The U.S. Air Force seeks to improve lifecycle management of composite structures. Nondestructive characterization of damage is a key input to this framework. One approach to characterization is model-based inversion of ultrasound inspection data; however, the computational expense of simulating the response from damage represents a major hurdle for practicality. A surrogate forward model with greater computational efficiency and sufficient accuracy is, therefore, critical to enable damage characterization via model-based inversion. In this work, a surrogate model based on Gaussian process regression (GPR) is developed on the chirplet decomposition of the simulated quasi-shear scatter from delamination-like features that form a shadowed region within a representative composite layup. The surrogate model is called in the solution of the inverse problem for the position of the hidden delamination, which is achieved with <0.5% error in <20 min on a workstation computer for two unique test cases. These results demonstrate that solving the inverse problem from the ultrasonic response is tractable for composite impact damage with hidden delaminations.

References

1.
Mollenhauer
,
D.
,
Iarve
,
E.
,
Hoos
,
K.
,
Flores
,
M.
,
Zhou
,
E.
,
Lindgren
,
E.
, and
Schoeppner
,
G.
,
2016
, “
Damage Tolerance for Life Management of Composite Structures—Part 1: Modeling
,”
The Aircraft Structural Integrity Program Conference, ASIP Conference Proceedings
, San Antonio, TX, Nov. 28–Dec. 1, pp.
3
5
.
2.
U.S. Department of Defense,
2005
, “
Department of Defense Standard Practice: Aircraft Structural Integrity Program (ASIP)
,” U.S. Department of Defense, VA, Standard No.
MIL-STD-1530C
.http://everyspec.com/MIL-STD/MIL-STD-1500-1599/MIL-STD-1530D_55392/
3.
Wertz
,
J.
,
Wallentine
,
S.
,
Welter
,
J.
,
Dierken
,
J.
, and
Aldrin
,
J.
,
2017
, “
Volumetric Characterization of Delamination Fields Via Angle Longitudinal Wave Ultrasound
,”
AIP Conf. Proc.
,
1806
, p.
090006
.
4.
Aldrin
,
J.
,
Wertz
,
J.
,
Welter
,
J.
,
Wallentine
,
S.
,
Lindgren
,
E.
,
Kramb
,
V.
, and
Zainey
,
D.
,
2018
, “Review of Progress in Quantitative Nondestructive Evaluation,”
AIP Conf. Proc.
, 1949, p.
120005
.
5.
Johnston
,
P.
,
Appleget
,
C.
, and
Odarczenko
,
M.
,
2013
, “
Characterization of Delaminations and Transverse Matrix Cracks in Composite Laminates Using Multiple-Angle Ultrasonic Inspection
,”
AIP Conf. Proc.
,
1511
, pp.
1011
1018
.
6.
Bar-Cohen
,
Y.
, and
Crane
,
R.
,
1982
, “
Acoustic-Backscattering Imaging of Subcritical Flaws in Composites
,”
Mater. Eval.
,
40
(9), pp.
970
975
.https://www.researchgate.net/publication/279649239_ACOUSTIC-BACKSCATTERING_IMAGING_OF_SUBCRITICAL_FLAWS_IN_COMPOSITES
7.
Raju
,
B.
,
1986
, “
Acoustic-Backscattering Studies of Transverse Cracks in Composite Thick Laminates
,”
Exp. Mech.
,
26
(
1
), pp.
71
78
.
8.
Gorman
,
M.
,
1991
, “
Ultrasonic Polar Backscatter Imaging of Transverse Matrix Cracks
,”
J. Compos. Mater.
,
25
(
11
), pp.
1499
1514
.
9.
Spies
,
M.
, and
Jager
,
W.
,
2003
, “
Synthetic Aperture Focusing for Defect Reconstruction in Anisotropic Media
,”
Ultrasonics
,
41
(
2
), pp.
125
131
.
10.
Shlivinski
,
A.
, and
Langenberg
,
K.
,
2007
, “
Defect Imaging With Elastic Waves in Inhomogeneous–Anisotropic Materials With Composite Geometries
,”
Ultrasonics
,
46
(
1
), pp.
89
104
.
11.
Li
,
C.
,
Pain
,
D.
,
Wilcox
,
P.
, and
Drinkwater
,
B.
,
2013
, “
Imaging Composite Material Using Ultrasonic Arrays
,”
NDT E Int.
