Integrated theoretical and data-driven Gaussian Process NARX Model for the Simulation of Effluent Concentrations in Wastewater Treatment Plant

Abstract

Abstract This paper presents the data-driven modelling part of a multi-input multi-output hybrid model of the Wastewater Treatment Plant (WWTP) and the simulation of the WWTP effluent. The information about the future effluent concentrations is important since it is used for efficient managing of the plant, for example in decision making, predictive control, quality control, and detection of violation of effluent limits. The hybrid model consists of a theoretical model based on first principles upgraded with a probabilistic data-driven model. The integrated model is based on a multi-input multi-output autoregressive Gaussian process (GP) model where the exogenous inputs include the predictions from the theoretical model. This approach allows us to use all available information in a single integrated model. We show significant improvement over the theoretical model for one-day-ahead prediction and validate the model for simulation, which can also be used when the effluent concentrations are not measured in an on-line fashion.