Regularization of an Inverse Problem for Parameter Estimation in Water Distribution Networks

Abstract

An accurate hydraulic model of a water distribution network (WDN) is a critical prerequisite for a multitude of operational, optimization, and planning tasks. The accuracy of a hydraulic model can only be maintained through its periodic calibration and validation with acquired pressure and flow data from a WDN. It is important that this process be robust and computationally efficient. This paper describes the regularization of an inverse problem to deal with data uncertainties and ill-posedness of parameter estimation problems in WDNs. A novel data-driven strategy is presented for tuning the regularization hyperparameter for the inverse problem and also for validating the results on an independent set of operational hydraulic data. A limited-memory quasi-Newton method (L-BFGS-B) is implemented to solve the resulting regularized nonlinear inverse problem. Furthermore, the implemented method utilizes either the Darcy-Weisbach or Hazen-Williams head loss formulas and is investigated both with and without pipe grouping. An extensive experimental program was carried out to acquire unique hydraulic data from an operational WDN in order to investigate the robustness of the proposed parameter estimation method. The hydraulic model of the operational WDN and the acquired hydraulic data are provided as supplementary data to enable the comparison of hydraulic model calibration methods with operational data and encourage reproducible research.