Using DFP Algorithm for Nodal Demand Estimation of Water Distribution Networks

Nodal demand estimation of a Water Distribution Network (WDN) means calculating the estimated values of nodal demands with some measured parameter values through mathematical methods. The most existing methods are based on an constrained weighted least-squares model and repeated computation of Jacobian matrix for optimal solutions. In this paper a new nonlinear model combined with pseudo-measurements and pressure constraints was developed for solution uniqueness. Davidon-Fletcher-Powell (DFP) algorithm was proposed to search for the solution by one dimensional optimization and scale matrix calculation, which was easier than Jacobian matrix computation. Two cases, including a real-life WDN of X city in northwest China, were used to show the performance of the proposed algorithm. Encouraging results showed that the proposed method was effective and feasible macroscopically, and it had potential for practical applications of WDNs.