Near-field Acoustic Holography Research Articles

Application of compressive sensing to equivalent source method on near-field acoustic holography

Near-field acoustic holography (NAH) is an acoustic visualization technique that uses a microphone array to measure the radiated sound waves from a source in the near-field. In the present study, the equivalent source method (ESM) and the 2D spatial Fourier transform based on the generalized discrete Fourier series (GDFS) are compared, and the reconstruction performance of NAH using compressed sensing (CS) combined with both theories for NAH measurements is discussed. Additionally, the influence of different array designs (regular and pseudo-random) on the reconstruction performance of NAH is investigated. Simulations and experimentation are used to demonstrate its feasibility. In the simulation, three source models (dipole, longitudinal quadrupole and simply supported rectangular plate) are tested over a range of frequencies, SNR and reconstruction distances. The consequence indicates that use of GDFS results in a large reconstruction error in all test conditions under the rectangular array, especially in the high frequency range. The combination of a pseudo-random array and ESM-L1 provides the best reconstruction performance in most test conditions. In the experiment, two sets of pseudo-random microphone arrays with different diameters were used. They were tested separately for the dual loudspeakers and vibrating plate. ESM-L1 is suitable for reconstructing sound fields with sparse source distributions, whereas ESM-L2 is suitable for reconstructing sound fields with continuous source distributions, such as the radiated acoustic field of a vibrating plate. However, the use of pseudo-random arrays in combination with ESM is indeed a better solution for NAH.

Real-time nearfield acoustic holography using particle velocity.

In this paper, a series of impulse response functions between acoustic quantities on the source plane and particle velocity on the hologram plane are derived. In virtue of these functions, real-time nearfield acoustic holography (RT-NAH) is extended from pressure-based to particle velocity. Pressure, normal velocity, acceleration, and displacement radiated from planar sources can be reconstructed by measuring time-dependent particle velocity signals on the hologram plane. A simulation of an excited aluminum plate is performed to evaluate the difference in accuracy between RT-NAHs based on pressure and based on particle velocity. This study also examines the impact of impulse response functions on the reconstruction results, allowing for detailed analysis of the reconstruction accuracy based on these functions. The simulation results demonstrate that using RT-NAH based on particle velocity obtains significantly higher-accuracy reconstruction results when reconstructing normal velocity and displacement and slightly more accurate reconstructed pressure and normal acceleration.

Time-domain sound field reconstruction using a rigid spherical microphone array.

A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.

Experimental Validation of Reconstruction of Sound Source Radiation in an Underwater Half-Space Bounded by a Water-Air Interface

When a vibrating structure is located in a half-space bounded by a reflecting surface, the measured sound pressures are polluted by the reflection, so that they cannot show the actual sound radiation from the structure. The half-space spherical wave function expansion-based near-field acoustical holography approach is proposed to reconstruct the direct radiation from the sound source using the polluted sound pressures, which has been validated by numerical simulations. This paper deals with the experimental validation of this approach applied in an underwater half-space bounded by a water-air interface. The sound pressures measured in the half-space are used as the input data. The reconstructed sound pressures obtained are compared with benchmarks measured in a free space. The results indicate that the influences of the water-air interface reflection on the measured sound pressures can be greatly reduced in the entire frequency range investigated. The normalized relative reconstruction error introduced by the parameters of the hydrophone array and the water tank in the experiment is analyzed. The results of the experimental validation show that the proposed approach is promising for accurately measuring sound signals radiated from manned or unmanned vehicles or equipment underwater near a water-air interface.

High-efficiency prediction method for helicopter global/ground noise based on near-field acoustic holography

Noise reduction program design is an effective approach that relies on efficient noise prediction for reducing ground noise during flight. The existing noise prediction methods have the limitations of being computationally expensive or only applicable to far-fields. In this paper, a High-Efficiency Prediction Method (HEPM) for helicopter global/ground noise based on near-field acoustic holography is proposed. The HEPM can predict the global noise based on acoustic modal analysis and has the advantages of high prediction accuracy and low time cost. The process is given as follows: firstly, the rotor noise on the holographic surface in the specified flight is obtained by simulations or experiments. Secondly, the global noise model, which maps time-domain noise to acoustic modes, is established based on near-field acoustic holography and Fourier acoustic analysis methods. Finally, combined with acoustic modal amplitude, the model established enables efficiently predicting the global/ground noise in the corresponding flight state. To verify the accuracy of the prediction method, a simulation study is conducted in hovering and forward flight states using a model helicopter with a 2-meter rotor and Rotor Body Interaction (ROBIN) fuselage. The comparison of HEPM with numerical results shows that the average prediction errors of the global and ground noise are less than 0.3 dB and 0.2 dB, respectively. For a region containing 100,000 observers, the computation time of the HEPM is only one-fifth of that of the acoustic hemisphere method, demonstrating the rapidity of the proposed method.

