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Comparative responses of the two-loop network under the failure of one pipe. (a) Pareto fronts for both network robustness measures (i.e. resilience and robustness index). Inset shows the complete Pareto set. (b-c) Responses for the same cost solutions of the Pareto set.
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Robustness -or lack thereof- is a fundamental property of water distribution systems that has received considerable attention over the last decade. Remarkably, there is still no universally accepted measure of system robustness. Although the resilience index is generally used as a measure of robustness, it is not entirely clear to what extent the r...
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... α = 0.9 was used for all networks and all simulations. The number of iterations at the same temperature was fixed initially to 50 and every time the temperature was decreased, this number was increased by fixed factor β = 1.3 for Figures 1 and 2, and β = 1.1 for Figures 4 and 7. The above process of cooling was repeated a fixed number of 1.0×10 ! ...
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... Pareto set shown in Figures 1, 2 and 4 was constructed by starting with a candidate solution (i.e. a perturbed solution) from the nondominated set and its performance was analyzed by solving the hydraulic model with EPANET (Rossman, 2000). Since the optimization algorithm is linked with the libraries of functions given by the "EPANET Programmer's Toolkit", nodal pressures and demands were obtained in order to determine if this perturbed solution satisfied the hydraulic restrictions. ...
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... the analyses shown in Figures 2, 3, 4 and 7 were conducted on solutions of each Pareto set. A separate code searched the solutions on each set having the minimal (absolute) difference in cost. ...
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... separate code searched the solutions on each set having the minimal (absolute) difference in cost. For instance, the mean value of the difference in cost between two solutions belonging to each Pareto set in Figure 2 is 1.2x10 3 and the standard deviation 0.7x10 3 is (cost units). The results do not depend critically on this difference. ...
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... should be noted that maximizing the robustness index is equivalent to minimizing the fraction of nodes with pressure below the minimal pressure head. Figure 2a shows the Pareto front so obtained (squares) and that obtained by using the resilience index (circles). Inset shows the complete Pareto sets. ...
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... order to compare the two indexes properly, the study must be restricted to a subset of each Pareto front with solutions having (approximately) the same cost (see Methods). The response of the system is represented as the percentage of nodes with pressure deficits (Fig. 2b). It is observed that the solutions obtained with the robustness index are much less vulnerable to pipe failures than those obtained with the resilience index. Moreover, when both kinds of solutions are considered globally, the malfunctioning of the network decreases with increasing cost. However, this behavior is rather different for ...
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... with high degree of tolerance against pipe bursts. To better understand this result, the flow distribution is analyzed after a perturbation in structure. This is obtained by counting the number of pipes with velocities larger than 2 m/s as a consequence of removing a pipe. The process is repeated for all pipes and the result is finally averaged (Fig. 2c). It is found that, under these extreme conditions, the network shows high velocities for both indexes, but the solutions obtained with the robustness index display the best behavior. Indeed, tolerance to pipe failures comes at the expense of high velocities in other pipes. But velocities larger than 2 m/s in an increasing number of ...
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... velocities larger than 2 m/s in an increasing number of pipes cause increasing hydraulic losses, making the flow distribution between nodes highly inefficient. Table 3 shows pipe diameters for each solution of Figure 2b-c obtained with the resilience index. It is observed that the resiliencebased design assigns small diameters to pipes 4 and 6, giving more weight to 'vertical' pipes (i.e. 3, 5, 7 and 8). ...
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... 14 16 16 16 14 14 12 14 12 16 8 14 10 10 10 12 10 12 12 10 10 12 12 14 14 14 12 14 14 In that approach, pipes 4 and 6 are considered as redundant, with the main function of close loops, but without the capability to overcome the increased flow produced by the failure of any other pipe. In addition, note that the better performance of solution 13 (Fig. 2b-c), compared with solution 12, can mainly be explained by the increased diameter of pipe 4 (compare S 12 with S 13 in Table 3). Thus, despite the surplus head provided by the resilience-based design, the supply of water between nodes is increasingly difficult when the remaining pipes do not have the sufficient capability (i.e. diameter) ...
