# On the hierarchical Bayesian modelling of frequency response functions

arXiv: https://arxiv.org/abs/2307.06263 · HTML: https://mlsanity.com/paper/2307.06263/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 63 references that are in the map.
- First posted on arXiv 12 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Rank-normalization, folding, and localization: An improved widehatR for assessing convergence of MCMC](https://mlsanity.com/paper/1903.08008/) (2019)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Hamiltonian Monte Carlo for Hierarchical Models](https://mlsanity.com/paper/1312.0906/) (2013)
- [Vector-Valued Control Variates](https://mlsanity.com/paper/2109.08944/) (2021)
- [Hierarchical Bayesian Modelling for Knowledge Transfer Across Engineering Fleets via Multitask Learning](https://mlsanity.com/paper/2204.12404/) (2022)
- [Domain Adaptation for One-Class Classification: Monitoring the Health of Critical Systems Under Limited Information](https://mlsanity.com/paper/1907.09204/) (2019)
- [On statistic alignment for domain adaptation in structural health monitoring](https://mlsanity.com/paper/2205.12052/) (2022)
- [Deep Learning for Detecting Building Defects Using Convolutional Neural Networks](https://mlsanity.com/paper/1908.04392/) (2019)
- [Constraining Gaussian processes for physics-informed acoustic emission mapping](https://mlsanity.com/paper/2206.01495/) (2022)
- [Bayesian Modelling of Multivalued Power Curves from an Operational Wind Farm](https://mlsanity.com/paper/2111.15496/) (2021)
- [On the Integration of Physics-Based Machine Learning with Hierarchical Bayesian Modeling Techniques](https://mlsanity.com/paper/2303.00187/) (2023)
- [Bayesian Assessments of Aeroengine Performance with Transfer Learning](https://mlsanity.com/paper/2011.14698/) (2020)
- [Meta-models for transfer learning in source localisation](https://mlsanity.com/paper/2305.08657/) (2023)
- [Modelling variability in vibration-based PBSHM via a generalised population form](https://mlsanity.com/paper/2203.07115/) (2022)

## Built on by (most cited first, 6 of 6)

- [Quantifying the value of information transfer in population-based SHM](https://mlsanity.com/paper/2311.03083/) (2023)
- [Multitask learning for improved scour detection: A dynamic wave tank study](https://mlsanity.com/paper/2408.16527/) (2024)
- [Active learning for regression in engineering populations: A risk-informed approach](https://mlsanity.com/paper/2409.04328/) (2024)
- [Quantifying the value of positive transfer: An experimental case study](https://mlsanity.com/paper/2407.14342/) (2024)
- [Inter-turbine Modelling of Wind-Farm Power using Multi-task Learning](https://mlsanity.com/paper/2502.14527/) (2025)
- [Latent variable models for simultaneous EOV identification and removal in population-based SHM](https://mlsanity.com/paper/2608.11995/) (2026)

## Abstract (arXiv)

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.