An interval water demand prediction method to reduce uncertainty: A case study of Sichuan Province, China.

Effective prediction of water demand is a prerequisite for decision makers to achieve reliable management of water supply. Currently, the research on water demand prediction focuses on point prediction method. In this study, we constructed a GA-BP-KDE hybrid interval water demand prediction model by combining non-parametric estimation and point prediction. Multiple metaheuristic algorithms were used to optimize the Back-Propagation Neural Network (BP) and Kernel Extreme Learning Machine (KELM) network structures. The performance of the water demand point prediction models was compared by the Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Kling-Gupta Efficiency (KGE), computation time, and fitness convergence curves. The kernel density estimation method (KDE) and the normal distribution method were used to fit the distribution of errors. The probability density function with the best fitting degree was selected based on the index G. The shortest confidence interval under 95% confidence was calculated according to the asymmetry of the error distribution. We predicted the impact indicator values for 2025 using the exponential smoothing method, and obtained water demand prediction intervals for various water use sectors. The results showed that the GA-BP model was the optimal model as it exhibited the highest computational efficiency, algorithmic stability, and prediction accuracy. The three prediction intervals estimated after adjusting the KDE bandwidth parameter covered most of the sample points in the test set. The prediction intervals of the four water use sectors were evaluated as F values of 1.6845, 1.3294, 1.6237, and 1.3600, which indicates high accuracy and quality of the prediction intervals. The mixed water demand interval prediction based on GA-BP-KDE reduces the uncertainty of the point prediction results and can provide a basis for water resource management by decision makers.