Model averaging and probability of detection estimation under hierarchical uncertainties for Lamb wave detection

Abstract

Existing quantification models using Lamb waves are generally data-driven models, and the model choice can have a significant impact on the quantification results and the probability of detection (POD). This study develops a general method of model averaging and probability of detection estimation for Lamb wave detection. By treating each of the damage quantification models as a discrete uncertain variable, a hierarchical probabilistic model for Lamb wave detection 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 performance of a model can be assessed and averaged using the resulting posterior distributions of the model probability and its associated parameters. To evaluated all the quantities efficiently, the reservable jump Markov chain Monte Carlo method is proposed to evaluate the posterior distributions of the model, model parameters, and the model averaging results in one-pass. The overall method is demonstrated using specimens with naturally developed cracks, and the necessity of the method is verified by cross validation. The robustness of the proposed method is further validated using a naturally developed inclined crack, representing a realistic difference between the lab testing and an actual application. The results indicate that the proposed method is more robust compared with the individual models.