Jean-Hugh Thomas

Real-time near-field acoustic holography for continuously visualizing nonstationary acoustic fields

Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.

Forward propagation of time evolving acoustic pressure: Formulation and investigation of the impulse response in time-wavenumber domain

The aim of this work is to continuously provide the acoustic pressure field radiated from nonstationary sources. From the acquisition in the nearfield of the sources of a planar acoustic field which fluctuates in time, the method gives instantaneous sound field with respect to time by convolving wavenumber spectra with impulse response and then inverse Fourier transforming into space for each time step. The quality of reconstruction depends on the impulse response which is composed of investigated parameters as transition frequency and propagation distance. Sampling frequency also affects errors of the practically discrete impulse response used for calculation. To avoid aliasing, the impulse response is low-pass filtered with Chebyshev or Kaiser-Bessel filter. Another approach to implement the impulse response consists of applying an inverse Fourier transform to the theoretical transfer function for propagation. To estimate the performance of each processing method, a simulation test involving several source monopoles driven by nonstationary signals is executed. Some indicators are proposed to assess the accuracy of the temporal signals predicted in a forward plane. The results show that the use of a Kaiser-Bessel filter numerically implemented or that of the inverse Fourier transform can provide the most accurate instantaneous acoustic signals.

Wavelet preprocessing for lessening truncation effects in nearfield acoustical holography

The goal of planar nearfield acoustical holography (NAH) is to recover the sound field at the sound source from pressure measurements made close to the source plane. The theory requires the pressure to be measured over a complete plane. Because experimentation consists of acquiring only a finite measurement aperture of the pressure field, it naturally causes erroneous values in the reconstructed field. Wavelet preprocessing applied to the pressure measurements in the nearfield provides a solution to lessen the effects due to the truncation of the hologram. The approach is based on a multiresolution analysis of the field from different wave number bands followed by selective spatial filtering of effects highlighted by the first analysis. Experimental results show the relevance of the method by comparison to standard NAH involving exponential filtering in the wave number domain. The computation of objective indicators based on distance measurements between wave number spectra and comparisons between pattern...

Reconstruction of nonstationary sound fields based on the time domain plane wave superposition method

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.

Separation of nonstationary sound fields in the time-wavenumber domain

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.

Patch near-field acoustic holography: Regularized extension and statistically optimized methods

The patch holography method allows one to make measurements on an extended structure using a small microphone array. Increased attention has been paid to the two techniques, which are quite different at first glance. One is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing. A singular value decomposition formulation of the latter is proposed in this paper. The similarity of the two techniques is shown here. Both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure. By using the Morozov discrepancy principle to compute the regularization parameter, the two methods lead to very close results.

On the statistical errors in the estimate of acoustical energy density by using two microphones in a one dimensional field

It was recently shown that the statistical errors of the measurement in the acoustic energy density by the two microphone method in waveguide have little variation when the losses of coherence between microphones increase. To explain these intervals of uncertainty, the variance of the measurement is expressed in this paper as a function of the various energy quantities of the acoustic fields--energy densities and sound intensities. The necessary conditions to reach the lower bound are clarified. The results obtained are illustrated by an example of a one-dimensional partially coherent field, which allows one to specify the relationship between the coherence functions of the pressure and particle velocity and those of the two microphone signals.

Experimental modal decomposition of acoustic field in cavitation tunnel with square duct section

The operational requirements for naval and research vessels have seen an increasing demand for quieter ships either to comply the ship operational requirements or to minimize the influence of shipping noise on marine life. To estimate the future radiated noise of a ship, scale measurements are realized in a tunnel. DGA Hydrodynamics owns its cavitation tunnel with low background noise which allows such measurements. Understanding acoustic propagation in cavitation tunnel remains a challenge. The success of an accurate acoustic measurement depends both on a realistic propagation model and also on an efficient control of acoustic sensor characteristics. This short communication presents the results of experiments performed in GTH (Large Cavitation Tunnel) at DGA Hydrodynamics. An acoustic source radiates pure sine wave in the test section entry and generates an acoustic field measured with flush mounted hydrophones. A modal decomposition is then performed to fit measurements. Complex amplitudes of all propa...

Instantaneous Bayesian regularization applied to real-time near-field acoustic holography

Real-time near-field acoustic holography (RT-NAH) is used to recover non-stationary sound sources using a planar microphone array. Direct propagation is described by the convolution of the wavenumber spectrum of the source under study with a known impulse response. The deconvolution operation is achieved by a singular value decomposition of the propagator and Tikhonov regularization is performed to stabilize the solution. The inverse problem has an innate ill-posed characteristic, and the regularization process is the key factor in obtaining acceptable results. The purpose of this paper is to present the instantaneous regularization process applied to RT-NAH method. Bayesian estimation of the regularization parameter is introduced from prior knowledge of the problem. The computation of the regularization parameter is updated for each block of constant time interval allowing one to take into account the fluctuating properties of the sound field. The superiority of Bayesian regularization, compared to state-of-the art methods, is observed numerically and experimentally for reconstruction of non-stationary sources. RT-NAH is also enhanced to allow the reconstruction of long signals. Updating the regularization parameter accordingly to the fluctuations of the SNR is revealed to be a necessary effort to reconstruct highly non-stationary sources.

Bayesian regularization applied to real-time near-field acoustic holography

Real-Time Near-field Acoustic Holography is used to recover non stationary acoustic sound sources using a planar microphone array. In the direct way, describing propagation requires the convolution of the spatial spectrum of the source under study with a known impulse response. When the convolution operator is replaced with a matrix product, the propagation operator is re-written in a Toeplitz matrix form. Solving the inverse problem is based on a Singular value decomposition of this propagator and Tikhonov regularization is used to stabilize the solution. The purpose here is to study the regularization process. The formulation of this problem in the Tikhonov sense estimates the solution from the knowledge of the propagation model, the measurements and the regularization parameter. This parameter is calculated by making a compromise between the fidelity to the real measured data and the fidelity to available a priori information. A new regularization parameter is introduced based on a Bayesian approach to maximize the information taken into account. Comparisons of the results are proposed, using the L-Curve and the generalized cross validation. The superiority of the Bayesian parameter is observed for the reconstruction of a non stationary experimental source using real-time near-field acoustic holography.