Abstract
Scientific prediction of water consumption is beneficial for the management of water resources. In practice, many factors affect water consumption, and the various impact mechanisms are complex and uncertain. Meanwhile, the water consumption time series has a nonlinear dynamic feature. Therefore, this paper proposes a nonlinear autoregressive model with an exogenous input (NARX) neural network model based on rough set (RS) theory. First, the RS theory was used to analyze the importance of each attribute in water consumption. Then, the main influencing factor was selected as the input of the NARX neural network model, which was applied to predict water consumption. The proposed model is proved to give better results of a single NARX model and a back propagation neural network. The experimental results indicate that the proposed model has higher prediction accuracy in terms of the mean absolute error, mean absolute percentage error and root mean square error.
Highlights
The Attribute Reduction in Water Consumption Based on the Rough Set
Where xmax is the maximum value in the series, xmin is the minimum value in the series, and k is the given parameter, which is the number of intervals
The reduction results are used as the inputs of the predictive model, and the nonlinear autoregressive model with an exogenous input (NARX) neural network model is used to predict water consumption
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Many methods are based on time-series models, which focus on past behaviors of water consumption, and can be complemented by some exogenous variables, such as the statistical regression model [1,2]. The ANNs can learn from patterns and capture hidden functional relationships in given data, even if the functional relationships are unknown or difficult to identify This kind of ability makes them applicable to nonlinear time-series prediction with satisfactory prediction results. After establishing the NARX neural network model, the predictions for water consumption are generated. In the proposed RS-NARX model, (1) the RS theory can remove the redundant information and improve the interpretability of input variables, and (2) the NARX neural network can better fit the nonlinear dynamic sequence in macroscale (i.e., annual water consumption). The rest of this paper is organized as follows: Section 2 briefly introduces the RS theory and the NARX neural network; In Section 3, the related data and evaluation indexes are described; In Section 4, the experiments and results of the RS-NARX neural model are analyzed; Section 5 summarizes this paper
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