Contamination source determination for water networks

We formulate and solve an estimation problem for identifying both the time and location of contamination sources in municipal water networks using concentration measurements from a sparse sensor grid. Previous work showed that the direct sequential approach was insufficient to solve the time-dependent problem. Instead, a direct simultaneous approach is used, converging the network model and optimization problems simultaneously. An origin tracking algorithm is presented to reformulate the pipe expressions and characterize the time delays associated with network pipes. This algorithm removes the need to discretize along the length of the pipes and is efficient for large networks with many source and output nodes. The solution of the resulting nonlinear program provides the complete time-dependent injection profiles, identifying both the time and location of potential contamination sources. The effectiveness of this formulation is demonstrated on a network model for a real municipal water network.