A multilevel Bayesian method for ultrasound-based damage identification in composite laminates

Estimating deterministic single-valued damage parameters when evaluating the actual health state of a material has a limited meaning if one considers not only the existence of measurement errors, but also that the model chosen to represent the damage behavior is just an idealization of reality. This paper proposes a multilevel Bayesian inverse problem framework to deal with these sources of uncertainty in the context of ultrasound-based damage identification. Although the methodology has a broad spectrum of applicability, here it is oriented to model-based damage assessment in layered composite materials using through-transmission ultrasonic measurements. The overall procedure is first validated on synthetically generated signals and then evaluated on real signals obtained from a post-impact fatigue damage experiment in a cross-ply carbon-epoxy laminate. The evidence of the hypothesized model of damage is revealed as a suitable measure of the overall ability of that candidate hypothesis to represent the actual damage state observed by the ultrasound, thus avoiding the extremes of over-fitting or under-fitting the ultrasonic signal.