Mixed-Integer Approach for Obtaining Unique Solutions in Source Inversion of Water Networks

This paper addresses the problem of contamination source determination in municipal drinking water networks. In previous work, the authors introduced a large-scale nonlinear programming approach for identifying both the time and location of contamination sources given concentration information from a limited number of sensors. Due to the sparseness of the sensor grid, this problem inherently has nonunique solutions. The problem was therefore regularized, and the regularized solution provided an approximate linear combination of possible injection scenarios. In this paper, a mixed-integer quadratic program is presented to refine the solution provided by the nonlinear programming formulation. We introduce a two-phase approach. In the n-phase, the number of likely injection locations is estimated. Using this information, the $e$ -phase is performed to extract the likely injection scenarios from the family of nonunique solutions. This two-phase approach is tested on a realistic municipal water network model with approximately 400 nodes, simulating five different injection scenarios. In all five examples, the approach was able to determine the correct number of injection locations and identify a set of possible injection scenarios containing the actual simulated injections.