Predictive analysis of urban wastewater capacity using ANN and ODE model: A case study

The discharge of urban wastewater represents a significant aspect to be considered in the development and design of water and wastewater treatment projects. In this study, the annual urban wastewater discharge was estimated using an artificial neural network (ANN) and differential equations. In order to achieve this, data pertaining to the recorded wastewater per capita amount for the Kayseri province (located in Turkey) over a 17-year period between 2003 and 2020, the city's population, capacity, number of WWTPs, the amount of daily wastewater discharged per person, and the wastewater treated in WWTPs (y(t)) were collated. As the initial data set was insufficient, it was augmented using the ARIMA model and then normalised. The augmented and normalised data was trained with ANN on two occasions, thus demonstrating the impact of other variables on the y(t) variable. Additionally, mathematical ANN activation functions in the form of a tangent hyperbolic function were proposed for this variable. Subsequently, the arbitrary parameters employed in a linear system comprising differential equations representing the aforementioned five variables were estimated utilising the normalised original data, thereby facilitating the formulation of an Ordinary Differential Equation (ODE) model. The performance of two ANN and ODE models was evaluated on normalized real data, and the results were compared. Consequently, the estimation of the quantity of wastewater with the lowest error rate of 0.00001 MSE among the models incorporating four time-dependent variables as inputs was conducted using the ODE model. The model exhibited an R² value of 0.9363 and a MAPE value of 0.0231. The promising estimation results obtained demonstrate the potential utility of this approach for the efficient management of wastewater demand and the protection of valuable water resources.