Automatization of urban drainage modelling by hybridising domain knowledge and equation discovery

Urban drainage modelling (UDM) is widely used to assist decision-making process for numerous challenges related to urban water cycle. The procedure of UDM is quite complex, consisting of uncertain parameter values and alternative process formulations. In this research, we propose an automated urban drainage modelling approach, with the aim of improving the model selection and model calibration procedure. To this end, the automated modelling tool ProBMoT was used, based on equation discovery to (a) find the most suitable mathematical model among multiple alternatives for describing the selected (environmental) processes and (b) to calibrate model parameters on the measured data. ProBMoT takes into account domain-specific knowledge, formalized as templates for the components of the process-based models. It automatically identifies both the structure and parameter values of the appropriate model, given: a) a knowledge library representing mathematical formulations of environmental processes, b) a conceptual model of the observed system, and c) measurements. The knowledge library consists of entities that represent constituents of the dynamical systems in the selected domain and processes that correspond to interactions between the entities. This approach was applied to an urban catchment within the city of Ljubljana (Slovenia) to discover and calibrate hydrological models. The data for calibration were obtained by continuous measurements of flow rate in the sewer system. Three alternative equations for modelling surface runoff, i.e. SCS-CN, New PR and UKWIR, were encoded in the knowledge library. ProBMoT automatically constructed all viable alternative models and calibrated them against the measured data. Results show that all alternative models can be calibrated with similar accuracy. However, validation results show that some modelled rainfall events do not fit perfectly the measurements. Future work will focus on improving the reliability of modelling results by selecting the best model structure and parameters for a given type of rain events.