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... on the unaffected part of the network. This behavior is consistent with the scenario observed in Table 4: the robustness-based design does not give minor importance to pipes 4 and 6 than to any other pipe. The only exception is solution 1 (S 1 ), with 1-in-diameter in pipe 4, which displays a high number of pipes with velocity larger than 2 m/s (Fig. ...
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In many countries, water distribution systems consist of large, highly pressurized pipe networks that require an excessive amount of energy and that are vulnerable to large-scale contamination. To imagine the future of water distribution, we can learn from Hanoi, Vietnam, where water is distributed at low pressures and most buildings are equipped w...
The hydraulic analysis of water distribution systems (WDSs) is divided into two approaches, namely, a demand-driven analysis (DDA) and a pressure-driven analysis (PDA). In DDA, the basic assumption is that the nodal demand is fully supplied irrespective of the nodal pressure, which is mainly suitable for normal operating conditions. However, in abn...
Citations
... The studied area is the two-loop water distribution network presented by Alperovits and Shamir (1977) and also the three-loop Hanoi presented by Fujiwara and Khang (1990). The aforementioned networks have been examined by many previous researchers to test and evaluate the models presented by them (Tospornsampan et al. 2007;Páez et al. 2014;Puccini et al. 2016;Reca et al. 2017;Cassiolato et al. 2019;Zarei et al. 2022;etc.). As shown in Fig. 1, the network of Alperovits and Shamir (1977) consists of 7 nodes and 8 pipes with the same length of 1000 m, which are fed from a reservoir with a water level of 210 m. ...
Leakage from water distribution networks (WDNs) is inevitable. Therefore, during design a WDN, engineers add a percentage of each nodal water demand as leakage discharge to total node demand. The amount of leakage depends on the pressure, which is not known at the design stage. Considering a constant percentage of node demand in lieu of its leakage makes the problem worse. In this study, the effect of leakage on the optimal WDN design was investigated by developing the matrix form of the gradient algorithm while accounting for leakage using the pressure-dependent model. Non-dominated genetic algorithm version II (NSGA-II) was used as the optimization engine with two objectives which includes minimizing the network construction cost and minimizing the total network pressure deficiency. Two well-known two- and three-loop WDNs in literature were studied. The results indicated that the pressure-dependent leakage varies between 12.9 and 29.44% of the node demand while the network construction cost stays the same if compared with the fixed percentage leakage model, and the construction cost would increase by 17–31%, if leakage is not accounted for. This is expected the optimized diameters and hydraulic characteristics of the networks being affected by the leakage calculation method.
... Robustness studies can be categorized into two groups, i.e., those that develop robustness indicators and those that propose robustness frameworks from which robust solutions in the planning, design, operation, and management are derived ( Jung et al. 2019). Over the years, more studies (e.g., Giustolisi et al. 2009;Sun et al. 2011;Kang & Lansey 2012;Perelman et al. 2013;Puccini et al. 2016;etc) generally explored robustness in water network designs than those that introduced flexibility to cope with uncertainty (e.g., Basupi & Kapelan 2015;Marques et al. 2015;. ...
An integrated method that evaluates conflicting hydraulic performances of water distribution systems (WDSs) and sanitary sewers (SSs) considering water-saving schemes (WSSs) under fixed (deterministic) or uncertain water demands was formulated. WSSs considered include household water-saving fixtures and appliances whose water flows impact water distribution system (WDS) and sanitary sewer (SS) hydraulic performances in different ways. In the proposed flexible approach, a multi-objective optimisation problem was formulated and solved considering trade-offs of three objectives: (1) maximisation of the average cost savings (2) maximisation of the average WDS resilience index and (3) minimisation of the average SS self-cleansing velocity deficit factor. The decision variables include water-saving fixture and appliance capacities that are applied in a deterministic or flexible manner at a household level. The constraints include WDS and SS hydraulic requirements together with decision bounds of the available water-saving scheme capacities. The non-dominated sorting genetic algorithm was used to obtain trade-off solutions. This method was demonstrated in the corresponding WDS and SS network subsystems of Tsholofelo extension in Gaborone, Botswana. The results indicate that WSSs lead to visibly conflicting WDS and SS hydraulic performances. Moreover, considering the uncertainty inherent in water demand and the corresponding planning and management of WDSs and SSs provides more sustainable solutions as demand uncertainties unveil. HIGHLIGHTS
Performances of WSSs and water networks have been analysed considering water demand uncertainty.;
A method that considers trade-offs between water network hydraulics amidst WSSs has been articulated.;
Deterministic and flexible applications of WSSs have been examined.;
Considering demand uncertainty provides appropriate and more sustainable management of integrated water systems.;
... Chung et al. 2009;Housh et al. 2011). Robustness is usually treated as minimizing the failure intensity rather than focusing on the probability of a successful operation (Puccini et al. 2016). There are several works in the literature considering robustness in the field of water network design. ...
