Conditional entropy and value of information metrics for optimal sensing in infrastructure systems

• Sensor networks for infrastructure system monitoring can be evaluated with metrics.
• Conditional entropy and value of information are two such metrics.
• These metrics can be evaluated using probabilistic graphical models of the system.
• Sensor networks can be designed using these metrics and an optimization algorithm.
• Sensor network optimization using these metrics is demonstrated with an example.

Optimal allocation of monitoring efforts is necessary to cost-effectively obtain information to support the management of civil infrastructure. To optimize the design of sensing networks, pre-posterior analysis of the network can be conducted based on some metric for comparing alternative monitoring schemes. One such metric is conditional entropy, an information theoretic measure of the uncertainty in a set of random variables, conditioned on available sensor measurements. A second metric is the value of information, a decision theoretic metric which explicitly quantifies the benefit of sensor measurements in reducing the expected losses to a managing agent in the context of a decision-making problem under uncertainty. In this paper, we present a scalable probabilistic framework to perform pre-posterior analysis in large infrastructure systems using either metric. A discussion is also provided concerning situations in which either metric should be preferred. To demonstrate this framework, an example infrastructure monitoring problem related to seismic risk is presented and analyzed.