Contamination Source Identification in Water Systems: A Hybrid Model Trees–Linear Programming Scheme

This paper presents a new approach for contamination source identification in water distribution systems through a coupled model trees-linear programming algorithm. Model trees are an extension of regression trees (regression trees: tree-based models used to solve prediction problems in which the response variable is a numerical value) in the sense that they associate leaves with multivariate linear models. The model trees replace EPANET through learning (i.e., training and cross validation) after which a linear programming formulation uses the model trees linear rule classification structure to solve the inverse problem of contamination source identification. The use of model trees represents forward modeling (i.e., from root to leaves). The implementation of linear programming on the linear tree structure allows backward (inverse) modeling (i.e., from leaves to root) where the contamination injections characteristics are the problem unknowns. The proposed methodology provides an estimation of the time, location, and concentration of the contamination injection sources. The model is demonstrated using two example applications.