PROPOSITION OF FRACTAL DIMENSION APPLICATION FOR THE ESTIMATION OF CERTAINTY OF WATER DELIVERY
Free (open access)
15 - 25
DARIUSZ KOWALSKI, BEATA KOWALSKA, PAWEŁ SUCHORAB, MAŁGORZATA IWANEK
One of the most difficult steps during evaluating of the system safety plan is the evaluation of certainty of water delivery through the distribution network. So far, no universal method of this estimation has been fully elaborated. Most often, the various reliability factors are used. However, these factors does not always include the geometrical structure of distribution network. It can be analysed by methods of minimal cut or efficiency sets paths between water source and outtake or even all nodes. However, such methods are very laborious and their difficulty increases together with the increase of degree of network complexity. The aim of this paper is to present a proposition of an application of two methods: reference nodes and fractal dimension, for estimation of certainty of water delivery though complex distribution networks. Exemplary calculation presented in the paper, were conducted for 6 different models and real water supply networks. The conducted calculations indicated that reference nodes method has a limitation to maximum 6 looped networks. Fractal dimension method doesn’t have such limitation. The proved in the paper relationship between fractal dimension value and number of minimal efficiency sets paths indicates that this method can be used for complex networks estimation.
water delivery certainty, minimal efficiency paths, fractal dimension, looped networks