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    On Lyapunov stability of linearised Saint-Venant equations for a sloping channel
June  2009, 4(2): 189-210. doi: 10.3934/nhm.2009.4.189

Methods for the localization of a leak in open water channels

Nadia Bedjaoui 1, , Erik Weyer 1, and  Georges Bastin 2,

1. 

Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010, Australia, Australia
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  November 2008 Revised  January 2009 Published  June 2009

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.
Keywords: Open water channels, Hyperbolic partial differential equations, Observer design, Leak localization., Saint-Venant equations.
Mathematics Subject Classification: Primary: 35L40, 35B37; Secondary: 93C9.
Citation: Nadia Bedjaoui, Erik Weyer, Georges Bastin. Methods for the localization of a leak in open water channels. Networks & Heterogeneous Media, 2009, 4 (2) : 189-210. doi: 10.3934/nhm.2009.4.189
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