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Yu X, Wu Y, Meng F, Zhou X, Liu S, Huang Y, Wu X. A review of graph and complex network theory in water distribution networks: Mathematical foundation, application and prospects. Water Res 2024; 253:121238. [PMID: 38350191 DOI: 10.1016/j.watres.2024.121238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 01/28/2024] [Accepted: 01/29/2024] [Indexed: 02/15/2024]
Abstract
Graph theory (GT) and complex network theory play an increasingly important role in the design, operation, and management of water distribution networks (WDNs) and these tasks were originally often heavily dependent on hydraulic models. Facing the general reality of the lack of high-precision hydraulic models in water utilities, GT has become a promising surrogate or assistive technology. However, there is a lack of a systematic review of how and where the GT techniques are applied to the field of WDNs, along with an examination of potential directions that GT can contribute to addressing WDNs' challenges. This paper presents such a review and first summarizes the graph construction methods and topological properties of WDNs, which are mathematical foundations for the application of GT in WDNs. Then, main application areas, including state estimation, performance evaluation, partitioning, optimal design, optimal sensor placement, critical components identification, and interdependent networks analysis, are identified and reviewed. GT techniques can provide acceptable results and valuable insights while having a low computational burden compared with hydraulic models. Combining GT with hydraulic model significantly enhances the performance of analysis methods. Four research challenges, namely reasonable abstraction, data availability, tailored topological indicators, and integration with Graph Neural Networks (GNNs), have been identified as key areas for advancing the application and implementation of GT in WDNs. This paper would have a positive impact on promoting the use of GT for optimal design and sustainable management of WDNs.
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Affiliation(s)
- Xipeng Yu
- School of Environment, Tsinghua University, 100084, Beijing, PR China
| | - Yipeng Wu
- School of Environment, Tsinghua University, 100084, Beijing, PR China.
| | - Fanlin Meng
- School of Environment, Tsinghua University, 100084, Beijing, PR China
| | - Xiao Zhou
- College of Civil Engineering, Hefei University of Technology, 230009, Hefei, PR China
| | - Shuming Liu
- School of Environment, Tsinghua University, 100084, Beijing, PR China.
| | - Yujun Huang
- School of Environment, Tsinghua University, 100084, Beijing, PR China
| | - Xue Wu
- School of Environment, Tsinghua University, 100084, Beijing, PR China
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Sitzenfrei R, Hajibabaei M, Hesarkazzazi S, Diao K. Dual graph characteristics of water distribution networks-how optimal are design solutions? COMPLEX INTELL SYST 2023; 9:147-160. [PMID: 36844980 PMCID: PMC9947021 DOI: 10.1007/s40747-022-00797-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 05/27/2022] [Indexed: 10/17/2022]
Abstract
Urban water infrastructures are an essential part of urban areas. For their construction and maintenance, major investments are required to ensure an efficient and reliable function. Vital parts of the urban water infrastructures are water distribution networks (WDNs), which transport water from the production (sources) to the spatially distributed consumers (sinks). To minimize the costs and at the same time maximize the resilience of such a system, multi-objective optimization procedures (e.g., meta-heuristic searches) are performed. Assessing the hydraulic behavior of WDNs in such an optimization procedure is no trivial task and is computationally demanding. Further, deciding how close to optimal design solutions the current solutions are, is difficult to assess and often results in an unnecessary extent of experiment. To tackle these challenges, an answer to the questions is sought: when is an optimization stage achieved from which no further improvements can be expected, and how can that be assessed? It was found that graph characteristics based on complex network theory (number of dual graph elements) converge towards a certain threshold with increasing number of generations. Furthermore, a novel method based on network topology and the demand distribution in WDNs, specifically based on changes in 'demand edge betweenness centrality', for identifying that threshold is developed and successfully tested. With the proposed novel approach, it is feasible, prior to the optimization, to determine characteristics that optimal design solutions should fulfill, and thereafter, test them during the optimization process. Therewith, numerous simulation runs of meta-heuristic search engines can be avoided.
