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This paper proposes a distorted hologram data repair approach for sound field reconstruction. In this approach, an equivalent source model is established by placing a set of equivalent sources near the hologram surface to represent the measured hologram pressures. Each hologram pressure is simultaneously assigned an indicator to describe whether its measurement is corrupted by errors or not. This model is then formulated within a modal framework by utilizing the modes generated through the singular value decomposition of the transfer matrix between the hologram and nearby equivalent source surfaces. Subsequently, the indicators and modal coefficients are assigned the 0–1 and Gaussian prior distributions, respectively, and their posterior distributions are derived using the Bayesian method. The means of the posterior distributions are calculated to discriminate corrupted measurements and repair distorted hologram pressures. Repaired hologram pressures are finally utilized for reconstructions using the equivalent source method. Results from both numerical simulations conducted under various parameter settings and two experiments demonstrate the effectiveness of the proposed approach in automatically discriminating all the corrupted measurements and accurately repairing the distorted hologram pressures. Furthermore, the accuracy of the reconstructions using the repaired hologram pressures is comparable to that achieved with the correctly measured pressures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nearfield acoustic holography based on the compressed sensing theory can realize the accurate reconstruction of sound fields with fewer measurement points on the premise that an appropriate sparse basis is obtained. However, for different types of sound sources, the appropriate sparse bases are diverse and should be constructed elaborately. In this paper, a block sparse Bayesian learning (SBL) equivalent source method is proposed for realizing the reconstruction of the sound fields radiated by different types of sources, including the spatially sparse sources, the spatially extended sources, and the mixed ones of the above two, without the elaborate construction of the sparse basis. The proposed method constructs a block sparse equivalent source model and promotes a block sparse solution by imposing a structured prior on the equivalent source model and estimating the posterior of the model by using the SBL, which can achieve the accurate reconstruction of the radiated sound fields of different types of sources simply by adjusting the block size. Numerical simulation and experimental results demonstrate the validity and superiority of the proposed method, and the effects of two key parameters, the block size, and sparsity pruning threshold value are investigated through simulations. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to reconstruct the time-dependent forces acting on a vibrating structure from pressure measurements. In the approach, the pressures measured in the near field of the structure are related to the exciting forces at the reconstruction points by the transfer functions determined in an experimental way, whereupon the time-dependent forces can be reconstructed with these pressures as inputs. In the reconstruction process, an additional regularization with a mixed lp,q-norm term is introduced to resolve the ill-posed inverse problem, which is able to take advantage of the prior knowledge of space and time characteristics of the forces. A numerical simulation of reconstructing the time-dependent forces acting on a plate and two experiments of reconstructing the impact forces acting on a semi-cylindrical shell and an elliptically shaped structure are carried out. The results demonstrate the feasibility of the proposed approach for reconstructing the forces in both temporal and spatial domains from pressure measurements. The proposed approach provides a non-contact and real-time way to identify the locations of forces and reconstruct their time histories, which can be further used to reveal the mechanical cause of the radiated noise. [ABSTRACT FROM AUTHOR]

This paper proposes a sound field separation technique based on the time-domain equivalent source method with single layer pressure-velocity measurements to extract the nonstationary sound field radiated by the target source in a reverberant environment. This technique constructs a formulation that relates the pressures and particle velocities on a measurement surface to the strengths of time-domain equivalent sources arranged for modelling the outgoing and incoming waves. By solving the strengths of time-domain equivalent sources, the sounds coming from different sides of the measurement surface can be separated independently. In the proposed technique, the use of a time-domain equivalent source model allows the measurement surface to be arbitrarily shaped, thus providing the ability to analyze the arbitrarily shaped sources in a reverberant environment. Numerical simulations investigated the performance of the proposed technique when using different types of arrays, including planar, semi-cylindrical, and semi-spherical arrays, and an experiment with three loudspeakers located at two sides of the measurement surface was carried out to test the validity of the proposed technique. Both numerical and experimental results demonstrate that the proposed technique can remove the influence of disturbing sources in both time and space domains and separate out the target sound fields effectively. [ABSTRACT FROM AUTHOR]

A time domain angular spectrum method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of a series of plane wave bases, and the plane wave basis is constructed by an impulse response function that relates the time domain angular spectrum to the field point pressure. The impulse response function consists of two parts, the propagating plane waves and the evanescent plane waves, and their physical interpretation is provided. By discretizing the time convolution between the plane wave strength and the impulse response function, the reconstruction can be carried out at each time step, thus providing the advantage of real-time reconstructing sound fields. Since the real-time reconstruction process is non-recursive, it can provide a stable reconstruction. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain an appropriate estimation of the plane wave strength. Numerical simulations with an unsteady excitation plate and an experiment with an impacted plate were carried out to demonstrate the feasibility of the proposed method on reconstructing nonstationary sound fields. The effect of numerical parameters on the reconstruction accuracy was also investigated in the numerical simulations. [ABSTRACT FROM AUTHOR]

