Direct Inversion Algorithm for Pipe Resistance Coefficient Calibration of Water Distribution Systems

To enable a water distribution system (WDS) model to yield predictions with a reasonably good match to measurements, pipe resistance coefficients (PRCs) of the model often need to be calibrated. The majority of methods developed recently solve the PRCs' calibration problem using evolutionary algorithms. The common feature of these methods is to perform the forward computation (i.e.,solve the traditional hydraulic equation of networks) repeatedly to search optimal solutions. This paper presents a direct inversion algorithm for PRC calibration of WDSs, which has an identical framework with a global gradient algorithm (GGA) that has been proved to be the most effective method to solve networks and adopted by EPANET. Therefore, all advantages of GGA can be extended in terms of high computational efficiency and convergence, as well as being easy to understand and program. In addition, under the proposed framework, uncertainties propagated from measurement noises, nodal demand uncertainties, and model simplification errors to the estimates can be quantified individually or simultaneously in a flexible manner, enabling the identification of uncertainties source, as well as which kind of effort is preferred to reduce them. Three networks are applied to validate the proposed algorithm. Encouraging results achieved demonstrate that the proposed algorithm is valid for the calibration and uncertainty qualification of PRCs, as well as the uncertainty source identification.