Reconstruction Of Acoustic Field Research Articles

Method and apparatus for reconstructing and acoustic field

Acoustic field reconstruction is performed by expanding basis function which represent outgoing and incoming waves, without prior knowledge of the source geometry and dimensions. The reconstruction is based on acoustic pressures measured in the field only, and can be accomplished on a piece-wise basis. There are no restrictions on the locations of measurements. Moreover, the present invention can be used to reconstruct acoustic radiation from a plurality of sources or from a single source surrounded by multiple reflecting surfaces.

Development and validation of a computational process for pass-by noise simulation

The Indirect Boundary Element Analysis is employed for developing a computational pass-by noise simulation capability. An acoustic field reconstruction process is developed in order to generate the definition of the main pass-by noise sources in a numerical model. Numerical boundary element models that characterise the individual sources are combined with a vehicle model for developing a system model for pass-by noise simulation. The numerical algorithm for defining generic sources is validated initially by employing analytical solutions. The numerical techniques are also validated through comparison between numerical results and test data for component level and system level analyses. Specifically, the generic source definition capability is validated by comparing the actual and the computationally reconstructed acoustic field for an engine intake manifold. The overall pass-by noise simulation capability is validated by computing the maximum overall sound pressure level for a vehicle under two different ...

On the sampling conditions for reconstruction of an acoustic field from a finite sound source.

A simple and accurate method for the estimation of ultrasonic transducer fields is developed. In the method, the angular spectrum is employed to evaluate the three-dimensional propagation from a measured plane to an arbitrary parallel plane. The implementation uses a discrete convolution that is described in detail. Relative to conventional spatial-frequency representations, the implementation of the angular spectrum method in this paper has the advantage of being free from artifacts, enabling sample spacing to be greater than one half wavelength, using memory efficiently, and interpolating the measured data. The loosened sampling requirement and natural interpolation of the method permit efficient reconstruction of the full three-dimensional acoustic field from a coarse sound pressure measurement on single plane.

Visualization of acoustic radiation from a vibrating bowling ball.

This paper presents visualization of acoustic radiation from a vibrating bowling ball using the Helmholtz equation least squares (HELS) method. In conducting the experiments, the ball is excited by a vibration shaker using stationary random signals. The radiated acoustic pressures are measured using two microphones and taken as input to the HELS formulations. The reconstructed acoustic pressures on the bowling ball surface are compared with those measured at the same locations. Also shown are comparisons of the reconstructed and measured acoustic pressure spectra at various locations on the bowling ball surface. Results demonstrate that the accuracy of reconstruction based on measurements over a conformal surface is much higher than that over a finite planar surface. This is because the latter often extends beyond the near-field region, making the accuracy of measurements inconsistent. Nevertheless, satisfactory reconstruction of acoustic pressure fields over the entire bowling ball surface can still be obtained based on the measurements taken over a finite planar surface on one side of the source. In a similar manner, the normal component of the surface velocity is reconstructed. Once these acoustic quantities are determined, the time-averaged acoustic intensity is calculated. Also presented are the formulations for estimating a priori the numbers of expansion functions and measurements required by the HELS method and the guidelines for determining the reconstruction error and optimum measurement locations, given the overall dimensions of the source and the highest frequency of interest in reconstruction.

Development and validation of a computational process for pass-by noise simulation

The indirect boundary-element analysis is employed for developing a computational pass-by noise simulation capability. An acoustic field reconstruction process is developed in order to generate the definition of the main pass-by noise sources in a computational model. Numerical boundary-element models that characterize the individual sources are combined in order to develop a system model for the pass-by noise simulation. The acoustic field reconstruction process is validated initially by employing analytical solutions. The numerical techniques are also validated through comparison between numerical results and test data for component-level and system-level analyses. Specially, the source definition capability is validated by comparing the actual and the computationally reconstructed acoustic field for an engine intake manifold. The overall pass-by noise simulation capability is validated by computing the maximum overall sound-pressure level for a vehicle under two different driving conditions. [Research supported by the Ford University Research Program.]

