A key to successful damage diagnostics and quantification is damage imaging through ultrasonic guided wave tomography. We propose the implementation of least-squares reverse-time migration in a circular array for damage imaging in an aluminum plate. The theory of least-squares reverse-time migration is formulated for guided wave applications along with the summary of an efficient optimization algorithm: the conjugate gradient method. Numerical simulation and laboratory experiments are used to evaluate its performance with a circular array setup. In order to improve the data processing efficiency, the concept of using a limited number of actuators but a relatively large number of sensors is tested. Studies are conducted on three numerical cases, including a rectangular-shaped damage site, a complex-shaped damage site, and six other damage sites varying in size. As an inversion-based method, least-squares reverse-time migration shows significantly improved shape reconstruction with the amplitude quantification capability, compared to conventional reverse-time migration. Our experimental data are generated by piezoelectric wafers as actuators, measured by a scanning laser Doppler vibrometer to form a circular array on an aluminum plate, with a rectangular notch located in the inner region of the array. The damage images using experimental data show consistency in both the simulations using Born scattering and in altered material properties in the damaged region. According to the comparison, least-squares reverse-time migration for guided wave tomography is a promising technology to provide high-resolution large area damage imaging for plate-like structures.
CawleyP. Structural health monitoring: closing the gap between research and industrial deployment. Struct Health Monit2018; 17: 1225–1244.
2.
DohertyCChiuW. Scattering of ultrasonic-guided waves for health monitoring of fuel weep holes. Struct Health Monit2012; 11(1): 27–42.
3.
YuanFG. Structural health monitoring (SHM) in aerospace structures. Cambridge: Woodhead Publishing, 2016.
4.
LiuZYuHFanJ, et al. Baseline-free delamination inspection in composite plates by synthesizing non-contact air-coupled Lamb wave scan method and virtual time reversal algorithm. Smart Mater Struct2015; 24(4): 045014.
5.
HarbMYuanF. Barely visible impact damage imaging using non-contact air-coupled transducer/laser Doppler vibrometer system. Struct Health Monit2016; 16: 663–673.
6.
BhuiyanMYGiurgiutiuV. Multiphysics simulation of low-amplitude acoustic wave detection by piezoelectric wafer active sensors validated by in-situ AE-fatigue experiment. Materials2017; 10(8): 962.
7.
ZhouWLiHYuanFG. An anisotropic ultrasonic transducer for Lamb wave applications. Smart Struct Syst2016; 17(6): 1055–1065.
8.
RenBLissendenCJ. PVDF multielement Lamb wave sensor for structural health monitoring. IEEE T Ultrason Ferr2016; 63(1): 178–185.
9.
ParkBSohnHMalinowskiP, et al. Delamination localization in wind turbine blades based on adaptive time-of-flight analysis of noncontact laser ultrasonic signals. Nondestruct Test Eva2017; 32(1): 1–20.
10.
MalARicciFBanerjeeS, et al. A conceptual structural health monitoring system based on vibration and wave propagation. Struct Health Monit2005; 4(3): 283–293.
IhnJBChangFK. Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: II. Validation using riveted joints and repair patches. Smart Mater Struct2004; 13(3): 621.
13.
SohnHParkHWLawKH, et al. Damage detection in composite plates by using an enhanced time reversal method. J Aerospace Eng2007; 20(3): 141–151.
14.
WilcoxPDZhangJ. Quantification of the effect of array element pitch on imaging performance. IEEE T Ultrason Ferr2018; 65(4): 600–616.
15.
HunterAJDrinkwaterBWWilcoxPD. The wavenumber algorithm for full-matrix imaging using an ultrasonic array. IEEE T Ultrason Ferr2008; 55(11): 2450–2462.
16.
BudynNBevanRCroxfordAJ, et al. Sensitivity images for multi-view ultrasonic array inspection. AIP Conf Proc2018; 1949: 080001.
17.
MichaelsJE. Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors. Smart Mater Struct2008; 17(3): 035035.
18.
YuLGiurgiutiuV. In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection. Ultrasonics2008; 48(2): 117–134.
19.
