Contamination Source Determination in Water Distribution Networks

Abstract

We consider a water distribution network where at a finite number of nodes, contaminant injection can occur. We consider the problem of the identification of the contaminations. This problem can be considered as an optimal control problem with a networked system that is governed by a transport reaction equation. The identification is based upon observations from a finite number of sensors. The corresponding infinite-dimensional optimization problem is defined in a Hilbert space setting. In order to guarantee that our optimization problem has a unique solution, a quadratic regularization term is added in the objective function. Under certain assumptions on the relations of the travel times through the pipes we obtain a representation of this optimization problem that allows the computation of the solution on a discrete time grid by solving finite-dimensional linear least squares problems. On these time grids, there is no discretization error since our approach is based upon an exact representation of the system state. This is useful to minimize potential impacts of contamination emergencies on consumers by helping to select locations to flush the contaminant out of the distribution network.