Research Papers

Case Study of Model-Based Inversion of the Angle Beam Ultrasonic Response From Composite Impact Damage

[+] Author and Article Information
John Wertz

Air Force Research Laboratory,
2977 Hobson Way,
Wright-Patterson AFB, OH 45433
e-mail: john.wertz.1@us.af.mil

Laura Homa

Structural Materials Division,
University of Dayton Research Institute,
300 College Park,
Dayton, OH 45469

John Welter, Daniel Sparkman

Air Force Research Laboratory,
2977 Hobson Way,
Wright-Patterson AFB, OH 45433

John C. Aldrin

Computational Tools,
Gurnee, IL 60031

1Corresponding author.

Manuscript received October 27, 2017; final manuscript received May 7, 2018; published online June 5, 2018. Assoc. Editor: Paul Fromme. This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

ASME J Nondestructive Evaluation 1(4), 041001 (Jun 05, 2018) (10 pages) Paper No: NDE-17-1103; doi: 10.1115/1.4040233 History: Received October 27, 2017; Revised May 07, 2018

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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


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.
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/
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.
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.
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.
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
Raju, B. , 1986, “ Acoustic-Backscattering Studies of Transverse Cracks in Composite Thick Laminates,” Exp. Mech., 26(1), pp. 71–78. [CrossRef]
Gorman, M. , 1991, “ Ultrasonic Polar Backscatter Imaging of Transverse Matrix Cracks,” J. Compos. Mater., 25(11), pp. 1499–1514. [CrossRef]
Spies, M. , and Jager, W. , 2003, “ Synthetic Aperture Focusing for Defect Reconstruction in Anisotropic Media,” Ultrasonics, 41(2), pp. 125–131. [CrossRef] [PubMed]
Shlivinski, A. , and Langenberg, K. , 2007, “ Defect Imaging With Elastic Waves in Inhomogeneous–Anisotropic Materials With Composite Geometries,” Ultrasonics, 46(1), pp. 89–104. [CrossRef] [PubMed]
Li, C. , Pain, D. , Wilcox, P. , and Drinkwater, B. , 2013, “ Imaging Composite Material Using Ultrasonic Arrays,” NDT E Int., 53, pp. 8–17. [CrossRef]
Lane, C. , Dunhill, T. , Drinkwater, B. , and Wilcox, P. , 2010, “ 3D Ultrasonic Inspection of Anisotropic Aerospace Components,” Insight, 52(2), pp. 72–77. [CrossRef]
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. [CrossRef]
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
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. [CrossRef]
Ganansia, F. , Chahbaz, A. , and Mborokih, K. , 2000, “ Experimental Evaluation of Weld Defects Using Multi-Path SAFT,” AIP Conf. Proc., 509, p. 1341.
Hutt, T. , and Simonetti, F. , 2010, “ Reconstructing the Shape of an Object From Its Mirror Image,” J. Appl. Phys., 108(6), p. 064909. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
Tarantola, A. , 2005, Inverse Problem Theory, Society for Industrial and Applied Mathematics, Philadelphia, PA.
Bonnet, M. , and Constantinescu, A. , 2005, “ Inverse Problems in Elasticity,” Inverse Probl., 21(2), p. R1. [CrossRef]
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. [CrossRef]
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.
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.
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.
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.
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
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.
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.
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.
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. [CrossRef]
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. [CrossRef]
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.
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.
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. [CrossRef]
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. [CrossRef]
Martin, J. D. , and Simpson, T. W. , 2005, “ Use of Kriging Models to Approximate Deterministic Computer Models,” AIAA J., 43(4), pp. 853–863. [CrossRef]
Rasmussen, C. , and Williams, C. , 2006, Gaussian Processes for Machine Learning, Vol. 1, MIT Press, Cambridge, MA.
Friedman, J. , Hastie, T. , and Tibshirani, R. , 2001, The Elements of Statistical Learning, Vol. 1, Springer Series in Statistics, New York. [CrossRef]
Price, K. , Storn, M. , and Lampinen, J. , 2006, Differential Evolution: A Practical Approach to Global Optimization, Springer Science & Business Media, Berlin.


Grahic Jump Location
Fig. 1

Impact delamination in a composite coupon. Amplitude and time-of-flight data describes the complexity of composite impact damage and hidden delamination regions invisible to a normal incidence longitudinal wave single-sided inspection: (a) normal incidence C-Scan of impact damage with visible petal-shaped delaminations based on amplitude data and (b) representation of a hidden region (white) in a delamination field (black) based on time-of-flight data.

