Value of Information in the Design of Resilient Water Distribution Sensor Networks

Abstract

The ability to monitor the flow and how water transforms throughout water networks would greatly improve the management of those distribution systems. The sensor placement problem attempts to find the locations of monitoring devices that would optimally observe water quality and protect consumers from accidents and intrusions of contaminants. In some related critical scenarios, the absence of information about possible contamination events, including knowledge of the injection sources, contaminant types or mass, time of pollution, and the variability of water network input parameters, such as the nodal demands and the pipe roughness coefficients, raises several challenges that must be addressed by the sensor network design process. In this paper, the authors describe a stochastic parameterization and analysis of uncertainty for the design of sensor networks aimed at maximizing the probability of detection of accidents and intrusions in water distribution networks. A challenge with such an approach, in particular, when applied to large urban water networks is the size of the ensuing computational model and the associated numerical optimization problem. This problem is compounded in the presence of uncertainty, where the need to deal with a large number of statistically plausible scenarios underscores the need for efficient yet credible algorithms for addressing the sensor placement issue. In addition to modeling aspects, the authors also address a challenge associated with the computational feasibility and performance of relevant numerical algorithms. Specifically, and through the use of submodular cost functions, the authors are able to solve the optimization problem with a greedy algorithm, yielding sufficient computational performance that allows for the description of stochastic water demands in the context of Monte Carlo simulations. Imperfect sensors are further accounted for while maintaining submodularity. The results show that the optimal sensor network layout is highly dependent on whether uncertainty in the stochastic parameters has been introduced and whether individual sensors can fail or not.