A spectrum of physics-informed Gaussian processes for regression in engineering

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as ``big,'' they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a spectrum of possible Gaussian process models are introduced that enable the incorporation of different levels of expert knowledge of a system. Examples illustrate how these approaches can significantly reduce reliance on data collection whilst also increasing the interpretability of the model, another important consideration in this context.

Physics-informed machine learning for Structural Health Monitoring

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.

Constraining Gaussian processes for physics-informed acoustic emission mapping

The automated localisation of damage in structures is a challenging but critical ingredient in the path towards predictive or condition-based maintenance of high value structures. The use of acoustic emission time of arrival mapping is a promising approach to this challenge, but is severely hindered by the need to collect a dense set of artificial acoustic emission measurements across the structure, resulting in a lengthy and often impractical data acquisition process. In this paper, we consider the use of physics-informed Gaussian processes for learning these maps to alleviate this problem. In the approach, the Gaussian process is constrained to the physical domain such that information relating to the geometry and boundary conditions of the structure are embedded directly into the learning process, returning a model that guarantees that any predictions made satisfy physically-consistent behaviour at the boundary. A number of scenarios that arise when training measurement acquisition is limited, including where training data are sparse, and also of limited coverage over the structure of interest. Using a complex plate-like structure as an experimental case study, we show that our approach significantly reduces the burden of data collection, where it is seen that incorporation of boundary condition knowledge significantly improves predictive accuracy as training observations are reduced, particularly when training measurements are not available across all parts of the structure.