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

Abstract

Real-time control of urban drainage networks 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. These dynamics are approximated with kinematic waves where the network model is established with the water levels being the system states. Moving horizon estimation 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.

Learning-Based Predictive Control with Gaussian Processes: An Application to Urban Drainage Networks

“…Traditional techniques on conceptual modelling are reported in [1] and [2], where the capacity of pipes are collectively modelled as virtual buffers, and in [3], where the flow-to-level translation is modelled by polynomials. Grey-box modelling for level propagation in open pipes has been reported in [4], [5] and [6].…”

Real-time Data-driven Modelling and Predictive Control of Wastewater Networks

“…The two primary objectives of the research is, on the one hand, to establish a real-time decision-making toolchain to minimize the effect of increased meteorological load on sewer networks. On the other hand, to reduce the cost of infrastructure expansion by better utilizing the available storage capacity [Balla et al, 2022d]. Specifically, our aim is to develop a real-time and data-driven modelling and control framework that is practically and economically feasible to implement for utility operators.…”

“…where h(t k ) is the measured water level in the storage element. Upper and lower bounds of the inlet flow Q, Q correspond to the maximum and minimum flow capacity of the pumps [Balla et al, 2022d]. Threshold values h, h define the maximum and minimum allowed water levels in the storage element, respectively.…”

“….1: Level to volume conversion for a waste water tank equipped with retention area. Source: [Balla et al, 2022d] Hydraulic structures describing storage are typically linear tanks, setting relation between the volumetric flow to the level change. In the case of hydraulic structures where retention spaces are present, the non-linearity between level and flow is handled by the following assumption.…”

“…Semi-filled pipe segments regardless of their geometry are approximated with a rectangular pipe shape, as illustrated in Figure 4.2. Semi-filled circular pipe approximated with a rectangular geometry, parametrized by the width w. Source: [Balla et al, 2022d] The wetted perimeter P (x, t) and pipe area A(x, t) are formulated, i.e., A h(x, t) ≈ wh(x, t), (4.3a)…”