An acoustic imaging algorithm is proposed herein for transient noise source time reconstruction. Time domain formulations are not well suited for acoustic imaging because of the size of the resulting system to be inversed. Based on the phase coherence principle widely used in ultrasound imaging and image processing, the first step of the algorithm consists in proposing the phase coherence metric used to reject pixels that are unlikely to contribute to the radiated sound field. This translates in a reduction of the domain size and ill-posedness of the problem. In the second step, the inverse problem is solved using the Tikhonov regularization and the generalized cross-validation to extract the vibration field on the imaging domain. Two test cases are considered: a simulated baffled piston and a panel submitted to a mechanical impact in anechoic conditions. The actual vibration field of the panel is measured with an optical technique for reference. In both numerical and experimental cases, the reconstructed vibration field using the proposed approach compares well with their respective reference. The results confirm that transient excitations can be localized and quantified with the proposed approach, in contrast with the classical time-domain beamforming that dramatically overestimates its magnitude.

1.
H.
Krim
and
M.
Viberg
, “
Two decades of array signal processing research: The parametric approach
,”
IEEE Signal Process. Mag.
13
,
67
94
(
1996
).
2.
F.
Fahy
,
Sound Intensity
, 2nd ed. (
The Spon Press
,
London
,
1989
), pp.
38
99
.
3.
J. J.
Christensen
and
J.
Hald
,
Beamforming
(
Brüel & Kjaer
,
Naerum, Denmark
,
2004
), pp.
1
23
.
4.
Q.
Leclère
,
A.
Pereira
,
C.
Bailly
,
J.
Antoni
, and
C.
Picard
, “
A unified formalism for acoustic imaging based on microphone array measurements
,”
Int. J. Aeroacoust.
16
(
4–5
),
431
456
(
2017
).
5.
J.-M.
Attendu
and
A.
Ross
, “
Sparse regularization for reconstructing transient sources with time domain nearfield acoustical holography
,”
J. Acoust. Soc. Am.
143
(
6
),
3796
3806
(
2018
).
6.
X.-Z.
Zhang
,
C.-X.
Bi
,
Y.-B.
Zhang
, and
L.
Xu
, “
Transient nearfield acoustic holography based on an interpolated time-domain equivalent source method
,”
J. Acoust. Soc. Am.
130
(
3
),
1430
1440
(
2011
).
7.
M.
Fink
, “
Time-reversal acoustics
,”
J. Phys. Conf. Ser.
118
(
1
),
012001
(
2008
).
8.
D. H.
Johnson
and
D. E.
Dudgeon
,
Array Signal Processing—Concepts and Techniques
, 1st ed. (
Prentice Hall, Upper Saddle River, NJ
,
1993
), pp.
157
182
.
9.
G.
Chardon
,
L.
Daudet
,
A.
Peillot
,
F.
Ollivier
,
N.
Bertin
, and
R.
Gribonval
, “
Near-field acoustic holography using sparse regularization and compressive sampling principles
,”
J. Acoust. Soc. Am.
132
(
3
),
1521
1534
(
2012
).
10.
D. A.
Bies
,
C.
Hansen
, and
C.
Howard
,
Engineering Noise Control
(
CRC Press
,
Boca Raton, FL
,
2010
),
826
pp.
11.
I.
Rakotoarisoa
,
J.
Fischer
,
V.
Valeau
,
D.
Marx
,
C.
Prax
, and
L.-E.
Brizzi
, “
Time-domain delay-and-sum beamforming for time-reversal detection of intermittent acoustic sources in flows
,”
J. Acoust. Soc. Am.
136
(
5
),
2675
2686
(
2014
).
12.
A. V.
Oppenheim
and
J. S.
Lim
, “
Importance of Phase in Signals
,”
Proc. IEEE
69
(
5
),
529
541
(
1980
).
13.
P.
Kovesi
, “
Phase congruency: A low-level image invariant
,”
Psychol. Res.
64
(
2
),
136
148
(
2000
).
14.
Y.
Shechtman
,
Y. C.
Eldar
,
O.
Cohen
,
H. N.
Chapman
,
J.
Miao
, and
M.
