Fractal Analysis of the Optimal Hydraulic Gradient Surface in Water Distribution Networks

Abstract

This study aimed to examine the fractal properties of the optimal hydraulic gradient surface (OHGS), a geometrical body that describes the way in which the available energy should be spent within a water distribution network to ensure the calculation of a minimum capital cost design. For this purpose, multiple benchmark and Colombian systems were optimized and then analyzed to compute the fractal dimension of the OHGS and of the underlying structure of each network, which included the examination of randomly generated nonoptimal designs to recognize the differences in the fractal behavior of a least-cost and a more expensive solution. The results showed a dependency between the fractal properties of the OHGS and those of the topological structure, flow, and energy distribution inside the corresponding optimized network. Moreover, it was found that the degree of irregularity of the OHGS tended to be higher compared to a nonoptimal energy dissipation pattern. This suggests the applicability of the fractal analysis in optimization and operational improvement procedures. © 2022 This work is made available under the terms of the Creative Commons Attribution 4.0 International license,.