Hierarchical Bayesian modelling of a family of FRFs

Population-based structural health monitoring (PBSHM) aims to share valuable information among members of a population, such as normal- and damage-condition data, to improve inferences regarding the health states of the members. Even when the population is comprised of nominally-identical structures, benign variations among the members will exist as a result of slight differences in material properties, geometry, boundary conditions, or environmental effects (e.g., temperature changes). These discrepancies can affect modal properties and present as changes in the characteristics of the resonance peaks of the frequency response function (FRF). The hierarchical Bayesian approach provides a useful modelling structure for PBSHM, as population- and domain-level distributions are learnt simultaneously to bolster statistical strength among the parameters, and reduce variance among the parameter estimates. This paper provides an overview of current work, where hierarchical Bayesian models are developed for a small population of nominally-identical helicopter blades, using FRF data. These models account for benign variations that present as differences in the underlying dynamics across the input space, while also considering (and utilising) the similarities among the blades.