Bayesian Defect Signal Analysis

We develop a Bayesian framework for estimating defect signals from noisy measurements. We propose a parametric model for the shape of the defect region and assume that the defect signal within this region is random with unknown mean and variance. Markov chain Monte Carlo (MCMC) algorithms are derived for simulating from the posterior distributions of the model parameters and defect signals. These algorithms are utilized to identify potential defect regions and estimate their size and reflectivity. We specialize the proposed framework to elliptical defect shape and Gaussian signal and noise models and apply it to experimental ultrasonic C‐scan data from an inspection of a cylindrical titanium billet.