  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.
