Near-field Acoustic Holography Research Articles

Sound source identification using the boundary element method in a sparse framework

Traditional near-field acoustic holography (NAH) based on the boundary element method (BEM) exhibits good performance for sound source identification. However, good reconstruction results can only be guaranteed if a sufficient number of sampling points are used. In this paper, the unitary matrix is used as the sparse basis matrix of source surface velocity and is obtained from the transfer matrix between the source surface sound pressure and vibration velocity by singular value decomposition (SVD). Based on this sparse basis, a sparse Bayesian learning (SBL) algorithm is introduced into BEM-based NAH to address the case of few sampling points. The use of a standard SBL algorithm in BEM-based NAH leads to hyperparameters that are overly sparse due to the large number of iterations, which results in large reconstruction errors. To solve this problem, a modified SBL algorithm is proposed. Good reconstruction results are maintained by selecting appropriate hyperparameters and revising the results using the steepest descent method. A simulated cuboid shell is used to explore the influence of the (i) number of sampling points and (ii) signal-to-noise ratio (SNR) on the reconstruction. Numerical results show that the proposed method can achieve effective reconstruction when the number of sampling points is approximately one-tenth of the number of discrete points on the source surface. The validity of the proposed method is verified by a comparison with experimental results.

Reconstruction of transient acoustic field using sparse real-time near-field acoustic holography

A sparse real-time near-field acoustic holography method is proposed to precisely and stably reconstruct a transient sound field. By a time-domain impulse response function, a time domain convolution equation between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established. Then, a smoothed ℓ0-norm optimization algorithm is applied to solve the serious ill-conditioned problem of the inverse process to get the pressure time-wavenumber spectrum of the reconstruction plane. The key part of solving this problem is to approximate replace the discontinuous ℓ0-norm by using a suitable continuous Gaussian function family, and a steepest ascent algorithm is introduced to minimize the continuous function for obtaining the optimal solution. Finally, the pressure time-wavenumber spectra of the reconstruction plane for all wavenumbers at all times are solved, and the corresponding time-dependent pressures are gained by the two-dimensional space inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation effect prove that the proposed method can accurately reconstruct the transient sound field, and its reconstruction results are compared to those of the real-time near-field acoustic holography (RTNAH) with Tikhonov regularization and YALL1 modal for verifying the superiority of the proposed method. The YALL1 module utilizes an alternating direction algorithm for solving the ℓ1 minimization problems. Several parameters including the noise, position of the holograph plane and two initialization values are discussed in the simulation. The comparison and discussion results show that the reconstruction effect of the proposed method is much better than those of RTNAH with Tikhonov regularization and YALL1 modal under different parameter configurations. An experiment with a percussive steel plate is implemented for further validating the effectivity of the proposed method.

Application of equivalent source intensity density interpolation in near-field acoustic holography

The spatial resolution of near-field acoustic holography based on the equivalent source method (ESM) is closely related to the number of measurement points, the higher the number of measurement points, the higher the resolution. However, the number of measurement points in the actual measurement cannot be increased infinitely. To solve the contradiction between the resolution and the number of measurement points, this paper proposes an equivalent source density interpolation method (ESDIM). First, the equivalent source intensity is obtained using the sound pressure measured by the array element and the Green function, and the equivalent source intensity density is obtained based on the equivalent source intensity and grid area. Second, the Hermite interpolation function was used to obtain the interpolated equivalent source intensity density. However, as the number of interpolated grids increased, the resolution, computation, and running time of ESDIM increased, and the number of subdivided grids per unit grid was 9–25 in this study. Finally, the sound field was reconstructed based on the obtained interpolated equivalent source intensity and Green transfer function, and the reconstruction accuracies of ESDIM and ESM were compared and analyzed. The simulation and experimental data processing results showed that the resolution of the equivalent source intensity density interpolation method was higher than that of the ESM.

