Abstract
Abstract In this work, an unsupervised model selection procedure for identifying data-driven forecast models for urban drainage systems is proposed and evaluated. Specifically, we consider the case of predicting inflows to wastewater treatment plants for activating wet weather operation (aeration tank settling, ATS) using Box–Jenkins models. The model selection procedure considers different model structures and different objective functions. The hyperparameter search space is constrained based on the time of concentration in the catchment. Objective function criteria that minimize one-step-ahead as well as multi-step prediction errors are considered. Finally, we consider two criteria for unsupervised selection of the best-performing model. These measure the agreement of observed and predicted hydrographs (persistence index), as well as the binary exceedance of critical flow thresholds (critical success index (CSI)). Our work shows that forecast models can be developed in an unsupervised manner, and ATS activation is correctly forecasted in 60–90% of the events. The selected model structures reflect the physical behaviour of the catchment. Models should not be selected on operational criteria like the CSI due to a risk of overfitting. The degree to which rainfall input improves forecasts depends on the specific catchment, and the objective function criterion that should be used for coefficient estimation depends on the application context.
Highlights
Urban drainage systems (UDS) are increasingly challenged as a result of on-going urbanization (European Commission 2016) and changing rainfall patterns (Arnbjerg-Nielsen 2012)
Panel (b) compares the best-performing models that were trained using single and multi-step criteria (SSE and step objective function criterion (SC)), and panel (c) compares models that were selected considering the persistence index and critical success index (PI and CSI), respectively (PI was applied as a selection criterion in panels (a) and (b))
We developed a method for unsupervised identification of data-driven models that forecast inflow to wastewater treatment facilities
Summary
Urban drainage systems (UDS) are increasingly challenged as a result of on-going urbanization (European Commission 2016) and changing rainfall patterns (Arnbjerg-Nielsen 2012). The potential of real-time operation of integrated urban wastewater infrastructures (Lund et al 2019a; Wong et al 2020) has been demonstrated in various contexts (García et al 2015; Shishegar et al 2018) These include using urban surfaces as a multifunction retention space for rainwater during heavy rainfall (Lund et al 2019a), dynamically optimizing water distribution within the sewer system to minimize emissions to the environment (Fradet et al 2011; Langeveld et al 2013; Löwe et al 2016), reducing the energy demand from sewer operations (Kroll et al 2018) while maximizing the use of electricity from renewable sources (Stentoft et al 2020), and increasing the treatment capacity of wastewater treatment plants (WWTPs) during and after wet weather events (e.g. aeration tank settling, ATS; Sharma et al 2013). All of these applications either require or can be improved by the availability of a forecast of expected sewer flows, typically over forecast horizons ranging from 30 min up to 24 h
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