Value-of-information in spatio-temporal systems: Sensor placement and scheduling

The management of infrastructure involves accounting for factors which vary in space over the system domain and in time as the system changes. Effective system management should be guided by models which account for uncertainty in these influencing factors as well as for information gathered to reduce this uncertainty. In this paper, we address the problem of optimal information collection for spatially distributed dynamic infrastructure systems. Based on prior information, a monitoring scheme can be designed, including placement and scheduling of sensors. This scheme can be adapted during the management process, as more information becomes available. Optimality can be defined in terms of the value of information (VoI), which provides a rational metric for quantifying the benefits of data gathering efforts to support system management decision-making. However, the computation of this metric in spatially and temporally extensive systems can present a practical impediment to its implementation. We describe this complexity, and investigate a special case of system topology, termed as a temporally decomposable system with uncontrolled evolution, in which the complexity of assessing VoI grows at a manageable rate with respect to the system management time duration. We demonstrate the evaluation and optimization of the VoI in an example of such a system.