A Novel Probability of Detection Assessment Considering Model Uncertainty for Lamb Wave Detection

Abstract

Uncertainty in Non-Destructive Evaluation (NDE) arises from many sources, e.g., manufacturing variability, environmental noise, and inadequate measurement devices. The reliability of the NDE measurements is typically quantified by the probability of detection (POD). With the advent and technical developments of the simulation method and computer science, efforts have been devoted to generating and estimating the POD curve for Lamb wave damage detection. However, few studies have been reported on the POD evaluation considering model selection uncertainty. This paper presents a novel POD assessment method incorporating model selection uncertainty for Lamb wave damage detection. By treating the flaw quantification model as a discrete uncertain variable, a hierarchical probabilistic model for Lamb wave POD is formulated in the Bayesian framework. Uncertainties from the model choice, model parameters, and other variables can be explicitly incorporated using the proposed method. The Bayes factor is used to evaluate the performance of models. The posterior distributions of model parameters and the model fusion results are calculated through the Bayesian update using the reversible jump Markov chain Monte Carlo method. A fatigue problem with naturally developed cracks is used to demonstrate the proposed method.