,
53
, pp.
8
17
.
12.
Lane
,
C.
,
Dunhill
,
T.
,
Drinkwater
,
B.
, and
Wilcox
,
P.
,
2010
, “
3D Ultrasonic Inspection of Anisotropic Aerospace Components
,”
Insight
,
52
(
2
), pp.
72
77
.
13.
Fahim
,
A.
,
Gallego
,
R.
,
Bochud
,
N.
, and
Rus
,
G.
,
2013
, “
Model-Based Damage Reconstruction in Composites From Ultrasound Transmission
,”
Compos. Part B
,
45
(
1
), pp.
50
62
.
14.
Lorenz
,
M.
,
Van der Wal
,
F.
, and
Berkhout
,
A.
,
1993
, “
Optimization of Ultrasonic Defect Reconstruction With Multi-SAFT
,”
Rev. Prog. Quant. Nondestr. Eval.
, 12(A), pp.
851
858
15.
Lorenz
,
M.
, and
Wielinga
,
T.
,
1993
, “
Ultrasonic Characterization of Defects in Steel Using Multi-SAFT Imaging and Neural Networks
,”
NDT E Int.
,
26
(
3
), pp.
127
133
.
16.
Ganansia
,
F.
,
Chahbaz
,
A.
, and
Mborokih
,
K.
,
2000
, “
Experimental Evaluation of Weld Defects Using Multi-Path SAFT
,” AIP Conf. Proc.,
509
, p.
1341
.
17.
Hutt
,
T.
, and
Simonetti
,
F.
,
2010
, “
Reconstructing the Shape of an Object From Its Mirror Image
,”
J. Appl. Phys.
,
108
(
6
), p.
064909
.
18.
Löer
,
K.
,
Meles
,
G.
, and
Curtis
,
A.
,
2015
, “
Automatic Identification of Multiply Diffracted Waves and Their Ordered Scattering Paths
,”
J. Acoust. Soc. Am.
,
137
(
4
), pp.
1834
1845
.
19.
Labyed
,
Y.
, and
Huang
,
L.
,
2014
, “
TR-MUSIC Inversion of the Density and Compressibility Contrasts of Point Scatterers
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
,
61
(
1
), pp.
16
24
.
20.
Tarantola
,
A.
,
2005
,
Inverse Problem Theory
,
Society for Industrial and Applied Mathematics
, Philadelphia, PA.
21.
Bonnet
,
M.
, and
Constantinescu
,
A.
,
2005
, “
Inverse Problems in Elasticity
,”
Inverse Probl.
,
21
(
2
), p.
R1
.
22.
Sabbagh
,
H.
,
Murphy
,
R.
,
Sabbagh
,
E.
,
Aldrin
,
J.
, and
Knopp
,
J.
,
2013
,
Computational Electromagnetics and Model-Based Inversion—A Modern Paradigm for Eddy-Current Nondestructive Evaluation
,
Springer
, New York.
23.
Welter
,
J.
,
Wertz
,
J.
,
Aldrin
,
J.
,
Kramb
,
V.
, and
Zainey
,
D.
,
2018
, “
Model-Driven Optimization of Oblique Angle Ultrasonic Inspection Parameters for Delamination Characterization
,”
AIP Conf. Proc.
, 1949, p.
130005
.
24.
Deydier
,
S.
,
Leymarie
,
N.
,
Calmon
,
P.
, and
Mengeling
,
V.
,
2006
, “
Modeling of the Ultrasonic Propagation Into Carbon-Fiber-Reinforced Epoxy Composites, Using a Ray Theory Based Homogenization Method
,”
AIP Conf. Proc.
,
820
, pp.
972
978
.
25.
Reverdy
,
F.
,
Mahaut
,
S.
,
Dominguez
,
N.
, and
Dubois
,
P.
,
2015
, “
Simulation of Ultrasonic Inspection of Curved Composites
Using a Hybrid Semi-Analytical/Numerical Code,”
AIP Conf. Proc.
,
1650
, pp.
1047
1055
.
26.
Wojcik
,
G.
,
Vaughan
,
D.
,
Murray
,
V.
, and
Mould
,
J.
,
1994
, “
Time-Domain Modeling of Composite Arrays for Underwater Imaging
,”
IEEE
Ultrasonics Symposium, Cannes, France, Oct. 31–Nov. 3, pp.
