On the hierarchical Bayesian modelling of frequency response functions

TL;DR

This paper develops a hierarchical Bayesian model for frequency response functions to improve structural health monitoring of similar structures with limited data, leveraging information sharing and physics-based knowledge.

Contribution

It introduces a combined probabilistic FRF model using hierarchical Bayesian structure for small populations and incorporates physics-based knowledge for better generalization.

Findings

Reduces variance in parameter estimates with limited data

Supports information transfer across similar structures

Enhances model generalization with physics-based knowledge

Abstract

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.