Segev
, “
Phase retrieval with application to optical imaging: A contemporary overview
,”
IEEE Signal Process. Mag.
32
(
3
),
87
109
(
2015
).
15.
C.
Fritsch
,
J.
Camacho
, and
M.
Parrilla
, “
New ultrasound imaging techniques with phase coherence processing
,”
Ultrasonics
50
(
2
),
122
126
(
2010
).
16.
J.
Camacho
and
C.
Fritsch
, “
Phase coherence imaging of grained materials
,”
IEEE Trans. Ultrason., Ferroelec., Freq. Control
58
(
5
),
1006
1015
(
2011
).
17.
J. F.
Cruza
,
J.
Camacho
, and
C.
Fritsch
, “
Plane-wave phase-coherence imaging for NDE
,”
NDT E Int.
87
,
31
37
(
2017
).
18.
N.
Quaegebeur
,
T.
Padois
,
P.
Gauthier
, and
P.
Masson
, “
Enhancement of time-domain acoustic imaging based on generalized cross-correlation and spatial weighting
,”
Mech. Syst. Signal Process.
75
,
515
524
(
2016
).
19.
V. P.
Minotto
,
C. R.
Jung
,
L. G.
da Silveira
, Jr.
, and
B.
Lee
, “
GPU-based approaches for real-time sound source localization using the SRP-PHAT algorithm
,”
Int. J. High Perform. Comp. Appl.
27
(
3
),
291
306
(
2012
).
20.
M.
Bilodeau
,
N.
Quaegebeur
,
A.
Berry
, and
P.
Masson
, “
Phase coherence imaging of vibroacoustic sources
,” in
Proceedings of the 7th Berlin Beamforming Conference
(
2018
), pp.
1
11
.
21.
T.
Padois
,
O.
Doutres
,
F.
Sgard
, and
A.
Berry
, “
Time domain localization technique with sparsity constraint for imaging acoustic sources
,”
Mech. Sys. Signal Process.
94
,
85
93
(
2017
).
22.
P.
Nelson
and
S.
Yoon
, “
Estimation of acoustic source strength by inverse methods: Part I, Conditioning of the inverse problem
,”
J. Sound Vib.
233
(
4
),
639
664
(
2000
).
23.
S.
Yoon
and
P.
Nelson
, “
Estimation of acoustic source strength by inverse methods: Part II, Experimental investigation of methods for choosing regularization parameters
,”
J. Sound Vib.
233
(
4
),
665
701
(
2000
).
24.
P. C.
Hansen
, “
Regularization tools version 4.0 for Matlab 7.3
,”
Numerical Algorithms
46
,
189
194
(
2007
).
25.
B. R.
Treeby
and
B. T.
Cox
, “
k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields
,”
J. Biomed. Opt.
15
(
2
),
021314
(
2010
).
26.
O.
Robin
,
J.-D.
Chazot
,
R.
Boulandet
,
M.
Michau
,
A.
Berry
, and
N.
Atalla
, “
A plane and thin panel with representative simply supported boundary conditions for laboratory vibroacoustic tests
,”
Acta Acust. Acust.
102
(
1
),
170
182
(
2016
).
27.
A.
Giraudeau
,
F.
Pierron
, and
E. P.
Tomasini
, “
Measurement of vibrating plate spatial responses using deflectometry and high speed camera
,”
AIP Conf. Proc.
1253
,
241
246
(
2010
).
28.
P.
O'Donoughue
,
O.
Robin
, and
A.
Berry
, “
Time-resolved identification of mechanical loadings on plates using the virtual fields method and deflectometry measurements
,”
Strain
54
(
3
),
e12258
(
2018
).
29.
Y.
Liu
,
X.
Su
,
Q.
Zhang
,
P. K.
Rastogi
, and
E.
Hack
, “
Precision displacement measurement based on phase measuring deflectometry
,”
AIP Conf. Proc.
1236
,
459
463
(
2010
).
30.
P.
Donoughue
,
O.
Robin
, and
A.
Berry
, “
Measuring the vibration response of plane panels under stationary and transient mechanical excitations using deflectometry
,” in
Inter-Noise 2016
(
2016
), pp.
615
621
.
You do not currently have access to this content.