A hybrid nearfield acoustic holography based on the mapping relationship and boundary element method

The nearfield acoustic holography (NAH) based on mapping relationship (MRS) had been developed. However, it is superior to the reconstructions on regular shapes by using the MRS-based NAH with spherical fundamental solutions (FS). In contrast, the boundary element method (BEM) based NAH is capable of handling complex shapes but requires relatively more measurement points. In this work, a hybrid method is developed by combing the MRS with spherical FS and the BEM. To circumvent the non-unique problems associated with the conventional BEM, the Burton-Miller formulation is adopted into the BEM based NAH. The merit of easy measurement setup, such as the determination of positions and number of microphones in the array is preserved in the hybrid method. Furthermore, it is possible to recast the reconstruction operation by the BEM-based NAH with sufficient measurements data on an artificial hologram that are implicitly interpolated by the MRS-based NAH. In conjunction with regularization techniques, results with improved accuracy are clearly observed in the velocity reconstructions for irregular shapes by the hybrid NAH. It is validated by numerical examples especially for an irregular box that the hybrid NAH is capable of producing reconstructions with significant improvement of accuracy even with small signal-to-noise ratio (SNR) as compared with the MRS-based NAH. An experiment is setup to further demonstrate the potential of the hybrid NAH for practical reconstruction of an irregular radiator. More robust and accurate reconstructions are achieved in contrast with the MRS-based NAH, which clearly illustrated advantages of the hybrid NAH.

Numerical Simulation Results of Double Nearfield Acoustic Holography method with extrapolation

In my laboratory, the new sound localization method, Double Nearfield Acoustic Holography (DNAH) method is being developed. This method has high resolution in low frequency sound localization. It is presented at former inter-noise. On the other hand, the extrapolation of measurement points is effective for Nearfield Acoustic Holography method in low frequency. Therefore, the extrapolation technique is also applied for DNAH method. In this presentation, the numerical simulation results of DNAH method with extrapolation of measurement points is reported. With extrapolation, the DNAH shows higher resolution in low frequency sound localization than DNAH method without extrapolation, and higher resolution in low frequency sound localization than NAH method with extrapolation.

Numerical Analysis and Measurement Techniques for Aircraft Cabin Noise Using JAXA's Jet-FTB "HISHO"

The reduction of aircraft cabin noise is one of the important issues not only to increase passenger comfort but also to strengthen international competitiveness in aircraft development. JAXA has been conducting research activities on numerical and experimental prediction techniques of aircraft cabin noise. This paper focuses on the development of our cabin noise prediction tool using the Finite-Difference Time-Domain method, and in-flight noise measurement in the JAXA's Jet-Flying Test Bed (Jet-FTB) "HISHO" with the aim of grasping the cabin noise characteristics. The measurement data include the noise level near interior walls using the near-field acoustic holography method, the wall impedance, and structural vibrations, acquired through some flight test / ground test campaigns. The authors also explain validation results of our numerical prediction tool using microphone data measured in the Jet-FTB.

Experimental research on global active rotor noise control using near-field acoustic holography and sound field reproduction

This study employs a 1.6 m diameter rotor to validate the global active noise control method, developed from our previously work, which is based on near-field acoustic holography and sound field reproduction. The validation is conducted through experiments in an anechoic chamber. Additionally, we achieved control over nearly all acoustic modal components of multiple blade passing frequency (BPF) noises of the rotor by extending the time-domain least mean square (LMS) to the acoustic modal domain. The experimental results from near-field acoustic holography revealed that each BPF noise contained 3–4 main acoustic modal components, accounting for almost 90 % of the sound power. The global active noise control experiments demonstrated that the adaptive algorithm in the acoustic modal domain effectively mitigates the influence of rotation speed fluctuations, resulting in steady-state global noise reduction through sound field reproduction. Furthermore, for the first 3 BPF noise, our method achieved noise reduction of 9, 11, and 6 dB by controlling the first 3–4 main acoustic modal components, respectively. The concurrent reduction of various harmonic noises at all observation points validates the method's capability to globally control multiple harmonic noises.

