A Bayesian time-of-flight estimation for ultrasonic damage detection

SHM methods for damage detection and localisation in plate-like structures have typically relied on post-processing of ultrasonic guided waves (GWs) features. The time-of-flight is one of these features, which has been extensively used by the SHM community. A followed technique to obtain the time of flight is by applying a particular time-frequency (TF) transform to get the frequency and energy content of the wave at each instant of time. From these transforms, the selection of a TF model has typically been based on experience, or simply based on minimising the computational cost. In this paper, a full probabilistic method based on the Bayesian inverse problem (BIP) is originally proposed to obtain the most probable model over a set of candidates. To this end, the problem of TF model selection is addressed using a two-stage BIP: (i) first, the posterior PDF of the dispersion parameter is obtained and then, (ii) the most plausible a posteriori value is introduced in the likelihood function to estimate the most evident TF model. The results have revealed the efficiency of the proposed methodology in automatically selecting the most suitable TF model for a relevant case study. No preference for any particular TF model has been found; the most probable TF model is case specific.