A gradient method for fuzzy analysis of water distribution networks

Abstract

In the analysis of water distribution networks (WDNs) facing uncertainty, fuzzy set theory is suggested as an applicable stochastic analysis approach when the probability distributions of the information are not available. This technique can recognize the extreme values of unknown variables when uncertain input information varies between pre-specified extremes. Current approaches proposed in the literature for the fuzzy analysis of WDNs are computationally burdensome, and therefore restricted in their applicability to large networks. In this paper, elements of the Jacobian matrix of network equations, with respect to the unknown variables are calculated. Based on the negative and positive signs of the Jacobian matrix elements, the extreme values of fuzzy memberships for nodal pressures and flows can be approximated, which accelerates the fuzzy analysis process. Numerical results of analysis for three networks show that the proposed gradient method finds accurate solutions and significantly reduces computational time, relative to the existing approaches.

Keywords:

• Fuzzy analysis
• gradient method
• pipe networks
• water distribution