantages of NAH without any treatment method in a semi-free field are demonstrated.

Comparison of numerical methods for noise source identification

The identification of sound sources is difficult in the presence of many potential sources that interact. Nearfield Acoustical Holography (NAH), which refers to a process by which all aspects of the sound field in a three-dimensional volume can be reconstructed based on sound pressure measurements on a two-dimensional surface conceptually, allows the identification of complex noise sources that are otherwise difficult to characterize. Conventional NAH has been applied most commonly in simple geometries such as planar, cylindrical and spherical surfaces. Since most noise sources are not simple geometrically, it is not possible to project to the actual surface of the source in most instances, thus limiting the ability of conventional NAH to resolve the source structure accurately. Numerical acoustics procedures based on the Helmholtz integral equation have been developed that allow sound fields to be projected into arbitrarily-shaped interior or exterior domains from measured sound pressure field. Two commonly implemented procedures are the inverse Boundary Element Method (BEM) and the Helmholtz Equation Least-Squares (HELS) method. An Enhanced Surface Potential (ESP) based formulation was recently developed and promised to overcome some of the drawbacks of the BEM-based formulation. In this paper, these three methods are compared through a numerical example.

Source visualization by using statistically optimized near-field acoustical holography in cylindrical coordinates

Nearfield acoustical holography (NAH) is a useful tool for visualizing noise sources. However, to avoid spatial Fourier transform-related truncation effects, the measurement, or hologram, surface must extend beyond the source to a region where the sound pressure drops to a level significantly lower than the peak level within the measurement aperture. Statistically optimized nearfield acoustical holography (SONAH), first derived by Steiner and Hald in planar geometry, is based on a formulation similar to that of NAH. However, in SONAH, surface-to-surface projection of the sound field is performed by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy: i.e., no spatial Fourier transforms are performed. Thus the requirement that the measurement surface be extended is eliminated without compromising the accuracy of the procedure. In the present work, SONAH was re-formulated in cylindrical coordinates and was applied to the measurement of the sound field radiated by a refrigeration compressor. It was found that it is possible to visualize source regions accurately by using SONAH while using fewer measurement positions than would be required to achieve a similar level of accuracy when using conventional NAH procedures.

Two-microphone nearfield acoustical holography

In conventional Nearfield acoustical holography (NAH), a large number of measurements is required to cover the entire source area. In addition, when the complete source comprises several incoherent sub-sources, the sound field must be decomposed into coherent partial fields before projection. The latter operation is made possible by using a fixed array of reference microphones and computing the reference cross-spectral matrix and the transfer functions between the reference microphones and the field microphones. Here it is shown that by combining the transfer functions from the reference to the field microphones obtained from one measurement with reference cross spectra measured in another, the sound field radiated any combination of different level (fixed-directionality) subsources can be visualized from measurements made with only enough reference microphones to represent the incoherent sources. The implementation of the procedure will be illustrated using an array of two loudspeakers, each fed by an independent white noise source. Comparisons are made of directly measured partial fields and those generated using only the reference information. By using this procedure, it is possible to avoid repetitive measurements when visualizing the sound fields radiated by different combinations of subsources having different levels, so long as the directionality of each subsource is fixed.