A hierarchical Bayesian approach for parameter identification in structural deterioration models using probabilistic surrogate models

Most structural systems currently in operation are subjected to potentially multiple deterioration processes, for which different models exist to describe their evolution in time. The quantities of interest (QoIs) involved in them are often directly unobservable. However, advances in Structural Health Monitoring (SHM) have enabled gathering structural response data which can be used to indirectly make inferences on unobservable (state) quantities through Bayesian inference. Obtaining updated estimates of deterioration model parameters, given observed data, enables them to be used to predict future health states of interest for the structure, which constitutes a core tenet of condition-based maintenance (CBM). Key to obtaining robust parameter estimates is accounting for different uncertain quantities involved in the model that transforms unobservable quantities to observable ones, which in a Bayesian context is achieved through the likelihood function. This work presents an offline, flexible hierarchical framework to tackle this problem that employs probabilistic reduced order models (ROMs) in the construction of the likelihood function, that enable marginalizing out these uncertain quantities. The approximate likelihood function is then used within a typical Markov Chain Monte Carlo (MCMC) setting for parameter estimation. The framework is demonstrated in applications related to deterioration processes common to ship structures.