Uncertainty evaluation for constrained state estimation in water distribution systems Articles uri icon

publication date

  • August 2016


  • 12


  • 142

International Standard Serial Number (ISSN)

  • 0733-9496


  • In this paper, an alternative uncertainty treatment for the traditional unconstrained weighted-least-squares (WLS) method is presented. This treatment enables hydraulic constraints (i.e., null demands at transit nodes or null flows at closed pipes, pumps, or valves, etc.), high-precision measurements, and upper and lower variable bounds (i.e., head levels at tanks) to be included within the state estimation (SE) problem for water distribution systems. With this approach, there is no need to choose appropriate weights associated with these types of measurements in order to correctly assess uncertainty for the SE problem. The method set out herein tackles these as constraints and works with the linear system of equations derived from imposing first-order optimality conditions for the constrained SE problem. This approach enables general quantification of the SE uncertainty for all the hydraulic variables within the water system by applying the first-order second-moment (FOSM) method. Moreover, it enables standard computation of the covariance residual matrix associated with it, which is necessary to detect erroneous measurements. An illustrative example and a case study are shown to bring out the fact that the SE uncertainty results are more accurate and to show how the numerical conditioning of the system is affected, which may be crucial when dealing with large-scale water networks.


  • Environment


  • exact measurements; residuals treatment; uncertainty analysis; weighted least squares