Efficient numerical approach for simultaneous calibration of pipe roughness coefficients and nodal demands for water distribution systems

Hydraulic models have been widely used to facilitate the design, management, and operation of water distribution systems (WDS). However, model parameters including pipe roughness coefficients (PRCs) and nodal demands (NDs) must be calibrated before practical applications, and the calibration accuracy and efficiency is important to enable their wide uptake in practice. This therefore motivates intensive studies to develop approaches for model calibration focusing on either optimization algorithms or numeric methods. Although these previous studies have advanced this research area, the calibration efficiency and effectiveness need to be further improved, especially when dealing with real-world problems. To attain this objective, this paper proposes an efficient numerical approach to simultaneously calibrate PRCs and NDs for WDS. Within this method, the calibration objective function is formulated as a least-square equation, followed by the derivation of iterative formulas according to a local sensitivity analysis. These formulas allow PRCs and NDs to be iteratively updated in an efficient manner until the given convergence criteria are met. To further improve the efficiency, the pipes and nodes are grouped according to their physical properties, which allows the calibration dimensions to be significantly reduced. Additionally, within the calibration process, values of PRCs and NDs are restricted into specified ranges to ensure the calibrated results are practically meaningful. Two case studies are used to demonstrate the utility of the proposed method, and results show that this approach is able to simultaneously calibrate PRCs and NDs efficiently, with the modeled hydraulic parameter values (pipe flows and nodal pressures) matching well with observations.