Partially Structured Gaussian Processes for Grey-Box Learning in SHM

Abstract

Combining physics with data-driven learning seeks to harness the benefits of the expressivity of machine learners whilst having known physical laws that the model must adhere to. Building these types of models have the advantage of being able to represent phenomena more complex than can be described with simplified analytical equations, whilst simultaneously allowing for greater prediction confidence and interpretability, as well as providing a mechanistic basis that predictions can revert to when data becomes scarce. With operators more frequently carrying out monitoring campaigns, and decades of engineering knowledge to call upon, it is a natural step for health monitoring practitioners to adopt physics-informed learning strategies for monitoring structures. In many engineering scenarios, it is often the case that one will not have complete physical knowledge of a structure or system of interest, but partial knowledge, for which it is desirable to encode in a machine learning model. In this paper, we will explore how this type of knowledge can be embedded into Gaussian process models for processes that naturally exist as products of constituent functions, such as for processes that have both spatial and temporal dependencies. Focus will be placed on how the properties of the covariance function that has embedded physical structure dictates the predictive regime that the model may operate in within the partial knowledge setting. Application of the developed models includes learning the decoupled response of a beam under random loading into the constituent mode shapes and temporal response.