Enhanced Artificial Neural Networks Estimating Water Quality Constraints for the Optimal Water Distribution Systems Design

Optimal water distribution system (WDS) design including the layout and pipe sizes is invariably complex, even when hydraulic constraints alone are considered. The addition of water quality (WQ) constraints adds to the computational demands. Using conventional WQ models to evaluate the feasibility of the many networks that must be analyzed can extend the optimization process beyond acceptable limits. Artificial neural networks (ANNs) can approximate disinfectant concentrations in a fraction of the time required by deterministic WQ models, and thus have been used for WDS pipe optimization as fast surrogates of these models. This study seeks to improve the performance of ANNs applied to the optimal design of WDSs by comparing their outcomes on the basis of ANN architecture and data used for ANN training, two factors that affect their speed and accuracy. ANNs were trained to forecast the disinfectant concentration at the relevant nodes of two case studies: A simple WDS (common in the literature of WDS pipe optimization) and a complex WDS that supplies an actual community in the city of Maricopa, Arizona. The results obtained for the first case study showed that ANNs estimated disinfectant concentrations with a satisfactory accuracy, regardless of their architecture or data used for their training. Results obtained for the second case study, however, showed that ANNs with a conventional architecture (wherein multiple ANNs are required to forecast the disinfectant concentration at relevant nodes of the WDS) offered advantages in terms of accuracy over two alternative architectures (that each required a single ANN for the same purpose). However, ANNs trained with a conventional random data set showed a poor performance when compared to ANNs trained with an alternative data set that was obtained with the probabilistic approach described in this paper.