This paper presents a reduced-order approach to near-field acoustical holography (NAH) that allows the user to account for sound fields generated by multiple spatially separated sources. In this method, an equivalent wave model (EWM) of a given field is formulated to include combinations of planar, cylindrical, spherical, or other elementary wave functions in contrast to an EWM restricted to a single separable coordinate system. This can alleviate the need for higher-order functions, reduce the number of measurements, and decrease error. The statistically optimized near-field acoustical holography (SONAH) algorithm is utilized to perform the NAH projection after the formulation of the multisource EWM. The combined process is called multisource statistically optimized near-field acoustical holography (M-SONAH). This method is used to reconstruct simulated sound fields generated by combinations of a vibrating piston in a sphere and linear arrays of monopole sources. It is shown that M-SONAH can reconstruct near-field pressures in multisource environments with lower errors and fewer measurements than a strictly plane or cylindrical-wave formulation using the same simulated measurement.
References
1.
Antoni
, J.
(2012
). “A Bayesian approach to sound-source reconstruction: Optimal basis, regularization, and focusing
,” J. Acoust. Soc. Am.
131
(4
), 2873
–2890
.2.
Bai
, M. R.
(1992
). “Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries
,” J. Acoust. Soc. Am.
92
(1
), 533
–549
.3.
Cho
, Y. T.
, Bolton
, J. S.
, and Hald
, J.
(2005
). “Source visualization by using statistically optimized near-field acoustical holography in cylindrical coordinates
,” J. Acoust. Soc. Am.
118
, 2355
–2364
.4.
Fahy
, F.
, and Gardonio
, P.
(2007a
). Sound and Structural Vibration: Radiation, Transmission and Response
(Academic Press in an imprint of Elsevier
, Oxford, UK
), pp. 503
–515
.5.
Fahy
, F.
, and Gardonio
, P.
(2007b
). Sound and Structural Vibration: Radiation, Transmission and Response
(Academic Press in an imprint of Elsevier
, Oxford, UK
), pp. 227
–240
.6.
Gomes
, J.
, Jacobsen
, F.
, and Bach-Andersen
, M.
(2007
). “Statistically optimized near field acoustic holography and the Helmholtz equation least squares method: A comparison
,” in Proceedings of the 8th International Conference on Theoretical and Computational Acoustics
, July 2–5, 2007, Heraklion, Greece
.7.
Hald
, J.
(1989
). “STSF—A unique technique for scan-based Near-field Acoustic Holography without restrictions on coherence
,” Technical Report No. 1
, from Bruel & Kjaer, Naerum, Denmark.8.
Hald
, J.
(2005
). “An integrated NAH/beamforming solution for efficient broad-band noise source location
,” SAE Technical paper 2005-01-2537
.9.
Hald
, J.
(2006
). “Patch holography in cabin environments using a two-layer handheld array with an extended SONAH algorithm
,” in Proceedings of EuroNoise 2006
, Tampere, Finland
.10.
Hald
, J.
(2009
). “Basic theory and properties of statistically optimized near-field acoustical holography
,” J. Acoust. Soc. Am.
125
, 2105
–2120
.11.
Hald
, J.
(2014
). “Scaling of plane-wave functions in statistically optimized near-field acoustic holography
,” J. Acoust. Soc. Am.
136
(5
), 2687
–2696
.12.
Hart
, D. M.
, Neilsen
, T. B.
, Gee
, K. L.
, and James
, M. M.
(2013
). “A Bayesian based equivalent sound source model for a military jet aircraft
,” Proc. Mtg. Acoust.
19
, 055094
.13.
Huang
, Y.
(1990
). “Computer techniques for three-dimensional source radiation
,” Ph.D. dissertation, Pennsylvania State University
.14.
Jacobsen
, F.
, Chen
, X.
, and Jaud
, V.
(2008
). “A comparison of statistically optimized near field acoustic holography using single layer pressure-velocity measurements and using double layer pressure measurements (L)
,” J. Acoust. Soc. Am.
123
(4
), 1842
–1845
.15.
Koopmann
, G. H.
, and Benner
, H.
(1982
). “Method for computing the sound power of machines based on the Helmholtz integral
,” J. Acoust. Soc. Am.
71
, 78
–89
.16.
Koopmann
, G. H.
, Song
, L.
, and Fahnline
, J. B.
(1989
). “A method for computing acoustic fields based on the principle of wave superposition
,” J. Acoust. Soc. Am.
86
, 2433
–2438
.17.
Lee
, M.
, and Bolton
, J. S.
(2006
). “Scan-based near-field acoustical holography and partial field decomposition in the presence of noise and source level variation
,” J. Acoust. Soc. Am.
119
(1
), 382
–393
.18.
Maynard
, J. D.
, Williams
, E. G.
, and Lee
, Y.
(1985
). “Near field acoustic holography: 1. Theory of generalized holography and the development of NAH
,” J. Acoust. Soc. Am.
