Time Dependent Contamination Source Determination for Municipal Water Networks using Large Scale Optimization

Concern about malicious contamination of municipal drinking water networks requires us to consider additional protection measures over physical security alone. In the event of an accidental contamination or malicious attack, knowledge of the time and location of the contamination source can help infrastructure personnel stop the contamination and propose control strategies for containment or flushing. In this work, we develop a large scale, nonlinear program for identifying contamination sources given concentration measurements from a limited sensor grid installed in the water network. In a previous work [16], we demonstrated the potential for optimization techniques on the contamination source determination problem, but showed that the direct sequential approach was insufficient to solve the fully time dependent problem. In this current work, we use a direct simultaneous approach, converging the network model and optimization problems simultaneously. To obtain reasonable problem sizes, we present an origin tracking algorithm that reformulates the pipe expressions (partial differential equations in time and space) into a system of algebraic expressions in time alone. This algorithm provides a straightforward mathematical representation of the pipe boundary concentrations and is efficient for large networks with many source and output nodes. After reformulating the optimization constraints, we can solve the resulting nonlinear programming problem with large scale optimization tools. The fully time dependent solution gives complete injection profiles, identifying both the time and location of potential sources of contamination. We demonstrate the effectiveness of this formulation on a model for a real municipal water network. ∗Corresponding Author, email: [email protected]