Bayesian NDE Defect Signal Analysis

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We develop a hierarchical Bayesian approach for estimating defect signals from noisy measurements and apply it to nondestructive evaluation (NDE) of materials. We propose a parametric model for the shape of the defect region and assume that the defect signals within this region are 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 then utilized to identify potential defect regions and estimate their size and reflectivity parameters. Our approach provides Bayesian confidence regions (credible sets) for the estimated parameters, which are important in NDE applications. We specialize the proposed framework to elliptical defect shape and Gaussian signal and noise models and apply it to experimental ultrasonic <formula formulatype="inline"><tex>$C$</tex> </formula>-scan data from an inspection of a cylindrical titanium billet. We also outline a simple classification scheme for separating defects from nondefects using estimated mean signals and areas of the potential defects. </para>