Version 1
: Received: 30 December 2018 / Approved: 3 January 2019 / Online: 3 January 2019 (10:41:34 CET)
Version 2
: Received: 18 January 2019 / Approved: 20 January 2019 / Online: 20 January 2019 (10:25:36 CET)
Version 3
: Received: 4 February 2019 / Approved: 11 February 2019 / Online: 11 February 2019 (11:33:12 CET)
Magini, R.; Boniforti, M.A.; Guercio, R. Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks. Water2019, 11, 493.
Magini, R.; Boniforti, M.A.; Guercio, R. Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks. Water 2019, 11, 493.
Magini, R.; Boniforti, M.A.; Guercio, R. Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks. Water2019, 11, 493.
Magini, R.; Boniforti, M.A.; Guercio, R. Generating Scenarios of Cross-Correlated Demands for Modelling Water Distribution Networks. Water 2019, 11, 493.
Abstract
A numerical approach for generating a limited number of water demand scenarios and estimating their occurrence probabilities in a Water Distribution Network (WDN) is proposed. This approach makes use of the demand scaling laws in order to consider the natural variability and spatial correlation of nodal consumptions. The scaling laws are employed to determine the statistics of nodal consumption as a function of the number of users and the main statistical features of the unitary user's demand. Besides, consumption at each node is considered to follow a Gamma probability distribution. A high number of groups of cross-correlated demands, i.e., scenarios, for the entire network were generated using Latin Hypercube Sampling (LHS) and the numerical procedure proposed by Iman and Conover. The Kantorovich distance is used to reduce the number of scenarios and estimate their corresponding probabilities, while keeping the statistical information on nodal consumptions. By hydraulic simulation, the whole number of generated demand scenarios was used to obtain a corresponding number of pressure scenarios on which the same reduction procedure was applied. The probabilities of the reduced scenarios of pressure were compared with the corresponding probabilities of demand.
Keywords
uncertain water demand; scaling laws; scenario generation; scenario reduction; water distribution networks; hydraulic simulation
Subject
Engineering, Civil Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
