  In data-driven SHM, the signals recorded from systems in operation can be
noisy and incomplete. Data corresponding to each of the operational,
environmental, and damage states are rarely available a priori; furthermore,
labelling to describe the measurements is often unavailable. In consequence,
the algorithms used to implement SHM should be robust and adaptive, while
accommodating for missing information in the training-data -- such that new
information can be included if it becomes available. By reviewing novel
techniques for statistical learning (introduced in previous work), it is argued
that probabilistic algorithms offer a natural solution to the modelling of SHM
data in practice. In three case-studies, probabilistic methods are adapted for
applications to SHM signals -- including semi-supervised learning, active
learning, and multi-task learning.