A computational acoustic field reconstruction process based on an indirect boundary element formulation

The objective of the work presented in this paper is to develop a computational capability based on the indirect boundary element method (IBEM) for evaluating appropriate velocity boundary conditions on an assembly of piston type sources in order to recreate a prescribed acoustic field. Information for the acoustic pressure of the original acoustic field at certain field points constitutes the input to the developed process. The velocities on the piston type sources are computed from transfer functions evaluated between the field points where the acoustic pressure of the original field is prescribed and the velocity boundary condition on each element of the generic source. The IBEM is employed for computing the transfer functions in order to accommodate the presence of openings in the model and radiation from both sides of the piston type sources. Simulating the generic source as a thin surface that radiates from both sides eliminates the presence of irregular frequencies in the analysis. A singular value decomposition (SVD) solver is integrated with the IBEM computations in order to evaluate the velocity boundary conditions from the transfer functions. The number of field points where the acoustic pressure is defined can be considerably smaller than the number of elements where the velocity is computed. The solution that demonstrates the smallest magnitude is selected from all possible solutions. An algorithm is also developed for identifying the optimum field points where the acoustic pressure of the original field must be prescribed. The optimum field points are selected from a set of prescribed candidate points. The number of optimum points is considered smaller than the number of elements where the velocity is computed. The properties of the transformation matrix and the quality of the reconstruction depend on the location of the field points. Thus, the selection of the optimum points is based on achieving the highest possible orthogonality among the vectors that comprise the range of the transformation matrix. Several validation and application cases are presented.

On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method

This paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general, three-dimensional complex vibrating structure using the Helmholtz equation least-squares (HELS) method. The structure under consideration emulates a full-size four-cylinder engine. To simulate sound radiation from a vibrating structure, harmonic excitations are assumed to act on arbitrarily selected surfaces. The resulting vibration responses are solved by the commercial FEM (finite element method) software I-DEAS. Once the normal component of the surface velocity distribution is determined, the surface acoustic pressures are calculated using standard boundary element method (BEM) codes. The radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the Helmholtz integral formulation. These field pressures are taken as the input to the HELS formulation to reconstruct acoustic pressures on the entire source surface, as well as in the field. The reconstructed acoustic pressures thus obtained are then compared with benchmark values. Numerical results demonstrate that good agreements can be obtained with relatively few expansion functions. The HELS method is shown to be very effective in the low-to-mid frequency regime, and can potentially become a powerful noise diagnostic tool.

A computational acoustic field reconstruction process based on an indirect variational boundary element formulation

The objective of this work is to develop a computational capability based on the indirect variational boundary element method (IVBEM) to evaluate appropriate velocity boundary conditions on an assembly of piston-type sources such that they can recreate a prescribed acoustic field. Information for the acoustic pressure of the original acoustic field at certain field points constitutes the input to the developed process. Several new developments associated with the IVBEM are necessary for completing the field reconstruction process. The developed computational capability targets exterior radiation applications. Thus a new formulation for treating irregular frequencies in the IVBEM is developed and implemented in the field reconstruction process. The computation of the appropriate velocities for the piston-type sources is based on deriving transfer functions between the field points, where the acoustic pressure of the original field is prescribed, and the velocity assigned on each element of the generic source. A singular value decomposition solver is integrated with the IVBEM computations in order to evaluate the velocity boundary conditions from the transfer functions. Finally, an algorithm that identifies the optimum field points from a set of candidate points for prescribing the acoustic pressure of the original field is developed. [Research supported by a University Research Program award from Ford Motor Co.]

Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method

This paper extends the Helmholtz equation least-squares (HELS) method previously developed by Wang and Wu [J. Acoust. Soc. Am. 102, 2020–2032 (1997)] to reconstruction of acoustic pressure fields inside the cavity of a vibrating object. The acoustic pressures are reconstructed through an expansion of the acoustic modes generated by the Gram–Schmidt orthonormalization with respect to the particular solutions to the Helmholtz equation. Such an expansion is uniformly convergent because the selected acoustic modes consist of a uniformly convergent series of Legendre functions. The coefficients associated with these acoustic modes are determined by requiring the assumed-form solution to satisfy the pressure boundary condition at the measurement points. The errors incurred in this process are minimized by the least-squares method. Numerical examples of partially vibrating spheres and cylinders with various half-length to radius aspect ratios subject to different frequency excitations are demonstrated. The reconstructed acoustic pressures are compared with the analytic solutions and numerical ones obtained by using the standard boundary element method (BEM) codes.

