  Efficient integration of uncertain observations with decision-making
optimization is key for prescribing informed intervention actions, able to
preserve structural safety of deteriorating engineering systems. To this end,
it is necessary that scheduling of inspection and monitoring strategies be
objectively performed on the basis of their expected value-based gains that,
among others, reflect quantitative metrics such as the Value of Information
(VoI) and the Value of Structural Health Monitoring (VoSHM). In this work, we
introduce and study the theoretical and computational foundations of the above
metrics within the context of Partially Observable Markov Decision Processes
(POMDPs), thus alluding to a broad class of decision-making problems of
partially observable stochastic deteriorating environments that can be modeled
as POMDPs. Step-wise and life-cycle VoI and VoSHM definitions are devised and
their bounds are analyzed as per the properties stemming from the Bellman
equation and the resulting optimal value function. It is shown that a POMDP
policy inherently leverages the notion of VoI to guide observational actions in
an optimal way at every decision step, and that the permanent or intermittent
information provided by SHM or inspection visits, respectively, can only
improve the cost of this policy in the long-term, something that is not
necessarily true under locally optimal policies, typically adopted in
decision-making of structures and infrastructure. POMDP solutions are derived
based on point-based value iteration methods, and the various definitions are
quantified in stationary and non-stationary deteriorating environments, with
both infinite and finite planning horizons, featuring single- or
multi-component engineering systems.
