Proactive and Real-Time Optimal Control of Water Quality in Water Distribution Networks

Drinking water quality violations are widespread in the United States and elsewhere in the world. More than half of Americans are not confident in the safety of their tap water, especially after the 2014 Flint, Michigan water crisis. Other than accidental contamination events, stagnation is a major cause of water quality degradation. Thus, there is a pressing need to build a real-time control system that can make control decisions quickly and proactively so that the quality of water can be maintained at all times. However, towards this end, modeling the dynamics of water distribution systems are very challenging due to the complex fluid dynamics and chemical reactions in the system. This challenge needs to be addressed before moving on to modeling the optimal control problem. The research in this dissertation leverages statistical machine learning approaches in approximating the complex water system dynamics and then develops different optimization models for proactive and real-time water quality control. This research focuses on two effective ways to maintain water quality, flushing of taps and injection of chlorine or other disinfectants; both of these actions decrease the equivalent “water age”, a useful proxy for water quality related to bacteria growth. This research first develops linear predictive models for water quality and subsequently linear programming optimization models for proactive water age control via flushing. The second part of the research considers both flushing and disinfectant injections in the control problem and develops mixed integer quadratically constrained optimization models for controlling water age. Different control strategies for disinfectant injections are also evaluated: binary on-off injections and continuous injections. In the third part of the research, water demand is assumed to be uncertain and stochastic. The developed approach to control the system relates to learning the optimal real-time flushing decisions by combing reinforced temporal-difference learning approaches with linear value function approximation for solving approximately the underlying Markov decision processes. Computational results on widely used simulation models demonstrates the developed control systems were indeed effective for water quality control with known demands as well as when demands are uncertain and stochastic.