Bayesian Optimization for Contamination Source Identification in Water Distribution Networks

In the wake of the terrorist attacks of 11 September 2001, extensive research efforts have been dedicated to the development of computational algorithms for identifying contamination sources in water distribution systems (WDSs). Previous studies have extensively relied on evolutionary optimization techniques, which require the simulation of numerous contamination scenarios in order to solve the inverse-modeling contamination source identification (CSI) problem. This study presents a novel framework for CSI in WDSs using Bayesian optimization (BO) techniques. By constructing an explicit acquisition function to balance exploration with exploitation, BO requires only a few evaluations of the objective function to converge to near-optimal solutions, enabling CSI in real-time. The presented framework couples BO with EPANET to reveal the most likely contaminant injection/intrusion scenarios by minimizing the error between simulated and measured concentrations at a given number of water quality monitoring locations. The framework was tested on two benchmark WDSs under different contamination injection scenarios, and the algorithm successfully revealed the characteristics of the contamination source(s), i.e., the location, pattern, and concentration, for all scenarios. A sensitivity analysis was conducted to evaluate the performance of the framework using various BO techniques, including two different surrogate models, Gaussian Processes (GPs) and Random Forest (RF), and three different acquisition functions, namely expected improvement (EI), probability of improvement (PI), and upper confident bound (UCB). The results revealed that BO with the RF surrogate model and UCB acquisition function produced the most efficient and reliable CSI performance.