Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme

Abstract

Ultrasonic Guided Waves (GW) actuated by piezoelectric transducers installed on structures have proven to be sensitive to small structural defects, with acquired scattering signatures being dependent on the damage type. This study presents a generic framework for probabilistic damage characterization within complex structures, based on physics-rich information on ultrasound wave interaction with existent damage. To this end, the probabilistic model of wave scattering properties estimated from measured GWs is inferred based on absolute complex-valued ratio statistics. Based on the probabilistic model, the likelihood function connecting the scattering properties predicted by a computational model containing the damage parametric description and the scattering estimates is formulated within a Bayesian system identification framework to account for measurement noise and modelling errors. The Transitional Monte Carlo Markov Chain (TMCMC) is finally employed to sample the posterior probability density function of the updated parameters. However, the solution of a Bayesian inference problem often requires repeated runs of “expensive-to-evaluate” Finite Element (FE) simulations, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome the computational challenges of repeated likelihood evaluations, a cheap and fast Kriging surrogate model built and based on a set of training points generated with an experiment design strategy in tandem with a hybrid Wave and Finite Element (WFE) computational scheme is proposed in this study. In each “numerical experiment”, the training outputs (i.e. ultrasound scattering properties) are efficiently computed using the hybrid WFE scheme which combines conventional FE analysis with periodic structure theory. By establishing the relationship between the training outputs and damage characterization parameters statistically, the surrogate model further enhances the computational efficiency of the exhibited scheme. Two case studies including one numerical example and an experimental one are presented to verify the accuracy and efficiency of the proposed algorithm.