  A physics-informed machine learning model, in the form of a multi-output
Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given
appropriate datasets, the model can be used to regress the analytical value of
the structure's bending stiffness, interpolate responses, and make
probabilistic inferences on latent physical quantities. The developed model is
applied on a numerically simulated cantilever beam, where the regressed bending
stiffness is evaluated and the influence measurement noise on the prediction
quality is investigated. Further, the regressed probabilistic stiffness
distribution is used in a structural health monitoring context, where the
Mahalanobis distance is employed to reason about the possible location and
extent of damage in the structural system. To validate the developed framework,
an experiment is conducted and measured heterogeneous datasets are used to
update the assumed analytical structural model.