78
, 1395
–1413
.19.
Mollo-Christensen
, E.
(1967
). “Jet noise and shear flow instability seen from an experimenter's viewpoint
,” J. Appl. Mech.
34
, 1
–7
.20.
Moon
, T. K.
, and Stirling
, W. C.
(2000
). Mathematical Methods and Algorithms for Signal Processing
(Prentice Hall
, New York)
, pp. 139
and 183
.21.
Morgan
, J.
, Gee
, K. L.
, Neilsen
, T. B.
, and Wall
, A. T.
(2012
). “Simple-source model of military jet aircraft noise
,” Noise Control Eng. J.
60
, 435
–449
.22.
Morse
, P. M.
, and Ingard
, K. U.
(1968
). Theoretical Acoustics
(Princeton University Press
, Princeton, NJ
), pp. 332
–346
.23.
Rayess
, N.
, and Wu
, S. F.
(2000
). “Experimental validations of the HELS method for reconstructing acoustic radiation from a complex vibrating structure
,” J. Acoust. Soc. Am.
107
, 2955
–2964
.24.
Sarkissian
, A.
(2005
). “Method of superposition applied to patch near-field acoustic holography
,” J. Acoust. Soc. Am.
118
(2
), 671
–678
.25.
Semenova
, T.
, and Wu
, S. F.
(2005
). “On the choice of expansion functions in the Helmholtz equation least-squares method
,” J. Acoust. Soc. Am.
117
, 701
–710
.26.
Shah
, P. N.
, Vold
, H.
, and Yang
, M.
(2011
). “Reconstruction of far-field noise using multireference acoustical holography measurements of high-speed jets
,” AIAA Paper 2011-2772, Portland, OR.27.
Steiner
, R.
, and Hald
, J.
(2001
). “Near-field acoustical holography without the errors and limitations caused by the use of spatial DFT
,” Int. J. Sound Vib.
6
, 83
–89
.28.
Tam
, C. K. W.
, Viswanathan
, K.
, Pastouchenko
, N. N.
, and Tam
, B.
(2010
). “Continuation of the near acoustic field of a jet to the far field. Part II: Experimental validation and noise source characteristics
,” AIAA Paper 2010-3729, Stockholm, Sweden.29.
Tamura
, M.
(1990
). “Spatial Fourier transform method of measuring reflection coefficients at oblique incidence. I: Theory and numerical examples
,” J. Acoust. Soc. Am.
88
, 2259
–2264
.30.
Van Veen
, B. D.
, and Buckley
, K. M.
(1988
). “Beamforming: A versatile approach to spatial filtering
,” IEEE ASSP Magazine, pp. 4
–24
.31.
Veronesi
, W. A.
, and Maynard
, J. D.
(1989
). “Digital holographic reconstruction of sources with arbitrarily shaped surfaces
,” J. Acoust. Soc. Am.
85
, 588
–598
.32.
Wall
A. T.
(2013
). “The characterization of military aircraft jet noise using near-field acoustical holography methods
,” Ph.D. dissertation, Brigham Young University
.33.
Wall
, A. T.
, Gee
, K. L.
, and Neilsen
, T. B.
(2013a
). “Modified statistically optimized near-field acoustical holography for jet noise characterization
,” Proc. Mtg. Acoust.
19
, 055013
.34.
Wall
, A. T.
, Gee
, K. L.
, Neilsen
, T. B.
, and James
, M. M.
(2013b
). “Acoustical holography imaging of full-scale jet noise fields
,” in Proceedings of Noise-Con 2013
.35.
Wall
, A. T.
, Gee
, K. L.
, Neilsen
, T. B.
, Krueger
, D. W.
, James
, M. M.
, Sommerfeldt
, S. D.
, and Blotter
, J. D.
(2012
). “Full-scale jet noise characterization using scan-based acoustical holography
,” AIAA Paper 2012-2081, Colorado Springs, CO.36.
Wang
, Z.
, and Wu
, S. F.
(1997
). “Helmholtz equation–least-squares method for reconstructing the acoustic pressure field
,” J. Acoust. Soc. Am.
102
, 2020
–2032
.37.
Weinrich
, G.
, and Arnold
, E. B.
(1980
). “Method for measuring acoustic radiation fields
,” J. Acoust. Soc. Am.
68
(2
), 404
–411
.38.
Williams
, E. G.
(1999
). Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
(Academic Press
, San Diego, CA
), pp. 149
–182
.39.
Williams
, E. G.
(2001
). “Regularization methods for near-field acoustical holography
,” J. Acoust. Soc. Am.
110
, 1976
–1988
.40.
Williams
, E. G.
(2003
). “Continuation of acoustic near-fields
,” J. Acoust. Soc. Am.
113
, 1273
–1281
.41.
Wu
, S. F.
(2000
). “On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method
,” J. Acoust. Soc. Am.
107
, 2511
–2522
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