  The prospect of informed and optimal decision-making regarding the operation
and maintenance (O&M) of structures provides impetus to the development of
structural health monitoring (SHM) systems. A probabilistic risk-based
framework for decision-making has already been proposed. However, in order to
learn the statistical models necessary for decision-making, measured data from
the structure of interest are required. Unfortunately, these data are seldom
available across the range of environmental and operational conditions
necessary to ensure good generalisation of the model.
  Recently, technologies have been developed that overcome this challenge, by
extending SHM to populations of structures, such that valuable knowledge may be
transferred between instances of structures that are sufficiently similar. This
new approach is termed population-based structural heath monitoring (PBSHM).
  The current paper presents a formal representation of populations of
structures, such that risk-based decision processes may be specified within
them. The population-based representation is an extension to the hierarchical
representation of a structure used within the probabilistic risk-based decision
framework to define fault trees. The result is a series, consisting of systems
of systems ranging from the individual component level up to an inventory of
heterogeneous populations. The current paper considers an inventory of wind
farms as a motivating example and highlights the inferences and decisions that
can be made within the hierarchical representation.
