# Towards Multilevel Modelling of Train Passing Events on the Staffordshire Bridge

arXiv: https://arxiv.org/abs/2403.17820 · HTML: https://mlsanity.com/paper/2403.17820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 26 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming](https://mlsanity.com/paper/2004.11408/) (2020)
- [Hierarchical Bayesian Modelling for Knowledge Transfer Across Engineering Fleets via Multitask Learning](https://mlsanity.com/paper/2204.12404/) (2022)
- [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 partitioning of an SHM problem and parallels with transfer learning](https://mlsanity.com/paper/2203.01655/) (2022)

## Abstract (arXiv)

We suggest a multilevel model, to represent aggregate train-passing events from the Staffordshire bridge monitoring system. We formulate a combined model from simple units, representing strain envelopes (of each train passing) for two types of commuter train. The measurements are treated as a longitudinal dataset and represented with a (low-rank approximation) hierarchical Gaussian process. For each unit in the combined model, we encode domain expertise as boundary condition constraints and work towards a general representation of the strain response. Looking forward, this should allow for the simulation of train types that were previously unobserved in the training data. For example, trains with more passengers or freights with a heavier payload. The strain event simulations are valuable since they can inform further experiments (including FEM calibration, fatigue analysis, or design) to test the bridge in hypothesised scenarios.