On the hierarchical Bayesian modelling of frequency response functions
This work addresses data scarcity in SHM for similar structures like helicopter blades, though it is incremental as it applies an existing hierarchical Bayesian approach to a specific domain.
The paper tackled the challenge of sparse data in structural health monitoring (SHM) by developing a hierarchical Bayesian model for frequency response functions, applied to helicopter blades, which reduced variance in parameter estimates and improved generalization with physics-based knowledge.
For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn statistical distributions at the population (or parent) and the domain levels simultaneously, to bolster statistical strength among the parameters. As a result, variance is reduced among the parameter estimates, particularly when data are limited. In this paper, a combined probabilistic FRF model is developed for a small population of nominally-identical helicopter blades, using a hierarchical Bayesian structure, to support information transfer in the context of sparse data. The modelling approach is also demonstrated in a traditional SHM context, for a single helicopter blade exposed to varying temperatures, to show how the inclusion of physics-based knowledge can improve generalisation beyond the training data, in the context of scarce data. These models address critical challenges in SHM, by accommodating benign variations that present as differences in the underlying dynamics, while also considering (and utilising), the similarities among the domains.