Conical near-field acoustic holography based on cylindrical wave function of variable radius and nonconformal plane measurement

In practical acoustical measurement for large cones, maintaining coaxial and conformal between the holographic surface and reconstructed surface is usually tedious. To overcome this flaw, a conical near-field acoustic holography (NAH) based on cylindrical wave function of variable radius and nonconformal plane measurement is proposed in this paper. First, cylindrical wave function of variable radius (VR)–based modified statistically optimal cylindrical NAH (SOCNAH) method, entitled VR-SOCNAH, is proposed, which is more applicable to conical surfaces. Second, with the measured sound pressure data on the holographic plane, sound pressure on the conical conformal surface is first reconstructed using statistically optimal planar NAH (SOPNAH), and sound pressure on the reconstructed surface is then reconstructed using VR-SOCNAH. Third, fixed and variable radius measurement methods are comparatively studied, and the former is adopted. Furthermore, a measurement parameter optimization method based on orthogonal experiment is proposed to determine appropriate value ranges. Finally, the proposed NAH is applied to a test bed, and the robustness and accuracy of sound field reconstruction for large cones are significantly enhanced, which provides reliable scientific basis and engineering guidance for noise monitoring and control of mechanical equipment.

A Cylindrical Near-Field Acoustical Holography Method Based on Cylindrical Translation Window Expansion and an Autoencoder Stacked with 3D-CNN Layers.

The performance of near-field acoustic holography (NAH) with a sparse sampling rate will be affected by spatial aliasing or inverse ill-posed equations. Through a 3D convolution neural network (CNN) and stacked autoencoder framework (CSA), the data-driven CSA-NAH method can solve this problem by utilizing the information from data in each dimension. In this paper, the cylindrical translation window (CTW) is introduced to truncate and roll out the cylindrical image to compensate for the loss of circumferential features at the truncation edge. Combined with the CSA-NAH method, a cylindrical NAH method based on stacked 3D-CNN layers (CS3C) for sparse sampling is proposed, and its feasibility is verified numerically. In addition, the planar NAH method based on the Paulis-Gerchberg extrapolation interpolation algorithm (PGa) is introduced into the cylindrical coordinate system, and compared with the proposed method. The results show that, under the same conditions, the reconstruction error rate of the CS3C-NAH method is reduced by nearly 50%, and the effect is significant.

Sound field separation technique for nonplanar sources based on field prediction by using statistically optimized near-field acoustic holography

For the sound field of cylindrical or compact sources, the current sound field separation technique (FST) based on statistically optimized near-field acoustic holography (SONAH) uses planar wave for separation, and the effects of different wave functions have not yet been studied. However, the non-conformal problem between the hologram surface and the sound sources commonly has a risk of accuracy reduction. Here, an FST for nonplanar sources based on SONAH is proposed to solve this problem. First, considering that field prediction of near-field acoustic holography will attenuate errors, noise immunity of the FST is effectively improved in a noisy environment by moving the reconstruction surface to the prediction area. Subsequently, the appropriate conformal wave function is determined by combining the shape of the sound source and is substituted into the improved method in the first step to separate the free-field sound pressure. Finally, simulations, experiments using loudspeakers, and a cylindrical experiment platform prove the effectiveness of the proposed method, which can greatly improve the adaptability and reliability of the FST in nonplanar sound sources in mechanical systems.

Compressive equivalent source method based on particle velocity measurements for near-field acoustic holography

In order to solve the problems of spatial resolution limit and reduce the measurement cost, the compressive sensing theory and the sparse regularization are applied to the near-field acoustic holography (NAH) technology. In the previous works, the Equivalent Source Method (ESM)-based NAH has been extended in the sparsity framework by sampling the sound pressure signals sparsely. However, this Compressive ESM (CESM) mode would suffer from the low precision problem in the particle velocity reconstruction. To improve the reconstruction accuracy of the particle velocity, this paper is going to take the sparse particle velocity as the input of NAH to establish a new CESM mode based on the particle velocity measurement. In the meantime, the number of sampling points will be reduced greatly without losing the reconstruction accuracy when compared to the conventional ESM with the Tikhonov regularization based on the particle velocity measurement. Several numerical simulation experiments have been carried out to examine the performance of the proposed model. The results show that the proposed model delivers a satisfactory performance in the reconstruction of both the pressure and particle velocity on the condition that the number of sampling points is much smaller than that of the conventional ESM, and the proposed model performs much better than the existing CESM mode based on the sound pressure measurement especially when reconstructing the particle velocity.

