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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.

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References

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Figures

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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].

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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.

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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.

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