Biblio

In this paper, we study the sensor placement problem in urban water networks that maximizes the localization of pipe failures given that some sensors give incorrect outputs. False output of a sensor might be the result of degradation in sensor's hardware, software fault, or might be due to a cyber-attack on the sensor. Incorrect outputs from such sensors can have any possible values which could lead to an inaccurate localization of a failure event. We formulate the optimal sensor placement problem with erroneous sensors as a set multicover problem, which is NP-hard, and then discuss a polynomial time heuristic to obtain efficient solutions. In this direction, we first examine the physical model of the disturbance propagating in the network as a result of a failure event, and outline the multi-level sensing model that captures several event features. Second, using a combinatorial approach, we solve the problem of sensor placement that maximizes the localization of pipe failures by selecting $m$ sensors out of which at most $e$ give incorrect outputs. We propose various localization performance metrics, and numerically evaluate our approach on a benchmark and a real water distribution network. Finally, using computational experiments, we study relationships between design parameters such as the total number of sensors, the number of sensors with errors, and extracted signal features.

This paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be uniquely localized. This problem can be viewed as a minimum test cover (MTC) problem, which is NP-hard. We consider two approaches to obtain approximate solutions to this problem. In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem. In the second approach, we develop a new \textit{augmented greedy} algorithm for solving the MTC problem. This approach does not require the transformation of the MTC to MSC. Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach. We propose several metrics to evaluate the performance of the sensor placement designs. Finally, we present detailed computational experiments for a number of real water distribution networks.