Near-field acoustic holography for underwater moving surfaces

Near-field acoustic holography has been the standard technique to accurately image static structure vibration from nearby acoustic pressure measurements. The classical application bases the method on the stable solution of an integral surface representation of the acoustic pressure. In this work, we will be concerned with the extension of NAH to image a vibrating structure moving underwater. In an underwater medium, even at slow speeds, the action between the flow and structure produces many radiation sources that could severely limit the accuracy of the integral surface representation used for static NAH. Using the Lighthill acoustic analogy, we use an integral surface representation for the structure’s radiated sound and a quadrupole source that models the corresponding flow-induced sound. Finally, we will justify the validity of the proposed method for COMSOL numerically generated pressure data that results from the internal excitation of a cylindrical structure moving over an underwater medium. This work has been supported by the Office of Naval Research.

Fourier acoustics: Uncovering the origins of sound

No doubt, Jean-Baptiste Joseph Fourier has had a great impact in science. At the root of Fourier Acoustics, the Fourier series, when employed as a starting point and manipulated, allows us to uncover the origins of sound in a simple and elegant way, not only in acoustics but also in electromagnetics. A well-known stepping stone on the path is nearfield acoustical holography (NAH) and its theory can be recast almost completely, and simply, in terms of two-dimensional (2D) Fourier series and applied to any geometry. For separable coordinate systems, each of the components of the series can be propagated to a surface conformal to the measurement surface using an analytically defined propagator. But even when the surfaces are not part of a separable system, the spirit of Fourier’s expansions is mirrored with the singular value decomposition, applied to a numerically derived propagator constructed using the equivalent source method. A comprehensive demonstration of Fourier acoustics applied to aeroacoustics was in the cabin of a Boeing aircraft, in flight, using a two-dimensional spherical array. Reconstructions of vector intensity in a volume from correlations of the measured pressure to panel accelerometers showed the direction and location of the dominant fuselage sources of noise—uncovering the origin of sound. [Work supported by the Office of Naval Research.]

Frequency domain method for holographic localization of rotating sound sources

Most of the previous studies employed beamforming techniques for the localization of rotating sources. These methods usually rely on the use of a virtual rotating array (VRA), in which the Doppler effects caused by source rotation can be eliminated. The VRA signal generation can be achieved in both frequency and time domains. In this presentation, compressive sensing (CS) near-field acoustic holography (NAH) has been extended to the reconstruction of rotating sources using the frequency domain (FD) VRA method. This combination can provide an improved resolution of spatial reconstructions at low frequencies compared to beamforming methods. In addition to the direct combination of the FD-VRA method and CS acoustical holography techniques, a more efficient algorithm for FD-VRA was developed to address the shortcomings of the traditional approach, such as higher computational cost and the requirement of a circular array with equally spaced microphones. The proposed FD-VRA method only involves a direct summation of the rotating sidebands of signals measured on a stationary array, which effectively reduces the computational load. Furthermore, an arbitrary array of microphones can be used. It will be shown that the proposed algorithm works for narrowband sources without overlapping frequency components in the rotating sidebands.

A hybrid compressive sensing approach to noise source visualization: Application to a diesel engine

To identify sound source locations by using Fourier-based Near-field Acoustical Holography (NAH), a large number of microphone measurements is generally required to span the source region and ensure a sufficiently high spatial sampling rate. As a result, such measurements are costly, a fact which has discouraged the industrial application of NAH to identify sound source locations. However, recently, compressive sensing approaches have made it feasible to identify concentrated sound sources with a limited number of microphone measurements. In the present work, sound radiation from the front face of a diesel engine was measured by using one set of measurements from a 35-channel combo-array. The locations of significant noise sources were then identified by using three compressive sensing algorithms: Wideband Acoustical Holography (WBH), l1-norm minimization, and a hybrid approach which combined WBH and l1-norm minimization. The latter approach takes advantage of the l1’ norm’s ability to locate spatially distinct sources, and WBH’s ability to suppress “ghost” sources. It was found that the hybrid algorithm can localize and visualize the major noise sources over a broad range of frequencies, even though using a relatively small number of microphones. Finally, comments are made regarding sound field reconstruction differences between the algorithms.