AmbrozińskiŁStepinskiTUhlT. Efficient tool for designing 2D phased arrays in Lamb waves imaging of isotropic structures. J Intel Mat Syst Str2015; 26(17): 2283–2294.
20.
KerbratEIngRPradaC, et al. The D.O.R.T. method applied to detection and imaging in plates using lamb waves. AIP Conf Proc2001; 557: 934–940.
21.
HeJYuanFG. Lamb wave-based subwavelength damage imaging using the DORT-MUSIC technique in metallic plates. Struct Health Monit2016; 15(1): 65–80.
22.
FriswellMI. Damage identification using inverse methods. In: MorassiAVestroniF (eds) Dynamic methods for damage detection in structures. Vienna: Springer, 2008, pp. 13–66.
23.
InmanDJFarrarCRJuniorVL, et al. Damage prognosis: for aerospace, civil and mechanical systems. Hoboken, NJ: John Wiley & Sons, 2005.
24.
HuBHuNLiL, et al. Tomographic reconstruction of damage images in hollow cylinders using lamb waves. Ultrasonics2014; 54(7): 2015–2023.
25.
LiuYZhouSNingH, et al. An inverse approach of damage identification using lamb wave tomography. Sensors2019; 19(9): 2180.
26.
KoreckJValleCQuJ, et al. Computational characterization of adhesive layer properties using guided waves in bonded plates. J Nondestruct Eval2007; 26(2–4): 97–105.
27.
ZhaoJQiuJJiH. Reconstruction of the nine stiffness coefficients of composites using a laser generation based imaging method. Compos Sci Technol2016; 126: 27–34.
28.
HudsonTBYuanFG. Automated in-process cure monitoring of composite laminates using a guided wave-based system with high-temperature piezoelectric transducers. J Nondestruct Eval Diagn Progn Eng Syst2018; 1(2): 021008.
29.
CarcreffELarocheNBraconnierD, et al. Improvement of the total focusing method using an inverse problem approach. In: Proceedings of the 2017 IEEE international ultrasonics symposium (IUS), Washington, DC, 6–9 September 2017, pp. 1–4. New York: IEEE.
HuthwaiteP. Guided wave tomography with an improved scattering model. P R Soc A2016; 472(2195): 20160643.
37.
BriganteMSumbatyanM. Application of the inverse diffraction technique to the problem of reconstruction of complexly shaped flaws by ultrasonic methods. Russ J Nondestruct Test2010; 46(2): 98–111.
38.
DevaneyA. Inverse source and scattering problems in ultrasonics. IEEE T Son Ultrason1983; 30(6): 355–364.
39.
OgamEFellahZABakiP. The inverse problem of acoustic wave scattering by an air-saturated poroelastic cylinder. J Acoust Soc Am2013; 133(3): 1443–1457.
RaoJRatasseppMLisevychD, et al. On-line corrosion monitoring of plate structures based on guided wave tomography using piezoelectric sensors. Sensors2017; 17(12): 2882.
42.
RaoJRatasseppMFanZ. Guided wave tomography based on full waveform inversion. IEEE T Ultrason Ferr2016; 63(5): 737–745.
43.
WertzJHomaLWelterJ, et al. Case study of model-based inversion of the angle beam ultrasonic response from composite impact damage. J Nondestruct Eval Diagn Progn Eng Syst2018; 1(4): 041001.
44.
MaYHaleDGongB, et al. Image-guided sparse-model full waveform inversion. Geophysics2012; 77(4): R189–R198.
45.
ChangYZiYZhaoJ, et al. An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection. Meas Sci Technol2017; 28(3): 035002.
46.
HuthwaiteP. Accelerated finite element elastodynamic simulations using the GPU. J Comput Phys2014; 257: 687–707.
VolkerAvan ZonTEnthovenD, et al. 1D profiling using highly dispersive guided waves. AIP Conf Proc2015; 1650: 754–760.
49.
NishinoH. An investigation of reflection coefficients of the T(0, 1) mode guided waves at axisymmetric defects and inverse problem analyses for estimations of defect shapes. Mater Trans2015; 56(1): 120–128.
