A Data-Driven Surrogate Modelling Approach for Acceleration of Short-Term Simulations of a Dynamic Urban Drainage Simulator

Mahmood Mahmoodian,Ulrich Leopold,Jairo Arturo Torres-Matallana,Georges Schutz,Francois H L R Clemens

doi:10.3390/w10121849

Mahmood Mahmoodian, Ulrich Leopold + Show 3 more

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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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Surrogate modelling is an approach to develop a simpler and faster model emulating the outputs of a more complex simulator as a function of its inputs and parameters [1]
We focus on the application of Gaussian Process Emulator (GPE), since in addition to the above mentioned advantages, it provides estimation error bands which can be useful for uncertainty quantification purposes
The candidate simulator subject to surrogate modelling in this study is a 1D-2D Urban Drainage Modelling (UDM) developed in InfoWorks® ICM 8.5, which requires a detailed description of the structure and geometry of urban drainage network, as well as, numerous parameters and inputs for wastewater hydraulic and quality modelling

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Introduction

Surrogate modelling is an approach to develop a simpler and faster model emulating the outputs of a more complex simulator as a function of its inputs and parameters [1]. In Urban Drainage Modelling (UDM), most of the urban drainage simulators are among the computationally demanding modelling tools. This is often due to the consideration of a multitude of detailed processes with a large number of parameters, inputs, and detailed network geometries building the underlying equations. Based on reference [1], three main categories of surrogate models can be identified including: data-driven approaches; projection-based approaches; and hierarchical or multi-fidelity approaches. Hybrid approaches can be developed by combination of any of the three main categories [15]

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