# Physics-informed machine learning for Structural Health Monitoring

arXiv: https://arxiv.org/abs/2206.15303 · HTML: https://mlsanity.com/paper/2206.15303/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Modeling and interpolation of the ambient magnetic field by Gaussian processes](https://mlsanity.com/paper/1509.04634/) (2015)
- [Grey-box models for wave loading prediction](https://mlsanity.com/paper/2105.13813/) (2021)
- [A Bayesian methodology for localising acoustic emission sources in complex structures](https://mlsanity.com/paper/2012.11058/) (2020)
- [Probabilistic Inference for Structural Health Monitoring: New Modes of Learning from Data](https://mlsanity.com/paper/2103.01676/) (2021)
- [Structured Machine Learning Tools for Modelling Characteristics of Guided Waves](https://mlsanity.com/paper/2101.01506/) (2021)
- [Grey-box state-space identification of nonlinear mechanical vibrations](https://mlsanity.com/paper/1804.10758/) (2018)
- [Considering discrepancy when calibrating a mechanistic electrophysiology model](https://mlsanity.com/paper/2001.04230/) (2020)

## Built on by (most cited first, 8 of 8)

- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Physics-based Reduced Order Modeling for Uncertainty Quantification of Guided Wave Propagation using Bayesian Optimization](https://mlsanity.com/paper/2307.09661/) (2023)
- [Towards a population-informed approach to the definition of data-driven models for structural dynamics](https://mlsanity.com/paper/2307.09862/) (2023)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables](https://mlsanity.com/paper/2508.00959/) (2025)
- [From Grey-Box to Green-Box: When can Physics-Informed Machine Learning Reduce Carbon Footprints in Structural Health Monitoring?](https://mlsanity.com/paper/2609.33387/) (2026)

## Abstract (arXiv)

The use of machine learning in Structural Health Monitoring is becoming more common, as many of the inherent tasks (such as regression and classification) in developing condition-based assessment fall naturally into its remit. This chapter introduces the concept of physics-informed machine learning, where one adapts ML algorithms to account for the physical insight an engineer will often have of the structure they are attempting to model or assess. The chapter will demonstrate how grey-box models, that combine simple physics-based models with data-driven ones, can improve predictive capability in an SHM setting. A particular strength of the approach demonstrated here is the capacity of the models to generalise, with enhanced predictive capability in different regimes. This is a key issue when life-time assessment is a requirement, or when monitoring data do not span the operational conditions a structure will undergo. The chapter will provide an overview of physics-informed ML, introducing a number of new approaches for grey-box modelling in a Bayesian setting. The main ML tool discussed will be Gaussian process regression, we will demonstrate how physical assumptions/models can be incorporated through constraints, through the mean function and kernel design, and finally in a state-space setting. A range of SHM applications will be demonstrated, from loads monitoring tasks for off-shore and aerospace structures, through to performance monitoring for long-span bridges.