50.
ZhouWLiHYuanFG. Fundamental understanding of wave generation and reception using d36 type piezoelectric transducers. Ultrasonics2015; 57: 135–143.
51.
ZhouWYuanFGShiT. Guided torsional wave generation of a linear in-plane shear piezoelectric array in metallic pipes. Ultrasonics2016; 65: 69–77.
52.
WangBHiroseS. Inverse problem for shape reconstruction of plate-thinning by guided SH-waves. Mater Trans2012; 53(10): 1782–1789.
53.
HeJYuanFG. Lamb-wave-based two-dimensional areal scan damage imaging using reverse-time migration with a normalized zero-lag cross-correlation imaging condition. Struct Health Monit2016; 16: 444–457.
54.
HeJYuanFG. A quantitative damage imaging technique based on enhanced CCRTM for composite plates using 2D scan. Smart Mater Struct2016; 25(10): 105022.
55.
BaysalEKosloffDDSherwoodJW. Reverse time migration. Geophysics1983; 48(11): 1514–1524.
56.
RoseLFChanEWangCH. A comparison and extensions of algorithms for quantitative imaging of laminar damage in plates. I. Point spread functions and near field imaging. Wave Motion2015; 58: 222–243.
57.
HeJYuanFG. Damage identification for composite structures using a cross-correlation reverse-time migration technique. Struct Health Monit2015; 14(6): 558–570.
DuanYSavaP. Scalar imaging condition for elastic reverse time migration. Geophysics2015; 80(4): S127–S136.
60.
RochaDSavaPTanushevN. Acoustic wavefield imaging using the energy norm. In: SEG technical program expanded abstracts 2015, New Orleans, LA, 18–23 October 2015, pp. 4085–4090. Tulsa, OK: Society of Exploration Geophysicists.
61.
RochaDTanushevNSavaP. Isotropic elastic wavefield imaging using the energy norm. Geophysics2016; 81(4): S207–S219.
62.
RochaDTanushevNSavaP. Anisotropic elastic wavefield imaging using the energy norm. Geophysics2017; 82: S225–S234.
63.
RaoJRatasseppMFanZ. Limited-view ultrasonic guided wave tomography using an adaptive regularization method. J Appl Phys2016; 120(19): 194902.
64.
KuehlHSacchiM. Robust AVP estimation using least-squares wave-equation migration. In: SEG technical program expanded abstracts 2002, Salt Lake City, UT, 6–11 October 2002, pp. 281–284. Tulsa, OK: Society of Exploration Geophysicists.
DongSCaiJGuoM, et al. Least-squares reverse time migration: towards true amplitude imaging and improving the resolution. In: SEG technical program expanded abstracts 2012, Las Vegas, NV, 4–9 November 2012, pp. 1–5. Tulsa, OK: Society of Exploration Geophysicists.
67.
RochaDSavaP. Elastic least-squares reverse time migration using the energy norm. Geophysics2018; 83(3): S237–S248.
68.
RochaDSavaPGuittonA. 3D acoustic least-squares reverse time migration using the energy norm. Geophysics2018; 83(3): S261–S270.
69.
HeJRochaDCLeserPE, et al. Least-squares reverse time migration (LSRTM) for damage imaging using Lamb waves. Smart Mater Struct2019; 28(6): 065010.
70.
GlaessgenEStargelD. The digital twin paradigm for future NASA and US Air Force vehicles. In: Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference 20th AIAA/ASME/AHS adaptive structures conference 14th AIAA, Honolulu, HI, 23–26 April 2012, p. 1818. Reston, VA: AIAA.
AokiNSchusterGT. Fast least-squares migration with a deblurring filter. Geophysics2009; 74(6): WCA83–WCA93.
76.
VolkerAvan ZonTvan der LedenE. Field trials results of guided wave tomography. AIP Conf Proc2015; 1650: 615–621.
77.
HeJLeserPELeserWP, et al. IWSHM 2017: damage-scattered wave extraction in an integral stiffened isotropic plate: a baseline-subtraction-free approach. Struct Health Monit2018; 17: 1365–1376.
