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Blockage detection in networks: The area reconstruction method

1 Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong
2 Jockey Club Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong
3 Department of Mathematics and Statistics, University of Helsinki, Finland

This contribution is part of the Special Issue: Inverse problems in imaging and engineering science
Guest Editors: Lauri Oksanen; Mikko Salo
Link: https://www.aimspress.com/newsinfo/1270.html

Special Issues: Inverse problems in imaging and engineering science

In this note we present a reconstructive algorithm for solving the cross-sectional pipe area from boundary measurements in a tree network with one inaccessible end. This is equivalent to reconstructing the first order perturbation to a wave equation on a quantum graph from boundary measurements at all network ends except one. The method presented here is based on a time reversal boundary control method originally presented by Sondhi and Gopinath for one dimensional problems and later by Oksanen to higher dimensional manifolds. The algorithm is local, so is applicable to complicated networks if we are interested only in a part isomorphic to a tree. Moreover the numerical implementation requires only one matrix inversion or least squares minimization per discretization point in the physical network. We present a theoretical solution existence proof, a step-by-step algorithm, and a numerical implementation applied to two numerical experiments.
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Keywords impulse response; blockage detection; transient flow; area reconstruction; network; boundary control; reconstruction algorithm

Citation: Emilia Blåsten, Fedi Zouari, Moez Louati, Mohamed S. Ghidaoui. Blockage detection in networks: The area reconstruction method. Mathematics in Engineering, 2019, 1(4): 849-880. doi: 10.3934/mine.2019.4.849

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