Simultaneous zonation and calibration of pipe network parameters

A procedure for simultaneously zoning and calibrating pipe network parameters is proposed and applied to the determination of pipe resistance coefficients. The methodology is aimed at grouping the parameters of all the pipes into a small number of zone parameters, constrained to keep the difference between the computed and the measured water heads below a given tolerance. It is shown that, in the case of nonlooped networks, the methodology leads to a linear minimization problem where the objective function is a measure of the heterogeneity of the estimated parameters. In the case of looped networks an iterative procedure, where the linear problem is coupled with a nonlinear problem having a restricted number of decision variables, is proposed and demonstrated. Application of the procedure to a hypothetical example is shown. In a lab experiment, the model of a pipe network made by two different types of links has been calibrated using two measurement points and three different measured data sets, each of which was obtained by adjusting the valves located in the network to modify the pressure field. Comparison of the measured and the estimated resistance coefficients shows good correlation.