On reconstruction of acoustic pressure fields using the HELS method

The Helmholtz equation-least squares (HELS) method was recently developed by Wang and Wu [J. Acoust. Soc. Am. 102, 2020–2032 (1997)] to reconstruct the acoustic pressures generated by an arbitrary vibrating structure. In this method the acoustic pressures are expressed in terms of an expansion of ‘‘acoustic modes.’’ The coefficients associated with these acoustic modes are determined by requiring the assumed-form solution to satisfy the pressure boundary condition at measurement points. The errors incurred in this process are minimized by the least-squares method. The advantages of this method are that (1) acoustic pressures can be reconstructed over the entire surface; (2) solutions thus obtained are unique; and (3) efficiency of numerical computation is high, because the number of measurements is determined by that of expansion terms, which is small when a right coordinate system is selected for a particular source geometry under consideration. Such an approach is applicable to both exterior and interior regions. For exterior problems, the reconstructed acoustic pressures can be accurate when the points fall outside the minimum circumscribing spheroidal surface which encloses the vibrating surface, but approximate when they are inside. For interior problems, the accuracy of reconstruction is high because the entire region is inside the minimum circumscribing spheroidal surface. In both cases, the accuracy of reconstruction is limited by excitation frequencies, which is inherent in all expansion theories. [Work supported by NSF.]

Tomographic reconstruction of transient acoustic fields recorded by pulsed TV holography

Pulsed TV holography combined with computerized tomography (CT) are used to evaluate the three-dimensional distribution of transient acoustic fields in air. Experiments are performed with an electrical discharge between two electrodes as the sound source. Holograms from several directions of the acoustic field are recorded directly onto a CCD detector by use of a double-pulsed ruby laser as the light source. Phase maps, representing projections of the acoustic field, are evaluated quantitatively from the recorded holograms. The projections are used for the CT reconstruction to evaluate the pressure-field distribution in any cross section of the measured volume of air.

Reconstruction of acoustic pressure fields inside a vibrating cavity

The Helmholtz equation–least-squares (HELS) method developed by Wang and Wu [J. Acoust. Soc. Am. (to be published)] is extended to reconstruction of acoustic pressure fields inside a vibrating cavity. In this method, the acoustic pressures are reconstructed through an expansion of acoustic modes, or a set of independent functions generated via an orthonormalization with respect to the particular solutions to the Helmholtz equation on the particular surface under consideration. The coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points. The errors incurred in this process are minimized by the least-squares method. Numerical examples of partially vibrating spheres and cylinders with various half-length to radius ratios and dimensionless frequencies are demonstrated. The results thus obtained are compared with the numerical solutions obtained by using a direct boundary-element method (BEM). Results show that the HELS method enables one to reconstruct the radiated acoustic pressure fields much more effectively and accurately than BEM does. [Work supported by the Institute for Manufacturing Research at Wayne State University.]

Measurement of the acoustic intensity in the nearfield of a fluid-loaded, point-driven cylinder using nonplanar nearfield acoustical holography

Nearfield acoustical holography (NAH) is confined to the reconstruction of acoustic fields in parallel planes with a hologram consisting of a measurement of the acoustic pressure over a plane boundary. Although ideal for planar sources, such as vibrating plates, NAH encounters problems in dealing with nonplanar sources. Therefore, we have modified the technique to apply specifically to a cylindrical geometry with a hologram comprising a cylindrical contour. The cylindrical hologram consists of the measurement of the amplitude and phase of the pressure field at 4096 points on this cylindrical contour. This contour is located close, and concentric with, a radiating cylindrical source (in this case a finite, point-driven cylindrical shell submerged in our underwater tank facility). We show how this hologram is processed in a rigorous manner to map the pressure, vector velocity, and vector intensity (real and reactive components) from the surface of the source into the farfield. The vector intensity maps are shown to be helpful, in many cases, in identifying the location of the point driver attached inside the shell. Both the active and reactive intensity fields will be shown. Since the vector velocity is also obtained from the cylindrical hologram, we can identify the radial mode shape of vibration from the radial velocity component at the shell surface, and along with the reconstructed surface pressure (which provides the fluid loading) we can also map the surface intensity. This latter quantity is used to compute the total power radiated by this mode shape. This new technique provides a comprehensive method to study radiation from cylinders.

Bi-Dynamic Reverberation and Acoustic Field Reconstruction

A signal that is generated by a moving source is spatially encoded by both the angular dependent Doppler shift in frequency and the angular dependent beam patterns of the transmitter. This information is preserved in the resulting reverberation and it has been theorized [R. Halley, “An Application of the Analysis of Reverberation from a Remote Pinging Searchlight Sonar,” TM 262, Navy Electron. Lab., San Diego, Calif. (1957)] that it can be recovered by means of a spectral analysis of the reverberation that is collected by an arbitrarily positioned receiver. To investigate this theory a bi-dynamic model of reverberation has been developed that is based on the Poisson distributed discrete scatterer model of Faure, Olshevski, and Middleton. The correlation function of the reverberation field was developed for various cases and the corresponding time-dependent power spectra have been computed. Certain of these results have been compared with data that were collected at sea.