Sensor placement for fault location identification in water networks: A minimum test cover approach

TL;DR

This paper addresses the optimal placement of sensors in water networks to efficiently identify pipe failures, proposing two approximate algorithms for the NP-hard minimum test cover problem and validating them through experiments.

Contribution

It introduces a novel augmented greedy algorithm for sensor placement that improves computational efficiency without sacrificing approximation quality.

Findings

The augmented greedy algorithm outperforms traditional methods in computational speed.

Both algorithms achieve comparable approximation ratios for the sensor placement problem.

Experimental results demonstrate effectiveness on real water distribution networks.

Abstract

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.