Approach for Water Distribution System Model Calibration Based on Iterative Sherman–Morrison Formula

Abstract

Real-time modeling of water distribution systems (WDSs) has received much attention in WDS operation and management. As the model input, nodal water demand must be calibrated in a timely manner. However, for the large-scale WDSs, real-time calibration of nodal water demand can become very computationally expensive, as the computation complexity of the Hessian matrix inversion grows exponentially with the increasing number of nodal water demands. To address the difficulty, an efficient algorithm to calibrate the nodal water demand is developed. The algorithm can solve the Hessian matrix inversion based on the iterative Sherman–Morrison formula. By adopting parallel programming, the developed approach can efficiently shorten the computation time. The performance of the algorithm is evaluated by a set of networks with the number of nodal water demands ranging from 31 to 12,523. Results show that this approach can accurately calibrate the nodal water demand and the computation efficiency is significantly improved, especially when the number of measurements is far less than the number of nodal water demands. This approach is expected to improve modeling accuracy and computational efficiency for the real-time modeling of WDSs.