  A primary motivation for the development and implementation of structural
health monitoring systems, is the prospect of gaining the ability to make
informed decisions regarding the operation and maintenance of structures and
infrastructure. Unfortunately, descriptive labels for measured data
corresponding to health-state information for the structure of interest are
seldom available prior to the implementation of a monitoring system. This issue
limits the applicability of the traditional supervised and unsupervised
approaches to machine learning in the development of statistical classifiers
for decision-supporting SHM systems.
  The current paper presents a risk-based formulation of active learning, in
which the querying of class-label information is guided by the expected value
of said information for each incipient data point. When applied to structural
health monitoring, the querying of class labels can be mapped onto the
inspection of a structure of interest in order to determine its health state.
In the current paper, the risk-based active learning process is explained and
visualised via a representative numerical example and subsequently applied to
the Z24 Bridge benchmark. The results of the case studies indicate that a
decision-maker's performance can be improved via the risk-based active learning
of a statistical classifier, such that the decision process itself is taken
into account.
