Nodal Pressure Heads Research Articles

WLS Method for Parameter Estimation in Water Distribution Networks

The weighted-least-squares method based on the Gauss-Newton minimization technique is used for parameter estimation in water distribution networks. The parameters considered are: element resistances (single and/or group resistances, Hazen-Williams coefficients, pump specifications) and consumptions (for single or multiple loading conditions). The measurements considered are: nodal pressure heads, pipe flows, head loss in pipes, and consumptions/inflows. An important feature of the study is a detailed consideration of the influence of different choice of weights on parameter estimation, for error-free data, noisy data, and noisy data which include bad data. The method is applied to three different networks including a real-life problem.

Parameter Estimation for Water Distribution Networks

Calibration of a water distribution network is a long, tedious task, if analyzed by an engineer, with no guarantee of determining the proper system parameters. In addition, more utilities are moving toward automated control and wish to estimate the state of the network based upon telemetry data, A rigorous, nonlinear programming algorithm, which incorporates a network simulation model, is presented to solve these problems. The model is capable of analyzing one or more independent demand patterns, or extended period simulations, or both. The model assumes the measurements are exact and has an objective of minimizing the sum of the squares or absolute values of the differences between observed and estimated values of pipe flows and nodal pressure heads. The model consistently finds optimal solutions with the objective function equal to zero with exact data. However, the estimated parameters (pipe roughness coefficients, valve settings, and nodal demands) are not always the true values, which points to a nee...

Reliability‐Based Optimization Model for Water Distribution Systems

This paper presents the basic framework for a model that can be used to determine the optimal (least‐cost) design of a water distribution system subject to continuity, conservation of energy, nodal head bounds, and reliability constraints. Reliability is defined as the probability of satisfying nodal demands and pressure heads for various possible pipe failures (breaks) in the water distribution system. The overall model includes three that are linked: a steady‐state simulation model, a reliability model, and an optimization model. The simulation model is used to implicitly solve the continuity and energy constraints and is used in the reliability model to define minimum cut sets. The reliability model, which is based on a minimum cut‐set method, determines the values of system and nodal reliability. The optimization model is based on a generalized reduced‐gradient method. Examples are used to illustrate the model.