Phenomenological detectors for crack echo families in elastic solids

• The potential performance of low-complexity phenomenological detectors for crack echo families in elastic solids is evaluated. Ultrasonic echoes from a strip-like crack residing in an isotropic elastic solid with coarse microstructure are considered and the achieved detector performance is compared to the theoretical upper bounds (constrained only by the underlying physics) obtained by means of a recently presented physics-based optimal detector. A phenomenological signal model for the scattering process is formulated based on the time-domain impulse-response method and used to derive detectors of low numerical complexity which are dependent on a small number of parameters. The proposed detectors are compared in terms of receiver operating characteristic curves, which are computed by means of Monte Carlo simulations for the case of a strip-like crack with uncertain angular orientation. The minimum probability of error criterion is used to optimize the detector parameters for the simulation study and shown to be useful even for small training data sets. These results show that the proposed detectors have close to optimal performance in particular for the case of high signal-to-noise ratios.

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