Transient nearfield acoustic holography based on the time domain equivalent source method suffers from the instability that is caused by the use of the time marching scheme. In this paper, the time marching scheme is reformulated to a large iterative scheme. By conducting the eigenanalysis of this large iterative scheme, a necessary condition for stability, i.e., the maximum magnitude of eigenvalues should not be larger than one, can be obtained. Moreover, the causes of instability are analyzed according to the eigenvalues distribution. By virtue of the eigenanalysis, the mechanisms and drawbacks of three previous stabilization methods based on the Tikhonov regularization, the truncated singular value decomposition (TSVD), and the multistep approach are analyzed. To overcome their drawbacks, the classical golden section method is applied to search the regularization parameters and filter parameters based on the necessary condition for stability. Furthermore, the time averaging technique is introduced into the stabilization methods based on the Tikhonov regularization and the TSVD to eliminate the high-frequency oscillation and release the difficulty of searching the filter parameter, respectively. Numerical simulation results indicate that all the improved methods can realize the stabilization of solutions. [ABSTRACT FROM AUTHOR]

An analytical far field solution for a rotating point dipole source in a plug flow is derived. The shear layer of the jet is modelled as an infinitely thin cylindrical vortex sheet and the far field integral is calculated by the stationary phase method. Four numerical tests are performed to validate the derived solution as well as to assess the effects of sound refraction from the shear layer. First, the calculated results using the derived formulations are compared with the known solution for a rotating dipole in a uniform flow to validate the present model in this fundamental test case. After that, the effects of sound refraction for different rotating dipole sources in the plug flow are assessed. Then the refraction effects on different frequency components of the signal at the observer position, as well as the effects of the motion of the source and of the type of source are considered. Finally, the effect of different sound speeds and densities outside and inside the plug flow is investigated. The solution obtained may be of particular interest for propeller and rotor noise measurements in open jet anechoic wind tunnels. [ABSTRACT FROM AUTHOR]

Stability of the inverse time domain boundary element method (ITBEM) for near-field acoustic holography is investigated. An eigenvalue system is built by reformulating the ITBEM to an iterative format. Through the analysis of the eigenvalue system, a stabilization criterion is derived. Then the stabilization criterion is utilized to reveal the stabilization mechanism of the TSVD method which plays an important role in the ITBEM. Furthermore, a method for properly choosing the ratio of truncated singular values to ensure the stability is provided. Although stability can be managed by using the TSVD method, the accuracy of the results cannot always be guaranteed. To overwhelm this difficulty, an averaging technique is further introduced, and its stabilization mechanism is investigated by incorporating it into the ITBEM formulations. Numerical simulations are carried out to validate the stabilization criterion, and the stabilization mechanisms of TSVD and averaging are shown specifically with extensive eigenvalue analyses. [ABSTRACT FROM AUTHOR]

This paper examines the feasibility of extracting the non-stationary sound field generated by a target source in the presence of disturbing source from single layer pressure-velocity measurements. Unlike the method described in a previous paper [Bi, Geng, and Zhang, J. Acoust. Soc. Am. 135(6), 3474-3482 (2014)], the proposed method allows measurements of pressure and particle velocity signals on a single plane instead of pressure signals on two planes, and the time-dependent pressure generated by the target source is extracted by a simple superposition of the measured pressure and the convolution between the measured particle velocity and the corresponding impulse response function. Because the particle velocity here is measured directly, the error caused by the finite difference approximation can be avoided, which makes it possible to perform the separation better than the previous method. In this paper, a Microflown pressure-velocity probe is used to perform the experimental measurements, and the calibration procedure of the probe in the time domain is given. The experimental results demonstrate that the proposed method is effective in extracting the desired non-stationary sound field generated by the target source from the mixed one in both time and space domains, and it obtains more accurate results than the previous method. [ABSTRACT FROM AUTHOR]

Planar near-field acoustic holography has been successfully extended to reconstruct the sound field in a moving medium, however, the reconstructed field still contains the convection effect that might lead to the wrong identification of sound sources. In order to accurately identify sound sources in a moving medium, a time-domain equivalent source method is developed. In the method, the real source is replaced by a series of time-domain equivalent sources whose strengths are solved itera-tively by utilizing the measured pressure and the known convective time-domain Green's function, and time averaging is used to reduce the instability in the iterative solving process. Since these solved equivalent source strengths are independent of the convection effect, they can be used not only to identify sound sources but also to model sound radiations in both moving and static media. Numerical simulations are performed to investigate the influence of noise on the solved equivalent source strengths and the effect of time averaging on reducing the instability, and to demonstrate the advantages of the proposed method on the source identification and sound radiation modeling. [ABSTRACT FROM AUTHOR]

