POD curves for non-maximizable ultrasonic responses: Statistical derivation and application to solid freight axles

The most relevant standards on ultrasonic testing, and an effective inspection practice, require the maximization of echo responses due to indications before their evaluation in terms of amplitude and size. This is achieved effectively pointing the acoustic axis of the sound beam to the indication, in a way to get back the maximum possible sound energy. Considering some operative cases, however, such a response maximization is not always feasible, mainly due to geometrical constraints impeding the inspection of the whole control area with a constant sensitivity. The traditional end inspection of solid railway axles by a rotating probe mounting conventional sensors falls back into this kind of inspections. In particular, inspection angles are fixed and the probe holder cannot move along the axle allowing response maximization of in-service damages located, for example, along the cylindrical body. It follows some control areas cannot be inspected using the maximum sound pressure. The present research shows how the derivation of “Probability of Detection” curves for non-maximizable ultrasonic responses cannot be carried out by the traditional statistical approach and a novel one, of the “Model-Assisted Probability of Detection” kind, is consequently proposed based on experiments and numerical simulations.