Time-frequency representations, like the spectrogram or the scalogram, are widely used to characterize dispersive waves. The resulting energy distributions, however, suffer from the uncertainty principle, which complicates the allocation of energy to individual propagation modes (especially when the dispersion curves of these modes are close to each other in the time-frequency domain). This research applies the chirplet as a tool to analyze dispersive wave signals based on a dispersion model. The chirplet transform, a generalization of both the wavelet and the short-time Fourier transform, enables the extraction of components of a signal with a particular instantaneous frequency and group delay. An adaptive algorithm identifies frequency regions for which quantitative statements can be made about an individual mode’s energy, and employs chirplets (locally adapted to a dispersion curve model) to extract the (proportional) energy distribution of that single mode from a multimode dispersive wave signal. The effectiveness of this algorithm is demonstrated on a multimode synthetic Lamb wave signal for which the ground-truth energy distribution is known for each mode. Finally, the robustness of this algorithm is demonstrated on real, experimentally measured Lamb wave signals by an adaption of a correlation technique developed in previous research.

1.
D. E.
Chimenti
, “
Guided waves in plates and their use in materials characterization
,”
Appl. Mech. Rev.
50
,
247
284
(
1997
).
2.
M.
Niethammer
,
L. J.
Jacobs
,
J.
Qu
, and
J.
Jarzynski
, “
Time-frequency representation of Lamb waves
,”
J. Acoust. Soc. Am.
109
,
1841
1847
(
2001
).
3.
S.
Hurlebaus
,
L.
Gaul
, and
L. J.
Jacobs
, “
Localization of a ‘synthetic’ acoustic emission source on the surface of a fatigue specimen
,”
Res. Nondestruct. Eval.
13
,
105
117
(
2001
).
4.
S.
Hurlebaus
,
M.
Niethammer
,
L. J.
Jacobs
, and
C.
Valle
, “
Automated methodology to locate notches with Lamb waves
,”
ARLO
2
,
97
102
(
2001
).
5.
S.
Mann
and
S.
Haykin
, “
The chirplet transform: A generalization of Gabor’s logon transform
,”
Vision Interface
91
,
205
212
(
1991
).
6.
R. G.
Baraniuk
and
D. L.
Jones
, “
Wigner-based formulation of the chirplet transform
,”
IEEE Trans. Signal Process.
44
,
3129
3135
(
1996
).
7.
S.
Mann
and
S.
Haykin
, “
The chirplet transform: Physical considerations
,”
IEEE Trans. Signal Process.
43
,
2745
2761
(
1995
).
8.
R.
Gribonval
, “
Fast matching pursuit with a multiscale dictionary of Gaussian chirps
,”
IEEE Trans. Signal Process.
49
,
994
1001
(
2001
).
9.
J.-C.
Hong
,
K. H.
Sun
, and
Y. Y.
Kim
, “
Dispersion-based short-time Fourier transform applied to dispersive wave analysis
,”
J. Acoust. Soc. Am.
117
,
2949
2960
(
2005
).
10.
R.
Benz
,
M.
Niethammer
,
S.
Hurlebaus
, and
L. J.
Jacobs
, “
Localization of notches with Lamb waves
,”
J. Acoust. Soc. Am.
114
,
677
685
(
2003
).
11.
O.
Kotte
,
M.
Niethammer
, and
L. J.
Jacobs
, “
Lamb wave characterization by differential reassignment and nonlinear anisotropic diffusion
,”
NDT & E Int.
39
,
96
105
(
2006
).
12.
S.
Mallat
,
A Wavelet Tour of Signal Processing
(
Academic
,
New York
,
1999
).
13.
L.
Cohen
,
Time-Frequency Analysis
(
Prentice-Hall
,
New Jersey
,
1995
).
14.

The Wigner-Ville distribution does not result in any smoothing of the time-frequency representation, but is not guaranteed to be positive and suffers from signal interferences.

15.
J. D.
Achenbach
,
Wave Propagation in Elastic Solids
(
Elsevier
,
New York
,
1973
).
16.
R. L.
Weaver
and
Y. H.
Pao
, “
Axisymmetric elastic waves excited by a point source in a plate
,”
Trans. ASME, J. Appl. Mech.
49
,
821
836
(
1982
).
17.
P.
Wilcox
, “
Modelling the excitation of Lamb and SH waves by point and line sources
,” in
Review of Progress in Quantitative Nondestructive Evaluation
, edited by
D. O.
Thompson
and
D. E.
Chimenti
,
AIP Conf. Proc.
(
AIP
,
New York
,
2004
), Vol.
23A
, pp.
206
213
.
18.
H.
Kuttig
, “
Model-based signal processing of dispersive waves with chirplets
,” Diplomarbeit thesis, Institute A for Mechanics,
University of Stuttgart
(
2005
).
19.
R.
Benz
, “
Localization of notches with Lamb waves
,” Master thesis,
School of Civil and Environmental Engineering
, Georgia Institute of Technology (
2002
).
You do not currently have access to this content.