Abstract:
I will present the research I did with engineers from the Hong Kong University of Science and Technology in the past few years. The goal was to find and implement a method for detecting the location and size of blockages (oil, algae, mineral deposits etc.) in water pipe systems without having to dig up each pipe. The network structure gives complications in real life, but in this talk I will focus on the simpler case of a single pipe. We modelled the physics by a one-dimensional wave equation whose first-order coefficient determines the cross-sectional area of the pipe at any given location. Our proposed solution solves for the cross-sectional area along the pipe given impulse-response measurements (Neumann-to-Dirichlet data) at one end of the pipe. Time permitting, I will prove the reconstruction formula which is an application of control theory. This was a joint work with Fedi Zouari, Moez Louati and Mohamed S. Ghidaoui (Dept. of Civil and Environmental Engineering, HKUST).