1027
1032
.
27.
Dominguez
,
N.
, and
Reverdy
,
F.
,
2014
, “
Simulation of Ultrasonic Testing of Composite Structures
,”
11th European Conference on Non-Destructive Testing/ECNDT
, Prague, Czech Republic, Oct. 6–10, http://www.ndt.net/events/ECNDT2014/app/content/Paper/344_Dominguez.pdf
28.
Jezzine
,
K.
,
Ségur
,
D.
,
Ecault
,
R.
,
Dominguez
,
N.
, and
Calmon
,
P.
,
2017
, “
Hybrid Ray-FDTD Model for the Simulation of the Ultrasonic Inspection of CFRP Parts
,”
AIP Conf. Proc.
, 1806, p.
090016
.
29.
Shell
,
E.
,
Aldrin
,
J.
,
Sabbagh
,
H.
,
Sabbagh
,
E.
,
Murphy
,
R.
,
Mazdiyasni
,
S.
, and
Lindgren
,
E.
,
2014
, “
Demonstration of Model-Based Inversion of Electromagnetic Signals for Crack Characterization
,”
AIP Conf. Proc.,
1650
, pp.
484
493
.
30.
Wertz
,
J.
,
Homa
,
L.
,
Welter
,
J.
,
Sparkman
,
D.
, and
Aldrin
,
J.
,
2018
, “
Gaussian Process Regression of Chirplet Decomposed Ultrasonic B-Scans of a Simulated Design Case
,”
AIP Conf. Proc.
, 1949, p.
130007
.
31.
Lu
,
Y.
,
Demirli
,
R.
,
Cardoso
,
G.
, and
Saniie
,
J.
,
2006
, “
A Successive Parameter Estimation Algorithm for Chirplet Signal Decomposition
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
,
53
(
11
), pp.
2121
2131
.
32.
Demirli
,
R.
, and
Saniie
,
J.
,
2014
, “
Asymmetric Gaussian Chirplet Model and Parameter Estimation for Generalized Echo Representation
,”
J. Franklin Inst.
,
351
(
2
), pp.
907
921
.
33.
Saniie
,
J.
,
Lu
,
Y.
, and
Demirli
,
R.
,
2006
, “
3E-3 A Comparative Study of Echo Estimation Techniques for Ultrasonic NDE Applications
,”
IEEE
Ultrasonics Symposium
, Vancouver, BC, Oct. 2–6, pp.
436
439
.
34.
Homa
,
L.
,
Wertz
,
J.
,
Sparkman
,
D.
,
Welter
,
J.
, and
Aldrin
,
J.
,
2018
, “
Chirplet Decomposition for Surrogate Modeling of a Constrained Ultrasonic Design Case
,” AIP Conf. Proc., 1949, p.
130006
.
35.
Sparkman
,
D. M.
,
Millwater
,
H. R.
, and
Ghosh
,
S.
,
2013
, “
Probabilistic Sensitivity Analysis of Dwell-Fatigue Crack Initiation Life for a Two-Grain Microstructural Model
,”
Fatigue Fract. Eng. Mater. Struct.
,
36
(
10
), pp.
994
1008
.
36.
Santner
,
T. J.
,
Williams
,
B. J.
, and
Notz
,
W.
,
2003
,
The Design and Analysis of Computer Experiments. Springer Series in Statistics
,
Springer-Verlag Inc.
,
New York
.
37.
Martin
,
J. D.
, and
Simpson
,
T. W.
,
2005
, “
Use of Kriging Models to Approximate Deterministic Computer Models
,”
AIAA J.
,
43
(
4
), pp.
853
863
.
38.
Rasmussen
,
C.
, and
Williams
,
C.
,
2006
,
Gaussian Processes for Machine Learning
, Vol.
1
,
MIT Press
,
Cambridge
, MA.
39.
Friedman
,
J.
,
Hastie
,
T.
, and
Tibshirani
,
R.
,
2001
,
The Elements of Statistical Learning
, Vol.
1
,
Springer Series in Statistics
,
New York
.
40.
Price
,
K.
,
Storn
,
M.
, and
Lampinen
,
J.
,
2006
,
Differential Evolution: A Practical Approach to Global Optimization
,
Springer Science & Business Media
, Berlin.
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