To extract the desired non-stationary sound field generated by a target source in the presence of disturbing sources, a real-time sound field separation method with pressure and particle acceleration measurements is proposed. In this method, the pressure and particle acceleration signals at a time instant are first measured on one measurement plane, where the particle acceleration is obtained by the finite difference approximation with the aid of an auxiliary measurement plane; then, the desired pressure signal generated by the target source at the same time instant can be extracted in a timely manner, by a simple superposition of the measured pressure and the convolution between the measured particle acceleration and the derived impulse response function. Thereby, the proposed method possesses a significant feature of real-time separation of non-stationary sound fields, which provides the potential to in situ analyze the radiation characteristics of a non-stationary source. The proposed method was examined through numerical simulation and experiment. Results demonstrated that the proposed method can not only extract the desired time-evolving pressure signal generated by the target source at any space point, but can also obtain the desired spatial distribution of the pressure field generated by the target source at any time instant. [ABSTRACT FROM AUTHOR]

A time-domain plane wave superposition method is proposed to reconstruct nonstationary sound fields. In this method, the sound field is expressed as a superposition of time convolutions between the estimated time-wavenumber spectrum of the sound pressure on a virtual source plane and the time-domain propagation kernel at each wavenumber. By discretizing the time convolutions directly, the reconstruction can be carried out iteratively in the time domain, thus providing the advantage of continuously reconstructing time-dependent pressure signals. In the reconstruction process, the Tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time-wavenumber spectrum on the virtual source plane. Because the double infinite integral of the two-dimensional spatial Fourier transform is discretized directly in the wavenumber domain in the proposed method, it does not need to perform the two-dimensional spatial fast Fourier transform that is generally used in time domain holography and real-time near-field acoustic holography, and therefore it avoids some errors associated with the two-dimensional spatial fast Fourier transform in theory and makes possible to use an irregular microphone array. The feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers. [ABSTRACT FROM AUTHOR]

A number of sound field separation techniques have been proposed for different purposes. However, these techniques just consider the separation of sound fields in the space domain and are restricted to stationary sound fields. When the sound fields are nonstationary, it is also necessary to perform the separation in the time domain. Therefore, on the basis of the propagation principle of sound pressure in the time-wavenumber domain, a nonstationary sound field separation technique with two closely spaced parallel measurement surfaces is proposed. It can separate the nonstationary signals generated by the primary sources in both time and space domains when the disturbing sources exist on the other side of the measurement plane. The signals in time and space domains are separated by using the spatial Fourier transform method and the time domain deconvolution method. A simulation involving two monopoles driven by nonstationary signals demonstrates that the method proposed can remove the influence of disturbing sources in both time and space domains. The feasibility of this method is also demonstrated by an experiment with two loudspeakers located on two sides of measurement planes. Additionally, to comment more objectively on the separation results, some indicators are computed in both the simulation and experiment. [ABSTRACT FROM AUTHOR]

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method (ESM) is proposed to reconstruct transient acoustic fields directly in the time domain. Since the equivalent source strengths solved by the traditional time-domain ESM formulation cannot be used to reconstruct the pressure on the source surface directly, an interpolation function is introduced to develop an interpolated time-domain ESM formulation which permits one to deduce an iterative reconstruction process. As the reconstruction process is ill-conditioned and especially there exists a cumulative effect of errors, the Tikhonov regularization is used to stabilize the process. Numerical examples of reconstructing transient acoustic fields from a baffled planar piston, an impulsively accelerating sphere and a cube box, respectively, demonstrate that the proposed method not only can effectively reconstruct transient acoustic fields in the time domain, but also can visualize acoustic fields in the space domain. And, in the first numerical example, the cumulative effect of errors and the validity of using the Tikhonov regularization to suppress the errors are described. [ABSTRACT FROM AUTHOR]

The study of acoustic radiation from spherical sound sources plays a crucial role in understanding the thermoviscous effects in practical acoustic problems. However, finding a general solution of acoustic radiation from spherical sound sources in thermoviscous fluids remains a formidable challenge. To advance this issue, an analytical method is developed in this paper to calculate the acoustic field radiated by spherical sound sources with the isothermal boundary condition and arbitrary velocity boundary condition. The developed method is utilized to present the solutions of the acoustic field generated by an oscillating sphere and a general spherical sound source, and the accuracy and validity of these solutions are verified through analytical and numerical methods., (© 2024 Acoustical Society of America.)

The compressive-equivalent source method (C-ESM) can reconstruct the sound field radiated by sparsely distributed sound sources with a reduced number of sensors. To ensure the performance of the C-ESM, the transfer matrix between the sensors and equivalent point sources should exhibit sufficient incoherence. Given that the configuration of the sensor array affects this incoherence condition, concern regarding the sensor array design would arise. To address such concern, this paper proposes a sensor array design approach. The primary objective of this approach is to minimize the mean coherence of the transfer matrix within the developed iterative framework, providing the incoherence condition required by the C-ESM. Subsequently, the designed sensor array is utilized by the C-ESM for the reconstructions. The effectiveness and practicality of the proposed approach are validated through numerical simulations and experiments., (© 2024 Acoustical Society of America.)