Construction and Simulation Analysis of A New Transformer Noise Prediction Model

In recent years, more and more attention has been paid to the environmental impact of substation operation noise. Therefore, a suitable noise prediction model is needed to evaluate the noise impact. The noise in the substation mainly comes from the main transformer. The predictions of the main transformer noise model in the existing technical specifications often do not correspond to the actual situation. Therefore, based on the theory of planar Nearfield Acoustical Holography (NAH) equivalent source approach, a new transformer noise prediction model called the main transformer noise model of the directional dot-matrix equivalent source is established. Using this model, a typical 500 kV substation is simulated in Cadna/A, and the results are compared with the simulation values and measured data of the existing standard main trans-former noise model. The comparison shows that the new prediction model can accurately predict the noise value of the substation, and the error is less than 2 dB(A).

Methods for high-performance jet aircraft noise source imaging and sound field reconstruction

Source characterization and sound field reconstruction are vital to understanding noise radiation from turbulent, heated, supersonic jets produced by high-performance engines. This paper describes the application of two acoustic imaging methods to full-scale tactical aircraft noise analyses: statistically optimized near-field acoustical holography and hybrid beamforming. These methods constitute equivalent wave and equivalent source models, respectively. A review of these methods is given and their respective features are discussed.

Acousto-optic sensing for near-field acoustic holography

Near-field acoustic holography (NAH) is a very powerful and widely used technique for the study of complex acoustic radiators. NAH enables to quickly understand how a complex source radiates into the medium. The technique is particularly suitable at low frequencies. At high frequencies, a dense transducer interspacing is required, and the measurement microphones can disturb the studied sound field when their size is comparable to the acoustic wavelength. In this study we examine the use of acousto-optic sensing in NAH. Acousto-optic sensing uses light beams as the sensing element, making it possible to acquire remote and non-invasive measurements without introducing extraneous objects in the vicinity of the source. The pressure, particle velocity and intensity fields, as well as the sound power radiated by a complex source, are determined from measurements in the near-field with an optical interferometer. The presented results demonstrate the potential of optical sensing to non-intrusively characterize sound fields, particularly at high frequencies.

Investigation of potential benefits and functionality of a vibroacoustic camera by combining results of a common beamforming and nearfield holography acoustic camera and a highspeed camera, allowing to visualize structural vibration (optical flow tracking

In this paper potential benefits and functionality of a vibroacoustic camera are investigated by combining results of a common beamforming and nearfield holography acoustic camera using the software NoiseImage and a highspeed camera, allowing to visualize structural vibration (optical flow tracking) using the software WaveImage. Both results can be used to calculate color maps - mapped parameters are sound pressure, vibration displacement and its derivatives. The authors will investigate how the combination of methods might enhance understanding and interpretation of the vibroacoustic behavior of specimens in the overlapping frequency range. At low frequencies, the beamforming approach is limited due to main lobe width and array size. While the limits for source localization can be offset employing nearfield acoustic holography, those methods can be time consuming and might fail for complex 3-dimensional structures. It was also previously shown that mode shapes of 2-dimensional structures can be reproduced using nearfield acoustic holography (SONAH). The highspeed camera results present a way to provide positions of local vibration maxima and operating deflection shapes without accessing the acoustic nearfield. Accordingly, the approach could be viewed as a potential extension of the frequency range in which meaningful visualization of vibroacoustic data can be achieved from a single far field measurement from 0 Hz to the ultrasound frequency regime.

