A Nonlinear Predictive Control Approach for Urban Drainage Networks Using Data-Driven Models and Moving Horizon Estimation

Real-time control (RTC) of urban drainage networks (UDNs) is a complex task where transport flows are non-pressurized and therefore impose flow-dependent time delays in the system. Unfortunately, the installation of flow sensors is economically out of reach at most utilities, although knowing volumes and flows are essential to optimize system operation. In this article, we formulate joint parameter and state estimation based on level sensors deployed inside manholes and basins in the network. We describe the flow dynamics on the main pipelines by the level variations inside manholes, characterized by a system of coupled partial differential equations (PDEs). These dynamics are approximated with kinematic waves where the network model is established with the water levels being the system states. Moving horizon estimation (MHE) is developed where the states and parameters are obtained via the levels and estimated flow data, utilizing the topological layout of the network. The obtained model complexity is kept within practically achievable limits, suitable for nonlinear predictive control. The effectiveness of the control and estimation method is demonstrated on a high-fidelity model of a drainage network, acting as virtual reality. We use real rain and wastewater flow data and test the controller against the uncertainty in the disturbance forecasts.