In this paper, two types of controllers are proposed and compared to attain a better understanding of the potential of a real-time control (RTC) approach based on wastewater quantity and quality for combined sewer networks. The first controller is solely based on a wastewater quantity control approach, whilst, the second one is also considering wastewater quality modelling, as well as its uncertainty propagation. In fact, we have developed the first controller to achieve the second one without the requirement of adding new measurement devices to the given system. Model Predictive Control (MPC) approach is selected as the underlying control method. The control model in this study is a simple but fast model which is developed based on volume balance and mass balance laws in the tanks and time delay concept in the pipes. This model is described and applied to a simple case study to illustrate and discuss the results. The uncertainty propagation in the second controller is based on Taylor series of first order approximation. Based on the simulations and the achieved results, it was observed that the introduced pollution-based MPC approach is able to reduce significantly the volume of combined sewer overflows (CSOs) as well as the pollution load caused by them. Finally, it is concluded that considering the pollution load and its uncertainty propagation in the objective function of the optimization problem has a significant effect on the system performance improvement. This is a very important achievement because it can reduce the released pollution load to the environment without the requirement of additional equipment in the system. Because such elements (e.g. sensors) are normally expensive to purchase and maintain.
Urban drainage modelling typically requires development of highly detailed simulators due to the nature of various underlying surface and drainage processes, which makes them computationally too expensive. Application of such simulators is still challenging in activities such as real-time control (RTC), uncertainty quantification analysis or model calibration in which numerous simulations are required. The focus of this paper is to present a rather simple hybrid surrogate modelling (or emulation) strategy to simplify and accelerate a detailed urban drainage simulator (UDS). The proposed surrogate modelling strategy includes: a) identification of the variables to be emulated; b) development of a simplified conceptual model in which every component contributing to the variables identified in step (a) is replaced by a function; c) definition of these functions, either based on knowledge about the mechanisms of the simulator, or based on the data produced by the simulator; and finally, d) validation of the results produced by the surrogate model in comparison with the original detailed simulator. Herein, a detailed InfoWorks ICM simulator was selected for surrogate modelling. The case study area was a small urban drainage network in Luxembourg. An emulator was developed to map the rainfall time series, as input, to a storage tank volume and combined sewer overflow (CSO) in the case study network. The results showed that the introduced strategy provides a reliable method to simplify the simulator and reduce its run time significantly. For the specific case study, the emulator was approximately 1300 times faster than the original detailed simulator. For quantification of the emulation error, an ensemble of 500 rainfall scenarios with 1 month duration was generated by application of a multivariate autoregressive model for conditional simulation of rainfall time series. The results produced by the emulator were compared to the ones produced by the simulator. Finally, as an indicator of the emulation error, distributions of Nash-Sutcliffe efficiency (NSE) between the emulator and simulator results for prediction of storage tank volume and CSO flow time series were presented.
In this study, applicability of a data-driven Gaussian Process Emulator (GPE) technique to develop a dynamic surrogate model for a computationally expensive urban drainage simulator is investigated. Considering rainfall time series as the main driving force is a challenge in this regard due to the high dimensionality problem. However, this problem can be less relevant when the focus is only on short-term simulations. The novelty of this research is the consideration of short-term rainfall time series as training parameters for the GPE. Rainfall intensity at each time step is counted as a separate parameter. A method to generate synthetic rainfall events for GPE training purposes is introduced as well. Here, an emulator is developed to predict the upcoming daily time series of the total wastewater volume in a storage tank and the corresponding Combined Sewer Overflow (CSO) volume. Nash-Sutcliffe Efficiency (NSE) and Volumetric Efficiency (VE) are calculated as emulation error indicators. For the case study herein, the emulator is able to speed up the simulations up to 380 times with a low accuracy cost for prediction of the total storage tank volume (medians of NSE = 0.96 and VE = 0.87). CSO events occurrence is detected in 82% of the cases, although with some considerable accuracy cost (medians of NSE = 0.76 and VE = 0.5). Applicability of the emulator for consecutive short-term simulations, based on real observed rainfall time series is also validated with a high accuracy (NSE = 0.97, VE = 0.89).
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