A novel robust approach of 3D CNN and SAE-based near-field acoustical holography relying on self-identity constraint data for Kalman gain

A novel robust approach of 3D CNN and SAE-based near-field acoustical holography relying on self-identity constraint data for Kalman gain

Near-field modeling of the head-related transfer function by using the dummy head sound source

Various approaches based on direct measurement have been used to obtain the precise headrelated transfer function (HRTF). However, several problems persist, such as scattering of sound source and distance effect, which are related to the measurement configuration. In this work, the modified dummy head having two sound sources located at the ear positions is applied as the sound source reciprocally to overcome the trouble. By using the near-field acoustic holography, the sound sources located in the ear holes are reconstructed from the measured data in the near-field hologram. One can predict the acoustic transfer function between the ear holes and the field positions at any point using the recovered source information described in spherical harmonics. The obtained transfer function is valid for predicting the binaural response from any sound source position. This configuration is possible to measure the near-field response with the relatively small scattering effect because of the low Helmholtz number of microphones. The far-field reconstruction of HRTF is also possible with the near-field measurement data using acoustical holography. The proposed method is demonstrated with the modified B&K HATS system, in which the microphones in the ear holes are replaced by pipe sources connected to the loudspeaker.

Sound Field Reconstruction Using Prolate Spheroidal Wave Functions and Sparse Regularization.

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method.

Method of acoustic separation on the surface of cylindrical baffle

This paper suggests a statistically optimal near-field acoustic holography method based on the combination of plane waves and cylindrical waves, which is used for underwater cylindrical baffles. The method addresses the issue that the extraction of scattered acoustic waves from the surface of underwater cylindrical baffles requires too many measurement points in practical applications: separation of incident and dispersed sound fields and near-field measurements of sound fields at baffle surfaces.The underwater detection sound source is situated in the scatterer's far-field region, so in the actual application scenario for the surface acoustic scattering separation of the cylindrical baffle, the plane wave expansion is used to represent the surface incident acoustic wave and the cylindrical wave expansion is used to describe the scattered acoustic wave on the baffle surface. As a result, fewer expansion orders are required to describe the entire sound field on the baffle's surface. It is verified by simulation that the method is valid and efficient for near-field total sound field measurement and dispersed sound field separation of roughly cylindrical targets under underwater far-field incidence situations because the measurement holographic surface of the surface permits unlimited geometries.

Compressive nonstationary near-field acoustic holography for reconstructing the instantaneous sound field

A compressive nonstationary near-field acoustic holography based on time-domain plane wave superposition method is proposed to precisely reconstruct the instantaneous sound field using the fewer measurement points. In the proposed method, by means of an instantaneous propagation kernel, a time-domain convolution superposition formula is established for relating the time-variant pressure of the hologram plane to the pressure time-wavenumber spectra of the virtual source plane. Next, compressed sensing theory and sparse representation framework are introduced into the time-marching solving inverse process of the established formula, and the smoothed l0 norm and revised Newton optimization algorithm are employed to solve the serious cumulative ill-posed problem over time for acquiring the pressure time-wavenumber spectra. The key is to approximately replace the discontinuous ℓ0 norm by using a suitable continuous function, and the revised Newton algorithm is applied to minimize the continuous function for obtaining the optimal solution. Finally, with the aid of a time-domain convolution formula, the solved pressure time-wavenumber spectra are employed to calculate the time-variant pressure on the reconstruction plane. The proposed method not only can evidently suppress the ill-posed problem of time-marching solving inverse process for improving the reconstruction accuracy, but also can greatly reduce the measurement points and microphone number for drastically decreasing the measurement cost on the premise of ensuring the reconstruction accuracy and spatial resolution. A numerical simulation is conducted, and the simulation effects prove that the proposed method can accurately reconstruct the instantaneous sound field with the fewer measurement points in time–space domains. The reconstruction results are also compared to those of time-domain plane wave superposition method with Tikhonov regularization to verify the superiority of the proposed method with fewer measurement points under different parameter configurations. An experiment of an impaction steel plate is implemented for further validating the competence of the proposed method.

Statistically Optimized Near-Field Acoustic Holography Using Prolate Spheroidal Wave Functions

Near-field acoustic holography (NAH) is an effective tool for realizing accurate sound field reconstruction in three-dimensional space on the prerequisite that appropriate elementary wave functions are selected or constructed to match the characteristics of the sound sources. However, for elongated sources, common wave functions, i.e., plane, cylindrical, or spherical waves, sometimes do not perform well during the sound field projections. To solve this problem, statistically optimized near-field acoustical holography combined with prolate spheroidal wave functions is proposed. In the approach, the sound field is expanded by a series of prolate spheroidal wave functions, whose wavefronts can be set nearly conformal to the elongated sources. Based on these wave functions, fewer expansion terms are required to model the sound field, and the need for regularization can be reduced during the inverse solving process. Therefore, the accuracy of the reconstruction results can be further improved. Numerical simulations are conducted by two types of elongated source models, namely, spatially separated and extended. The results show that the proposed method can effectively reconstruct the sound pressures of elongated sources and perform robustly across a wide frequency range. Simultaneously, a designed experiment is carried out in an anechoic chamber, which demonstrates the feasibility of the proposed method.

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.