The University of Sheffield
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journal contribution
posted on 2017-09-01, 15:19 authored by Kegong Diao, David Butler, Bogumil Ulanicki
Fractals have been identified as a common feature of many natural and artificial systems that exhibit similar patterning at different scales. Understanding fractals is a critical aspect of decoding complex systems, as the pattern of such large systems can be revealed by identifying only a small part of the system. Furthermore, identify existing features of such systems can start at the large scale with the fewest details of the system under scrutiny before doing a more detailed analysis at finer scales. Such a process provides an efficient and reliable way of analysing and managing information of big data systems. This study revealed the fractality in water distribution networks (WDNs) based on research on fractals in complex networks. Specifically, we explored the existence of fractal patterns in six real world WDNs of different complexities (e.g. from a network with only 21 pipes to a network with 2465 pipes). The box-covering algorithm has been applied, which is the most widely used method to distinguish between fractal or non-fractal networks. The WDNs are first mapped into undirected graphs. Next, the method partitions the nodes into boxes of size l B , i.e. the maximal distance between nodes within each box is at most l B − 1 . By varying the box sizes, different minimum numbers of boxes N B required to cover the entire network can be identified. A network is fractal if the regression line for log ( N B ) and log ( l B ) is linear. The results demonstrate the existence of fractal patterns in all case study WDNs, as linear regression lines with coefficient of determination over 0.95 ( R 2 > 0 . 95 ) are obtained in all analyses. As further verification, the self-similarity on multiscales is revealed, i.e. the similarity in patterns of component criticality. Based on the fractal patterns, a systematic method is also developed for more efficient identification of critical pipes in WDNs, e.g. reducing the computational load by 61% in the case study.


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