Hybrid Water Demand Forecasting Model Associating Artificial Neural Network with Fourier Series

Abstract

This paper addressed the problem of water-demand forecasting for real-time operation of water supply systems. The present study was conducted to identify the best fit model using hourly consumption data from the water supply system of Araraquara, São Paulo, Brazil. Artificial neural networks (ANNs) were used in view of their enhanced capability to match or even improve on the regression model forecasts. The ANNs used were the multilayer perceptron with the back-propagation algorithm (MLP-BP), the dynamic neural network (DAN2), and two hybrid ANNs. The hybrid models used the error produced by the Fourier series forecasting as input to the MLP-BP and DAN2, called ANN-H and DAN2-H, respectively. The tested inputs for the neural network were selected literature and correlation analysis. The results from the hybrid models were promising, DAN2 performing better than the tested MLP-BP models. DAN2-H, identified as the best model, produced a mean absolute error (MAE) of 3:3 L∕s and 2:8 L∕s for training and test set, respectively, for the prediction of the next hour, which represented about 12% of the average consumption. The best forecasting model for the next 24 hours was again DAN2-H, which outperformed other compared models, and produced a MAE of 3:1 L∕s and 3:0 L∕s for training and test set respectively, which represented about 12% of average consumption.

A Short-Term Data Based Water Consumption Prediction Approach

“…Similarly, the work in [13] also employed ANNs in the forecasting of water demand for Araraquara, in the city of São Paulo, in Brazil. The authors tried to identify the model that fit better by using hourly consumption data.…”

Application of Wavelet Decomposition and Phase Space Reconstruction in Urban Water Consumption Forecasting: Chaotic Approach (Case Study)

“…to identify the relationship between the input and output variables. Conventional regression models [3], autoregressive integrated moving average (ARIMA) [23], autoregressive integrated moving average with explanatory variable (ARIMAX) [24,25], artificial neural networks (ANN) [9,[26][27][28][29], a combination of conventional and ANN [11,12,30], feedforward neural networks [12,31], general regression neural networks [32,33], support vector machines [14,9,[34][35][36][37], gene expression programming [14,38], fuzzy regression [39], neuro-fuzzy systems [40,41], Fourier analysis [4], hybrid models (e.g. combined wavelet-ANN and wavelet-GEP) [13,38], fuzzy cognitive map learning method [42,43].…”

“…Long-term urban demand forecasting (up to 25 years), mid-term (up to 2 years) and short-term values (up to 2 days) depends upon vital factors such as water supply planning, pipeline maintenance, and water distribution system optimization (e.g. optimized pumping, pipeline maintenance, minimize energy cost and water supply cost, improving system reliability and water quality), respectively [3][4][5]. While studies have advanced the understanding of nonlinear characteristics and high complexity of water consumption factors, further research is still required.…”

Nonlinear Dynamic Modeling of Urban Water Consumption Using Chaotic Approach (Case Study: City of Kelowna)

“…Therefore, considering reliable forecasting horizon can be beneficial in any management plan. Moreover, forecasting consumption values in short-, mid-, and long-term (i.e., less than a week, a week to a month, a month to a year or more, respectively) time periods play a crucial role in water distribution systems' (WDS) daily operation basis by informing important factors such as optimized pumping, pipeline maintenance, minimizing energy and water supply cost, improving system reliability and the quality of allocated water [7][8][9]. Recent studies have improved the understanding of the nonlinearity and complexity of water consumption factors; however, more study on these concepts is required.…”