Numerical instability is an important issue that should be addressed in the time-domain equivalent source method (TESM). This study proposes a multistep method to stabilize TESM when using the measured acoustic pressure data to optimize equivalent source strengths. Unlike the conventional single-step method that solves each time step in the time-marching process of TESM, the proposed method performs a one-time solution for several time steps. The multistep solution can potentially reduce the accumulation rate of error, and improves filtering effects by changing the structure of the matrix that needs to be inverted when the truncated singular value decomposition or Tikhonov regularization is used in the time-marching process. Numerical simulations with three examples demonstrate the effectiveness of the multistep method in improving the stability of solutions compared with the single-step method. Effects of the number of merged time steps on the solutions are also discussed to guide the selection process. Finally, the sensitivity of the multistep method to numerical parameters is investigated to demonstrate its consistency under different configurations of numerical parameters.

This paper examines the feasibility of extracting the non-stationary sound field generated by a target source in the presence of disturbing source from single layer pressure-velocity measurements. Unlike the method described in a previous paper [Bi, Geng, and Zhang, J. Acoust. Soc. Am. 135(6), 3474-3482 (2014)], the proposed method allows measurements of pressure and particle velocity signals on a single plane instead of pressure signals on two planes, and the time-dependent pressure generated by the target source is extracted by a simple superposition of the measured pressure and the convolution between the measured particle velocity and the corresponding impulse response function. Because the particle velocity here is measured directly, the error caused by the finite difference approximation can be avoided, which makes it possible to perform the separation better than the previous method. In this paper, a Microflown pressure-velocity probe is used to perform the experimental measurements, and the calibration procedure of the probe in the time domain is given. The experimental results demonstrate that the proposed method is effective in extracting the desired non-stationary sound field generated by the target source from the mixed one in both time and space domains, and it obtains more accurate results than the previous method.

Planar near-field acoustic holography has been successfully extended to reconstruct the sound field in a moving medium, however, the reconstructed field still contains the convection effect that might lead to the wrong identification of sound sources. In order to accurately identify sound sources in a moving medium, a time-domain equivalent source method is developed. In the method, the real source is replaced by a series of time-domain equivalent sources whose strengths are solved iteratively by utilizing the measured pressure and the known convective time-domain Green's function, and time averaging is used to reduce the instability in the iterative solving process. Since these solved equivalent source strengths are independent of the convection effect, they can be used not only to identify sound sources but also to model sound radiations in both moving and static media. Numerical simulations are performed to investigate the influence of noise on the solved equivalent source strengths and the effect of time averaging on reducing the instability, and to demonstrate the advantages of the proposed method on the source identification and sound radiation modeling.

To extract the desired non-stationary sound field generated by a target source in the presence of disturbing sources, a real-time sound field separation method with pressure and particle acceleration measurements is proposed. In this method, the pressure and particle acceleration signals at a time instant are first measured on one measurement plane, where the particle acceleration is obtained by the finite difference approximation with the aid of an auxiliary measurement plane; then, the desired pressure signal generated by the target source at the same time instant can be extracted in a timely manner, by a simple superposition of the measured pressure and the convolution between the measured particle acceleration and the derived impulse response function. Thereby, the proposed method possesses a significant feature of real-time separation of non-stationary sound fields, which provides the potential to in situ analyze the radiation characteristics of a non-stationary source. The proposed method was examined through numerical simulation and experiment. Results demonstrated that the proposed method can not only extract the desired time-evolving pressure signal generated by the target source at any space point, but can also obtain the desired spatial distribution of the pressure field generated by the target source at any time instant.

Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method (ESM) is proposed to reconstruct transient acoustic fields directly in the time domain. Since the equivalent source strengths solved by the traditional time-domain ESM formulation cannot be used to reconstruct the pressure on the source surface directly, an interpolation function is introduced to develop an interpolated time-domain ESM formulation which permits one to deduce an iterative reconstruction process. As the reconstruction process is ill-conditioned and especially there exists a cumulative effect of errors, the Tikhonov regularization is used to stabilize the process. Numerical examples of reconstructing transient acoustic fields from a baffled planar piston, an impulsively accelerating sphere and a cube box, respectively, demonstrate that the proposed method not only can effectively reconstruct transient acoustic fields in the time domain, but also can visualize acoustic fields in the space domain. And, in the first numerical example, the cumulative effect of errors and the validity of using the Tikhonov regularization to suppress the errors are described., (© 2011 Acoustical Society of America)