This paper focuses on the capacity uncertainty in water supply chains that occurs when facilities face disruption. A combination of scenario-based two-stage stochastic programming with the min-max robust optimization approach is proposed to optimize the water supply chain network design problem. In the first stage, the decisions are made on locations and capacities of reservoirs and water-treatment plants while recourse decisions including amount of water extraction, amount of water refinement, and consequently amount of water held in reservoirs are made at the second stage. The proposed robust two-stage stochastic programming model can help decision makers consider the impacts of uncertainties and analyze trade-offs between system cost and stability. The literature reveals that most exact methods are not able to tackle the computational complexity of mixed integer non-linear two-stage stochastic problems at large scale. Another contribution of this study is to propose two metaheuristics - a particle swarm optimization (PSO) and a bat algorithm (BA) - to solve the proposed model in large-scale networks efficiently in a reasonable time. The developed model is applied to several hypothetical cases of water resources management systems to evaluate the effectiveness of the model formulation and solution algorithms. Sensitivity analyses are also carried out to analyze the behavior of the model and the robustness approach under parameters variations.
... Puccini et al. [24] also proposed an ROB indicator for WDS design, which was computed from the average ratio of the number of nodes (N w ) with deficit pressure (node with pressure lower than the allowable minimum pressure) under single pipe failure conditions. The ROB indicator is calculated by 1 minus N w as follows: ...
The resilience of a water distribution system (WDS) is defined as its ability to prepare, respond to, and recover from a catastrophic failure event such as an earthquake or intentional contamination. Robustness (ROB), one of the components of resilience, is the ability to maintain functionality to meet customer demands. Recently, the traditional probability-based system performance perspective has begun to shift toward the ROB and system performance variation point of view. This paper provides a state-of-the-art review of WDS ROB-based approaches proposed in three research categories: Design, operation, and management. While few pioneering works have been published in the latter two areas, an ROB indicator was proposed and thoroughly investigated for WDS design. Then, some future works are recommended in each of the three domains to promote developments in WDS ROB. Finally, a brief summary of this paper is presented, from which the final conclusions of the state-of-the-art review and recommendations are drawn. The new paradigm of WDS ROB-based design, operation, and management is in its infant stage and should be carved out in future studies.
... In dead-end approach, the design engineer need to define paths and dead-ends while Hardy-Cross method is based on defining closed loops with branching pipes excluded from the analysis. Research on WDN design and operation is still ongoing with main focus especially on pressure-driven approach (PDA), rather than demand-driven approach (DDA), to solving nonlinear system of mass and energy balance equations [8][9][10][11][12][13][14][15][16]. In general, DDA to hydraulic analysis of WDNs in the design stage is considered to be safer since the design of WDNs is based on the assumption that the network will be capable of delivering desired operating pressures even under worst-case conditions. ...
... Thus, the problem of calibration cannot follow a deterministic approach, but rather a probabilistic approach, where metaheuristic optimization techniques have greater applicability. These have been used to solve problems related to water distribution systems (Puccini et al., 2016;Seyoum et al., 2016;Haghihi and Ramos, 2012;Christodoulou and Ellinas, 2011;especially the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are highlighted, and have presented good results. Jung e Karney (2008) applied both techniques, GA and PSO, to solve the inverse transient analysis, seeking the detection of leaks and friction factor. ...
