Adjoint-Based Probabilistic Source Characterization in Water-Distribution Systems with Transient Flows and Imperfect Sensors
Publication: Journal of Water Resources Planning and Management
Volume 141, Issue 9
Abstract
If a contamination event occurs in a water distribution system, sensors in the network may observe water quality changes. The data from these sensors can be used to identify the source of the contamination. The sensors can be binary sensors that record the presence or absence of contamination, fuzzy sensors that measure concentration within a set range, or perfect sensors that measure the exact concentration within the bounds of measurement uncertainty. This work presents an adjoint-based probabilistic approach for identifying the source node, source release time, and source strength for an instantaneous release of contamination based on sensor observations and known system hydraulics. In the adjoint approach, information is propagated upgradient from the sensors to the possible source nodes. EPANET is used to simulate the transient hydraulics of the pipe network and the upgradient propagation of the adjoint state through the network. The resulting adjoint states are related to probability density functions of the source release times at all possible source nodes. For fuzzy or perfect sensors, these probabilities can be used to determine the most likely source node. A hypothetical example is used to show that this method is accurate, even for a small number of sensor observations and complex hydraulics.
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Acknowledgments
This work was funded in part by the Air Force Medical Service Air Force Institute of Technology Civilian Institution Program and by the National Science Foundation under Grant DMS-0602284. The authors thank three anonymous reviewers for their valuable comments on this paper.
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Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 141 • Issue 9 • September 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Jun 19, 2014
Accepted: Dec 3, 2014
Published online: Jan 13, 2015
Discussion open until: Jun 13, 2015
Published in print: Sep 1, 2015
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