Observability and Generalized Sensor Placement for Nonlinear Quality Models in Drinking Water Networks

This paper studies the problem of optimal placement of water quality (WQ) sensors in water distribution networks (WDNs), with a focus on chlorine transport, decay, and reaction models. Such models are traditionally used as suitable proxies for WQ. The literature on this topic is inveterate, but has a key limitation: it utilizes simplified single-species decay and reaction models that do not capture WQ transients for nonlinear, multi-species interactions. This results in sensor placements (SP) that do not account for nonlinear WQ dynamics. Furthermore, as WQ simulations are parameterized by hydraulic profiles and demand patterns, the placement of sensors are often hydraulics-dependent. This study produces a greedy algorithm that addresses the two aforementioned limitations. The algorithm is grounded in nonlinear dynamic systems and observability theory, and yields SPs that are submodular and robust to hydraulic changes. Case studies on benchmark water networks are provided. The key findings provide practical recommendations for WDN operators.