The success of hydraulic simulation models of water distribution networks is associated with the ability of these models to represent real systems accurately. To achieve this, the calibration phase is essential. Current calibration methods are based on minimizing the error between measured and simulated values of pressure and flow. This minimization is based on a search of parameter values to be calibrated, including pipe roughness, nodal demand, and leakage flow. The resulting hydraulic problem contains several variables. In addition, a limited set of known monitored pressure and flow values creates an indeterminate problem with more variables than equations. Seeking to address the lack of monitored data for the calibration of Water Distribution Networks (WDNs), this paper uses a meta-model based on an Artificial Neural Network (ANN) to estimate pressure on all nodes of a network. The calibration of pipe roughness applies a metaheuristic search method called Particle Swarm Optimization (PSO) to minimize the objective function represented by the difference between simulated and forecasted pressure values. The proposed method is evaluated at steady state and over an extended period for a real District Metering Area (DMA), named Campos do Conde II, and the hypothetical network named C-town, which is used as a benchmark for calibration studies.
... The WATCH Forcing Data for ERA Interim (WFDEI) (Puccini et al., 2016) and downscaled climate data from five GCMs under two RCPs are used to drive a hydrological model (chain 1). Five GCMs selected in this study are the CNRM-CM5, HadGEM2-ES, IPSL-CM5A-LR, MPI-ESM-LR and EC-EARTH. ...
Water allocation is facing profound challenges due to climate change uncertainties. To identify adaptive water allocation strategies that are robust to climate change uncertainties, a model framework combining many-objective robust decision making and biophysical modeling is developed for large rivers. The framework was applied to the Pearl River basin (PRB), China where sufficient flow to the delta is required to reduce saltwater intrusion in the dry season. Before identifying and assessing robust water allocation plans for the future, the performance of ten state-of-the-art MOEAs (multi-objective evolutionary algorithms) is evaluated for the water allocation problem in the PRB. The Borg multi-objective evolutionary algorithm (Borg MOEA), which is a self-adaptive optimization algorithm, has the best performance during the historical periods. Therefore it is selected to generate new water allocation plans for the future (2079-2099). This study shows that robust decision making using carefully selected MOEAs can help limit saltwater intrusion in the Pearl River Delta. However, the framework could perform poorly due to larger than expected climate change impacts on water availability. Results also show that subjective design choices from the researchers and/or water managers could potentially affect the ability of the model framework, and cause the most robust water allocation plans to fail under future climate change. Developing robust allocation plans in a river basin suffering from increasing water shortage requires the researchers and water managers to well characterize future climate change of the study regions and vulnerabilities of their tools.
... This is while initial design has indubitable influence on the operational condition and rehabilitation scheduling of the network during its life cycle. For example, Puccini et al. (2016) and Zheng et al. (2017) studied on optimal design of WDNs. Dridi et al. (2009) and Siew et al. (2014) investigated optimal rehabilitation/replacement scheduling of WDNs. ...
Optimal design and rehabilitation scheduling of water distribution networks (WDNs) have been often dealt separately over the past few decades. However initial design (which is named as static design in this paper) has indubitable influence on the operational condition and rehabilitation scheduling of network. This paper introduces an approach for simultaneous optimization of initial design and rehabilitation scheduling of WDNs during their life cycle. In this approach which is named as dynamic design, pipe diameters in the first year and their rehabilitation/replacement in the next years of the expected life of the network are determined considering the nodal demands growth and increase in pipes’ roughness. The proposed model consists of a multiobjective ant colony optimization engine linked to a pressure dependent analysis model and a pipe break prediction model. This paper introduces the following contributions: (1) it implements dynamic design based on the pressure dependent analysis with considering leakage; (2) a support vector machine based sub model is used for pipe break prediction. Then pipe breaks and their repair costs are considered in dynamic design process; (3) a new reliability index is used as one of the objective functions. Two networks are used to investigate the impact of static and dynamic designs on the reliability and total cost of design and rehabilitation of WDNs during their life cycle. The results show that the dynamic design produces more reliable and lower cost networks in comparison to the ones resulted from either static design or rehabilitation scheduling separately.
