Embedded or surface-mounted piezoelectric wafers operated in pitch-catch mode can interrogate woven fiberglass/epoxy composites with low-frequency ultrasonic guided waves during fatigue loading, and the area enclosed by a selected contour of the Gabor wavelet transform (GWT) of the received signal has been proposed as a damage indicator. The indicator's trend appeared to track damage accumulation, but its quantitative correspondence to specific microstructural damage mechanisms - transverse crack density, delamination extent, and strand fracture - has never been established, nor has its probability of detection under realistic (non-Gaussian) noise, transducer-geometry and embedment variability, or the interrogation-frequency trade-offs required to detect earlier damage stages or individual crack events. The open problem is to convert this trend-level indicator into a validated, quantitatively interpretable damage identification method: establishing what damage mechanism(s) the contour metric actually measures - including whether it responds to damage at all rather than to the specimen's own stretching under loading, which complicates the local and global damage states - and validating or refuting the hypothesized correlation between its evolution and transverse-crack accumulation following the characteristic damage state.

Background

Structural health monitoring (SHM) aims to detect and characterize damage in load-bearing structures in service. In composite laminates, a standard approach is ultrasonic pitch-catch testing: a piezoelectric wafer (PZT, lead zirconate titanate) bonded to or embedded in the structure launches a transient elastic wave, and a second wafer receives it; changes in the received waveform reflect changes in the structure along the wave path. In thin plates these waves are guided (Lamb-type) modes, which are dispersive and multimodal, and in anisotropic, heterogeneous woven composites their interpretation is difficult. Fatigue damage in woven fiberglass/epoxy laminates develops through a well-documented sequence often called the characteristic damage state: first a saturating population of transverse matrix cracks in the fill (weft) plies, then coupled delamination and shear cracking, and finally fracture of the load-bearing strands (fiber bundles) at stress raisers. Transverse crack density (cracks per unit length counted on a polished or replicated specimen edge) is the standard independent measure of the first stage.

Because raw pitch-catch waveforms are noisy and non-stationary, La Saponara and co-workers introduced a signal-processing pipeline consisting of (a) denoising by wavelet thresholding (Donoho-type soft thresholding of wavelet coefficients, implemented in the WaveLab library, whose threshold theory assumes additive i.i.d. Gaussian noise), (b) computation of the continuous Gabor wavelet transform (GWT) - a joint time–frequency representation obtained by correlating the signal with scaled and translated Gaussian-windowed sinusoidal mother wavelets - and (c) extraction of a damage-sensitive feature from contour plots of the GWT magnitude: the area enclosed by a selected contour of the transform surface. In fatigue tests of woven fiberglass/epoxy specimens instrumented with two PZT geometries (7 mm x 0.2 mm PZT-5A and 5 mm x 0.4 mm PZT-4 wafers, embedded one ply below the surface or surface-mounted), the contour-area feature evolved with cycle count in a way that 'seemed to correlate' with the hypothesized accumulation of transverse cracks, but this correlation was never quantified: the edge-replication microscopy needed to count crack density at matched cycle counts was attempted but not completed. The interrogation frequencies (center frequencies from 10 kHz to 50 kHz) were deliberately low to limit attenuation, so the wavelengths are far larger than individual cracks and the method senses only accumulated global damage, not single crack-formation events.

Probability of detection (POD) - the NDE-standard characterization of a detection method as a curve of detection probability versus damage size, with quantified false-alarm behavior - has been developed for guided-wave SHM imaging systems and for embedded-PZT transducer comparison, but never applied to the GWT contour-area metric. The unresolved question is therefore whether this class of wavelet-contour damage indicators can be made a validated quantitative measure of specific composite fatigue damage mechanisms, rather than an empirical trend.

Problem Statement

Establish, quantitatively and with characterized uncertainty, what the Gabor-wavelet-transform contour-area damage indicator computed from embedded- or surface-mounted-PZT pitch-catch ultrasonic signals measures in fatigue-loaded woven fiberglass/epoxy composites. The objective - turning a trend-level indicator into a validated quantitative damage identification method - is the following mechanism-correspondence problem:

Measure, at matched cycle counts, both the contour-area metric and independent damage measures - transverse crack density from microscopy or edge replication, delamination extent, and strand fracture - and determine quantitatively which, if any, of these candidate mechanisms the metric tracks, including whether it responds to damage at all rather than to global strain or stiffness change. The transverse-crack-density determination thereby validates or refutes the prognostics hypothesis - stated qualitatively when the metric was introduced and never quantitatively tested - that the contour-area evolution under fatigue indirectly reflects transverse-crack accumulation following the characteristic damage state.

Several related questions lie outside the problem stated above: the metric's detection probability and false-alarm behavior, including any dependence on transducer geometry (e.g., 7 mm x 0.2 mm PZT-5A versus 5 mm x 0.4 mm PZT-4 wafers) and on embedment-induced manufacturing variability (resin pockets, local stress raisers), and the effect of the heuristic contour number and contour-selection rule on repeatability, have never been characterized; the wavelet-thresholding denoiser's additive-white-Gaussian-noise assumption has never been verified against the actual recorded noise statistics; and the 10–50 kHz band senses only accumulated global damage, with detection of individual cracks outside the source project's scope.

The problem is resolved by a demonstrated, uncertainty-quantified correspondence - or demonstrated absence of correspondence - between the contour-area metric and these candidate mechanisms at matched cycle counts, including whether the metric tracks any of them and separation of genuine damage sensitivity from global strain/stiffness effects. Any damage states used as ground truth must be specified independently of the metric being tested.

References

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