130 A. Gannon et al. Fig. 12.5 Baseline subtracted waveform (top), matched filter result (middle), RMLE result (bottom) I.x/ DX m wmΠm.x/ (12.8) The result of applying Eq. 12.8 to every pixel on the test structure is a heat map that gives an estimate for the most likely location of damage. The rate at which the likelihood values decrease in moving away from the hottest location gives an indication of the confidence associated with the estimate of damage location (Fig. 12.6). For a more comprehensive overview of RMLE, see Flynn et al. in [8]. 12.3.5 Stage 2 РHigh Fidelity Characterization Using Acoustic Wavenumber Spectroscopy While the rough localization in Stage 1 provides an approximate damage location, it would be ideal to produce an image of the defect to provide the operator with information about its size, shape, and depth to help drive decisions about replacement and mitigating actions. We use Acoustic Wavenumber Spectroscopy to produce such images from scans of the structure taken using a scanning Laser Doppler Vibrometer. The embedded transducers in the immediate vicinity of the damage are used to excite a steady state response in the structure. We take advantage of the distributed array of transducers and energize only those closest to the damage. After processing, we arrive at an estimate of wavenumber, the spatial equivalent of frequency, which corresponds to the thickness of the vibrating structure at each pixel scanned.
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