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Affiliation(s)
- Robert Sitzenfrei
- grid.5771.40000 0001 2151 8122Faculty of Engineering Sciences, Department of Infrastructure Engineering, University Innsbruck, Unit of Environmental Engineering, Technikerstrasse 13, Innsbruck, Austria
| | - Mohsen Hajibabaei
- grid.5771.40000 0001 2151 8122Faculty of Engineering Sciences, Department of Infrastructure Engineering, University Innsbruck, Unit of Environmental Engineering, Technikerstrasse 13, Innsbruck, Austria
| | - Sina Hesarkazzazi
- grid.5771.40000 0001 2151 8122Faculty of Engineering Sciences, Department of Infrastructure Engineering, University Innsbruck, Unit of Environmental Engineering, Technikerstrasse 13, Innsbruck, Austria
| | - Kegong Diao
- grid.48815.300000 0001 2153 2936Faculty of Computing, Engineering, and Media, De Montfort University, The Gateway, Leicester, LE1 9BH UK
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Mosbach J, Sonnenburg A, Fiedler JE, Urban W. Development of a New Method to Support a Participatory Planning for Piped Water Supply Infrastructure in Informal Settlements. Water 2022; 14:1316. [DOI: 10.3390/w14081316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
For decades, infrastructure planning in informal settlements has been a major challenge for urban planners and engineers. In particular, the planning process for the rapidly changing heterogeneous structures in these areas usually require individual and non-sustainable solutions. In this report, a method for the sustainable and practical planning of a piped water distribution system (WDS) that generates different expansion variants as a planning support tool is presented. In this tool, all real-world routing options are included in the decision-making process, based on the existing infrastructure, settlement structure, and identifiable open spaces. Additionally, proposals for the localization of the future public water points are supported by methods from Logistics. The consideration of the existing settlement structure and real route lengths (pedestrian walking distance) to a potential water point location lead to very practical and realizable results. The principle of participatory planning was considered, to easily include individual adjustments at any given timeframe. At the same time, automated processes generate fast results. The method is modular and linked to a geographic information system (GIS) to directly visualize the impacts and effects of the planning and decision-making process.
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Sugishita K, Abdel-Mottaleb N, Zhang Q, Masuda N. A growth model for water distribution networks with loops. Proc Math Phys Eng Sci 2021; 477:20210528. [PMID: 35153598 PMCID: PMC8610702 DOI: 10.1098/rspa.2021.0528] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 10/26/2021] [Indexed: 11/12/2022] Open
Abstract
Water distribution networks (WDNs) expand their service areas over time. These growth dynamics are poorly understood. One facet of WDNs is that they have loops in general, and closing loops may be a functionally important process for enhancing their robustness and efficiency. We propose a growth model for WDNs that generates networks with loops and is applicable to networks with multiple water sources. We apply the proposed model to four empirical WDNs to show that it produces networks whose structure is similar to that of the empirical WDNs. The comparison between the empirical and modelled WDNs suggests that the empirical WDNs may realize a reasonable balance between cost, efficiency and robustness in terms of the network structure. We also study the design of pipe diameters based on a biological positive feedback mechanism. Specifically, we apply a model inspired by Physarum polycephalum to find moderate positive correlations between the empirical and modelled pipe diameters. The difference between the empirical and modelled pipe diameters suggests that we may be able to improve the performance of WDNs by following organizing principles of biological flow networks.
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Affiliation(s)
- Kashin Sugishita
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
- Department of Transdisciplinary Science and Engineering, Tokyo Institute of Technology, 152-8550 Tokyo, Japan
| | - Noha Abdel-Mottaleb
- Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL 33620, USA
| | - Qiong Zhang
- Department of Civil and Environmental Engineering, University of South Florida, Tampa, FL 33620, USA
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, NY 14260-5030, USA
- Faculty of Science and Engineering, Waseda University, 169-8555 Tokyo, Japan
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Rehm I, Friesen J, Pouls K, Busch C, Taubenböck H, Pelz PF. A Method for Modeling Urban Water Infrastructures Combining Geo-Referenced Data. Water 2021; 13:2299. [DOI: 10.3390/w13162299] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Water distribution networks are the backbone of any municipal water supply. Their task is to supply the population regardless of the respective demand. High resilience of these infrastructures is of great importance and has brought these infrastructures into the focus of science and politics. At the same time, the data collected is highly sensitive and often openly unavailable. Therefore, researchers have to rely on models that represent the topology of these infrastructures. In this work, a model is developed that allows the topology of an urban water infrastructure to be mapped using the example of Cologne, Germany by combining freely available data. On the one hand, spatial data on land use (local climate zones) are used to disaggregate the water demand within the city under consideration. On the other hand, the parallelism of water and urban transportation infrastructures is used to identify the topology of a network by applying optimization methods. These networks can be analyzed to identify vulnerable areas within urban structures.
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Bach PM, Kuller M, McCarthy DT, Deletic A. A spatial planning-support system for generating decentralised urban stormwater management schemes. Sci Total Environ 2020; 726:138282. [PMID: 32481224 DOI: 10.1016/j.scitotenv.2020.138282] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2019] [Revised: 03/24/2020] [Accepted: 03/26/2020] [Indexed: 06/11/2023]
Abstract
Current Water Sensitive Urban Design (WSUD) models are either purely technical or overly simplified, lacking consideration of urban planning and stakeholder preferences to adequately support stakeholders. We developed the Urban Biophysical Environments and Technologies Simulator (UrbanBEATS), which integrates stormwater management with urban planning to support the design and implementation of WSUD. This study specifically describes and tests UrbanBEATS' WSUD Planning Module, which combines spatial analysis, infrastructure design, preference elicitation and Monte Carlo methods to generate feasible stormwater management and harvesting infrastructure options in greenfield and existing urban environments. By applying UrbanBEATS to a real-world greenfield development case study in Melbourne, Australia (with data sourced from the project's water management plans and design consultants), we explore the variety of options generated by the model and analyse them collectively to demonstrate that UrbanBEATS can design similar WSUD systems (e.g. select suitable technology types, their sizes and locations) to actual infrastructure choices.
