Short-term water demand predictions coupling an artificial neural network model and a genetic algorithm

The application of artificial neural network (ANN) models for short-term (15 min) urban water demand predictions is evaluated. Optimization of the ANN model’s hyperparameters with a genetic algorithm (GA) and use of a growing window approach for training the model are also evaluated. The results are compared to those of commonly used time series models, namely the Autoregressive Integrated Moving Average (ARIMA) model and a pattern-based model. The evaluations are based on data sets from two Canadian cities, providing 15 min water consumption records over respectively 5 years and 23 months, with a respective mean water demand of 14,560 and 887 m/d. The GA optimized ANN model performed better than the other models, with Nash–Sutcliffe Efficiencies of 0.91 and 0.83, and relative root mean square errors of 6 and 16% for City 1 and City 2, respectively. The results of this study indicate that the optimization of the hyperparameters of an ANN model can lead to better 15 min urban water demand predictions, which are useful for many real-time control applications, such as dynamic pressure control.


INTRODUCTION
Forecasting urban water demand (UWD) is a crucial issue to ensure the better design, operation, and management of water distribution systems (WDSs). While long-term forecasting is mainly required for planning and design, short-term forecasting is particularly used for operation and management.  short-term UWD for the city of Bangkok, Thailand. However, they showed that meteorological, water utility and socioeconomic variables have a greater influence on medium-term (e.g. monthly) predictions. The benefit of univariate models was also reported by Odan & Reis () where their ANN models for short-term UWD prediction did not require the use of weather variables, resulting in a simpler and faster model to train. Also, size of the data sets of case studies can affect the ANN model performance.
As Gagliardi et al. () showed, an ANN model applied to small districts, with a low number of users and more variability in water demands, can outperform a pattern-based model while, for districts that contain a large number of users, the pattern-based model tends to be more efficient than the ANN one.
Evolutionary algorithms (Bäck ) have been used along with AI techniques for UWD prediction, either for the optimization of training algorithms (Rangel et al. ) or optimization of model hyperparameters (Chen ). For their case study, they found that the growing window approach led to better results.
In terms of UWD, the definition of short-term predictions varied among authors. Although many of them consider predictions 1 h ahead as being short term (e.g.

).
To the best of the authors' knowledge, this is the first time that the performance of these three types of models in making predictions of UWD for time steps shorter than 1 h has been compared. Data sets provided by two Canadian cities are used for these evaluations.

METHODS Datasets
The datasets analyzed in this study were collected from two cities in the province of Quebec (Canada). The data con-   In this work, three ANN models are developed. In all cases, datasets were decomposed to the trend and cyclical components, and were used as inputs to the ANN models. (2) The model was coded using MATLAB 2014a software by considering, as most as possible, the steps and parameters

Performance indicators
The accuracies of the different models were evaluated using the following three statistical indices, namely the RRMSE,  Table 1, where N is the total number of forecasted values, C t is the measured value at time t,Ĉ t is the forecasted value at time t, and C is the mean of the measured values.

RESULTS AND DISCUSSION
The performance indices (RRMSE, MAPE and E) of the studied models for the test sets of the two case studies are presented in Table 2. Examples of results are illustrated for two specific days in Figure 4 for City 1 and City 2.   Another finding of this study was that hyperparameter optimization of the ANN model could enhance its prediction performance. This supports the findings of Romano & Kapelan () for the prediction of UWD 1 to 24 h ahead.
These authors reported Nash-Sutcliffe efficiencies higher than 0.9 for their adaptive ANN models for both daily and hourly forecasting. Their optimization procedure included six decision variables, namely the number of hidden neurons, the number of training cycles, the training algorithm regularization factor, the lag size, the time of the day and the day of the week.

CONCLUSIONS AND PERSPECTIVES
The 15 min UWD predictions obtained by different models were compared in this paper, based on data col-