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Networks and Heterogeneous Media

2009, Volume 4, Issue 2: 189-210. doi: 10.3934/nhm.2009.4.189
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Methods for the localization of a leak in open water channels

  • 1.
    Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010
  • 2.
    Center for Systems Engineering and Applied Mechanics (CESAME), Department of Mathematical Engineering, Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve
  • Received: 01 November 2008 Revised: 01 January 2009

  • Primary: 35L40, 35B37; Secondary: 93C95.

  • 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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  • 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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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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