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Affiliation(s)
- Peter M Bach
- Swiss Federal Institute of Aquatic Science & Technology (Eawag), Überlandstrasse 133, 8600 Dübendorf, Switzerland; Institute of Environmental Engineering, ETH Zürich, 8093 Zürich, Switzerland; Monash Infrastructure Research Institute, Civil Engineering Department, Monash University, Clayton, VIC 3800, Australia.
| | - Martijn Kuller
- Swiss Federal Institute of Aquatic Science & Technology (Eawag), Überlandstrasse 133, 8600 Dübendorf, Switzerland; School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia
| | - David T McCarthy
- Monash Infrastructure Research Institute, Civil Engineering Department, Monash University, Clayton, VIC 3800, Australia; Environmental and Public Health Microbiology (EPHM) Laboratory, Monash University, Clayton, VIC 380, Australia
| | - Ana Deletic
- School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia
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Zischg J, Rauch W, Sitzenfrei R. Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efficient and Reliable Supply. Entropy (Basel) 2018; 20:E708. [PMID: 33265797 DOI: 10.3390/e20090708] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Revised: 08/23/2018] [Accepted: 09/13/2018] [Indexed: 11/17/2022]
Abstract
Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined.
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Zischg J, Mair M, Rauch W, Sitzenfrei R. Enabling Efficient and Sustainable Transitions of Water Distribution Systems under Network Structure Uncertainty. Water 2017; 9:715. [DOI: 10.3390/w9090715] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper focuses on the performance of water distribution systems (WDSs) during long-term city transitions. A transition describes the pathway from an initial to a final planning stage including the structural and functional changes on the infrastructure over time. A methodology is presented where consecutive WDSs under changing conditions are automatically created, simulated and then analyzed at specific points in time during a transition process of several decades. Consequential WDS analyses include (a) uncertain network structure, (b) temporal and spatial demand variation and (c) network displacement. With the proposed approach, it is possible to identify robust WDS structures and critical points in time for which sufficient hydraulic and water quality requirements cannot be ensured to the customers. The approach is applied to a case study, where a WDS transition of epic dimensions is currently taking place due to a city relocation. The resulting necessity of its WDS transition is modelled with automatically created planning options for consecutive years of the transition process. For the investigated case study, we tested a traditional “doing-all-at-the-end” approach, where necessary pipe upgrades are performed at the last stages of the transition process. Results show that the sole design of the desired final-stage WDS is insufficient. Owing to the drastic network deconstruction and the stepwise “loss of capacity”, critical pipes must be redesigned at earlier stages to maintain acceptable service levels for most of the investigated future scenarios.
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Peña-guzmán CA, Melgarejo J, Prats D, Torres A, Martínez S. Urban Water Cycle Simulation/Management Models: A Review. Water 2017; 9:285. [DOI: 10.3390/w9040285] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Mair M, Zischg J, Rauch W, Sitzenfrei R. Where to Find Water Pipes and Sewers?—On the Correlation of Infrastructure Networks in the Urban Environment. Water 2017; 9:146. [DOI: 10.3390/w9020146] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Sitzenfrei R, Möderl M, Rauch W. Assessing the impact of transitions from centralised to decentralised water solutions on existing infrastructures--integrated city-scale analysis with VIBe. Water Res 2013; 47:7251-63. [PMID: 24210508 PMCID: PMC3857599 DOI: 10.1016/j.watres.2013.10.038] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2013] [Revised: 10/02/2013] [Accepted: 10/08/2013] [Indexed: 05/05/2023]
Abstract
Traditional urban water management relies on central organised infrastructure, the most important being the drainage network and the water distribution network. To meet upcoming challenges such as climate change, the rapid growth and shrinking of cities and water scarcity, water infrastructure needs to be more flexible, adaptable and sustainable (e.g., sustainable urban drainage systems, SUDS; water sensitive urban design, WSUD; low impact development, LID; best management practice, BMP). The common feature of all solutions is the push from a central solution to a decentralised solution in urban water management. This approach opens up a variety of technical and socio-economic issues, but until now, a comprehensive assessment of the impact has not been made. This absence is most likely attributable to the lack of case studies, and the availability of adequate models is usually limited because of the time- and cost-intensive preparation phase. Thus, the results of the analysis are based on a few cases and can hardly be transferred to other boundary conditions. VIBe (Virtual Infrastructure Benchmarking) is a tool for the stochastic generation of urban water systems at the city scale for case study research. With the generated data sets, an integrated city-scale analysis can be performed. With this approach, we are able to draw conclusions regarding the technical effect of the transition from existing central to decentralised urban water systems. In addition, it is shown how virtual data sets can assist with the model building process. A simple model to predict the shear stress performance due to changes in dry weather flow production is developed and tested.
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Affiliation(s)
- Robert Sitzenfrei
- Unit of Environmental Engineering, Institute of Infrastructure, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck,Austria.
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