Methods for the localization of a leak in open water channels
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Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010
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Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve
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Received:
01 November 2008
Revised:
01 January 2009
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Primary: 35L40, 35B37; Secondary: 93C95.
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In this paper, we present two methods for determining the position
of a leak in an open water channel. The available measurements
are the water level and the gate position at the upstream and
downstream end of a channel reach. We assume that the size of the
leak and the time it started are already estimated by a
leak-detection method. Both of the proposed methods make use of a
nonlinear Saint-Venant equation model of the channel where the
leak is modelled as a lateral outflow. The first method makes use
of a bank of $N$ models corresponding to $N$ possible positions of
the leak along the channel. The estimated position of the leak is
determined by the model which minimizes a quadratic cost function.
The second method is based on the same principle except that it
uses observers instead of pure models. The methods are tested on
both real and simulated data from the Coleambally Channel 6 in
Australia. It is further shown that the determination of the
position of a leak is an inherently difficult problem.
Citation: Nadia Bedjaoui, Erik Weyer, Georges Bastin. Methods for the localization of a leak in open water channels[J]. Networks and Heterogeneous Media, 2009, 4(2): 189-210. doi: 10.3934/nhm.2009.4.189
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Abstract
In this paper, we present two methods for determining the position
of a leak in an open water channel. The available measurements
are the water level and the gate position at the upstream and
downstream end of a channel reach. We assume that the size of the
leak and the time it started are already estimated by a
leak-detection method. Both of the proposed methods make use of a
nonlinear Saint-Venant equation model of the channel where the
leak is modelled as a lateral outflow. The first method makes use
of a bank of $N$ models corresponding to $N$ possible positions of
the leak along the channel. The estimated position of the leak is
determined by the model which minimizes a quadratic cost function.
The second method is based on the same principle except that it
uses observers instead of pure models. The methods are tested on
both real and simulated data from the Coleambally Channel 6 in
Australia. It is further shown that the determination of the
position of a leak is an inherently difficult problem.
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