Diesel Engine Noise Source Visualization by Using Compressive Sensing Algorithms

To identify sound source locations by using Near-field Acoustical Holography (NAH), a large number of microphone measurements is generally required in order to cover the source region and ensure a sufficiently high spatial sampling rate: it may require hundreds of microphones. As a result, such measurements are costly, a fact which has limited the industrial application of NAH to identify sound source locations. However, recently, it has been shown possible to identify concentrated sound sources with a limited number of microphone measurement based on Compressive Sensing theory. In the present work, sound radiation from the front face of a diesel engine was measured by using one set of measurements from a thirty-five-channel combo-array placed in front of the engine. The locations of significant noise sources were then identified by using two algorithms: i.e., l1-norm minimization and a hybrid approach which combined Wideband Acoustical Holography (WBH) and l1-norm minimization. It was found that both algorithms can successfully localize and visualize the major noise sources over a broad range of frequencies, even though using a relatively small number of microphones. Finally, comments are made on sound field reconstruction differences between the two algorithms.

Machine learning aided near-field acoustic holography based on equivalent source method.

In recent times, equivalent source method-based near-field acoustic holography methods have been extensively applied in sound source localization and characterization. The most commonly used equivalent sources are spherical harmonics. In a non-reverberant environment with no reflections, these equivalent sources could be the best choice since spherical harmonics are derived for the Sommerfeld boundary condition. However, these methods are not the best fit for reverberating environments. In such cases, a new relationship can be calculated between the field weights and the measured pressure with enough training examples. The proposed machine learning models include linear regression (LR) with adaptive moment estimation (Adam), LR with limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), and multi-layer perceptron with one and two hidden layers. These methods are tested for multiple monopoles and vibrating plate simulations in a room with different wall absorption coefficients. The data-driven methods are also studied on loudspeakers numerically and experimentally in a free field environment. The results from these methods are compared with the results of one norm convex optimization (L1CVX). LR with L-BFGS performed the best among all the methods studied and performed better than L1CVX for less absorption coefficient for geometrically separable sources. LR with L-BFGS also has much faster inference times.

Measurement of airborne sound insulation of building components by near-field acoustic holography

Taking the architectural acoustic design of a stadium and gymnasium in a sports center as an example, the acoustic parameters of large stadiums under different working conditions were explored. In order to improve the reliability of acoustic design of large stadiums, the acoustical environment of stadiums is simulated and matched with the design standard value by using the sound absorbing materials arranged in limited positions.

Experimental Results of Double Near-filed Holography method for a commercial Product

In my laboratory, the new localization method, Double Near-field Acoustic Holography (DNAH) method is being Developed. This method is developed to overcome the limit of acoustic holography methods, that the acoustic holography methods cannot measure low frequency noise precisely. In former presentations, the numerical simulation results, and basic experimental results are reported. In these presentations, it is verified that the DNAH method has good resolution for low frequency sound sources. But they are carried out for simple sound source(s), simulated point source(s). In this presentation, the experimental results for a commercial product will be presented. From these results, it is verified that the DNAH method has good resolution for low frequency noise of a commercial product between 10Hz and 200Hz, and the DNAH method has enough resolution for low frequency sound localization.

Equivalent source method based Near-field acoustic holography using machine learning

The equivalent source method has been one of the most commonly used methods for sound source localization. It involves equivalent sources spread over the source plane (or region). The pressure fields from these equivalent sources are usually spherical harmonics. But, the spherical harmonic fields are derived for the Sommerfeld boundary condition with no reflection or reverberation. Data-driven methods help perform sound source localization in a reverberant environment when no prior information about the surroundings is available. The methods studied are linear regression (LR) with Adam, linear regression with L-BFGS, multi-layer perceptron (MLP) with one and two hidden layers. The simulations are conducted for two monopoles in rooms with different reverberation times and compared with one norm convex optimization (L1CVX). It is observed that overall, LR with L-BFGS gave the best results. Also, for low reverberation time, LR with L-BFGS was able to localize the sources better than L1CVX.