Cascaded neural network surrogate modeling for real-time decision-making in long-distance water supply distribution

Effective water distribution in long-distance supply systems requires precise control over pump station operations and flow-regulating elements, such as pump speeds and valve openings, typically achieved through hydraulic models. However, traditional hydraulic models are time-intensive to develop and require frequent calibration, limiting their practicality for real-time applications. This paper presents a cascaded neural network (CNN) model that integrates classification and regression components to serve as an efficient surrogate model for real-time water distribution decision-making. In the proposed CNN model, the classification component identifies the number of pumps needed to meet system flow demands, while the regression component predicts target values for pump speeds and valve openings. Considering the nonlinear relationship between flow rate and regulating elements, flow error was introduced as an evaluation metric via Orthogonal-Triangular (QR) decomposition. The CNN model's performance and robustness were validated using data from an actual long-distance water supply system, including analyses of its sensitivity to uncertainties in the reservoir level and flow rate measurements. Results demonstrate that the CNN model achieves more accurate and efficient predictions compared to the traditional pure regression neural networks. Furthermore, uncertainty analysis reveals that while the CNN model is less affected by reservoir level measurement errors, it is more sensitive to flow rate measurement errors, underscoring importance of precise flow monitoring in practical applications.