Grahic Jump Location
Fig. 2

Schematics of surrogate model demonstration cases 1 (a) and 2 (b). The transducer is 6.35 mm in diameter, with a center frequency of 5 MHz and a 19.05 mm focal length. Delamination features are 12.7 mm long. The diagramed scan path is not to scale: (a) hidden delamination varying in x-direction, fixed z at z = 2 mm and (b) hidden delamination varying in z-direction, fixed x at x = 1.2 mm.

Grahic Jump Location
Fig. 3

Chirplet representation of an example B-scan. (a) The original B-scan from CIVA. (b) The chirplet reconstruction of the B-scan. (c) The residual between the original B-scan and the reconstruction. The color bar represents the amplitude of the response in (a) and (b) and the amplitude of the residual in (c) [34].

Grahic Jump Location
Fig. 4

Hidden delamination simulations for nine hidden delamination x-positions. The x-position range was selected to ensure that the delamination was hidden but not so far from the tip of the topmost delamination that indications from the hidden delamination were no longer visible. The color bar describes the amplitude of the response: (a) x = 0.8 mm, (b) x = 1.0 mm, (c) x = 1.2 mm, (d) x = 1.4 mm, (e) x = 1.6 mm, (f) x = 1.8 mm, (g) x = 2.0 mm, (h) x = 2.2 mm, and (i) x = 2.4 mm.

Grahic Jump Location
Fig. 5

Gaussian chirplet parameters and GPR estimates for case 1. Open circles are parameters from CIVA and closed circles are parameter estimates. (a) and (c) vary smoothly, while (e) and (f) exhibit strong variation. (a) Reflection 1 amplitude, (b) reflection 2 bandwidth, (c) reflection 1 time of arrival, (d) reflection 2 center frequency, (e) reflection 8 phase, and (f) reflection 3 chirp rate.

Grahic Jump Location
Fig. 6

Comparison of CIVA and surrogate model B-scans: (a)–(c) x = 1.2 mm and (d)–(f) x = 2.0 mm. (a) and (d) depict the original CIVA B-scan, (b) and (e) depict the chirplet reconstruction of the B-scan, and (c) and (f) depict the residual between the CIVA B-scan and the chirplet reconstruction. The residual is a mixture of untracked reflections and incomplete chirplet fitting and is everywhere low. (a) CIVA B-scan, x = 1.2 mm, (b) chirplet reconstruction, x = 1.2 mm, (c) residual, x = 1.2 mm, (d) CIVA B-scan, x = 2.0 mm, (e) chirplet reconstruction, x = 2.0 mm, and (f) residual, x = 2.0 mm.

Grahic Jump Location
Fig. 7

CIVA B-scan (a), inverse solution (b), surrogate model evaluated at the inverse solution (c), and the residual in decibels (d). The inverse solution has an error of 0.22%, and the surrogate model at the inverse solution compares very well with the CIVA B-scan. (a) CIVA B-scan for x = 1.3 mm, (b) inverse solution for 50 initial guesses over 20 iterations, (c) surrogate model evaluated at x = 1.297 mm, and (d) residual in decibels.

Grahic Jump Location
Fig. 8

Hidden delamination simulations for eight second-delamination z-positions. The z-position range was selected to ensure that the second delamination was hidden but not so close to the topmost delamination that the reflections fully merge and become indistinguishable. The color bar describes the amplitude of the response: (a) z = 1.1 mm, (b) z = 1.3 mm, (c) z = 1.5 mm, (d) z = 1.7 mm, (e) z = 1.9 mm, (f) z = 2.1 mm, (g) z = 2.3 mm, and (h) z = 2.5 mm.

Grahic Jump Location
Fig. 9

Comparison of CIVA and surrogate model B-scans, (a)–(c) z = 1.3 mm and (d)–(f) z = 2.1 mm. (a) and (d) depict the original CIVA B-scan, (b) and (e) depict the chirplet reconstruction of the B-scan, and (c) and (f) depict the residual between the CIVA B-scan and the chirplet reconstruction. The residual is a mixture of untracked reflections and incomplete chirplet fitting and is everywhere low: (a) CIVA B-scan, z = 1.3 mm, (b) chirplet reconstruction, z = 1.3 mm, (c) residual, z = 1.3 mm, (d) CIVA B-scan, z = 2.1 mm, (e) chirplet reconstruction, z = 2.1 mm, and (f) residual, z = 2.1 mm.

Grahic Jump Location
Fig. 10

CIVA B-scan (a), inverse solution (b), surrogate model evaluated at the inverse solution (c), and the residual in decibels (d). The inverse solution has an error of 0.41%, and the surrogate model at the inverse solution compares very well with the CIVA B-scan. (a) CIVA B-scan for z = 2.2 mm, (b) inverse solution for 50 initial guesses over 20 iterations, (c) surrogate model evaluated at z = 2.191 mm, and (d) residual in decibels.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In