Information-theoretic sensor placement for large sewer networks

Utility operators face a challenging task in managing wastewater networks to proactively enhance network monitoring. To address this issue, this paper develops a framework for optimized placing of sensors in sewer networks with the aim of maximizing the information obtained about the state of the network. To that end, mutual information is proposed as a measure of the evidence acquired about the state of the network by the placed sensors. The problem formulation leverages a stochastic description of the network states to analytically characterize the mutual information in the system and pose the sensor placement problem. To circumvent the combinatorial problem that arises in the placement configurations, we propose a new algorithm coined the one-step modified greedy algorithm, which employs the greedy heuristic for all possible initial sensor placements. This algorithm enables further exploration of solutions outside the initial greedy solution within a computationally tractable time. The algorithm is applied to two real sewer networks, the first is a sewer network in the South of England with 479 nodes and 567 links, and the second is the sewer network in Bellinge, a village in Denmark that contains 1020 nodes and 1015 links. Sensor placements from the modified greedy algorithm are validated by comparing their performance in estimating unmonitored locations against other heuristic placements using linear and neural network models. Results show the one-step modified greedy placements outperform others in most cases and tend to cluster sensors for efficiently monitoring parts of the network. The proposed framework and modified greedy algorithm provide wastewater utility operators with a sensor placement method that enables them to design the data acquisition and monitoring infrastructure for large networks.