Given the increasing trend in water scarcity, which threatens a number of regions worldwide, governments and water distribution system (WDS) operators have sought accurate methods of estimating water demands. While investigators have proposed stochastic and deterministic techniques to model water demands in urban WDS, the performance of soft computing techniques [e.g., Genetic Expression Programming (GEP)] and machine learning methods [e.g., Support Vector Machines (SVM)] in this endeavour remains to be evaluated. The present study proposed a new rationale and a novel technique in forecasting water demand. Phase space reconstruction was used to feed the determinants of water demand with proper lag times, followed by development of GEP and SVM models. The relative accuracy of the three best models was evaluated on the basis of performance indices: coefficient of determination (R 2 ), mean absolute error (MAE), root mean square of error (RMSE), and Nash-Sutcliff coefficient (E). Results showed GEP models were highly sensitive to data classification, genetic operators, and optimum lag time. The SVM model that implemented a Polynomial kernel function slightly outperformed the GEP models. This study showed how phase space reconstruction could potentially improve water demand forecasts using soft computing techniques.

This article proposes a new general approach in short-term water demand forecasting based on a two-stage learning process that couples time-series clustering with gene expression programming (GEP). The approach was tested on the real life water demand data of the city of Milan, in Italy. Moreover, multi-scale modeling using a series of head-time was deployed to investigate the optimum temporal resolution under study. Multi-scale modeling was performed based on rearranging hourly based patterns of water demand into 3, 6, 12, and 24 h lead times. Results showed that GEP should receive more attention among the emerging nonlinear modelling techniques if coupled with unsupervised learning algorithms in detailed spherical k-means.

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