Functional Feasibility in Optimal Evaluation of Water Distribution Network Performances
Abstract
:1. Introduction
1.1. Multi-Objective Optimization Algorithms
1.2. Account of Uncertainty in WDN Management
2. Materials and Methods
2.1. Optimization Model and Solution Algorithm
2.2. Performance Indices
- Demand deficit (DD) evaluated as the percentage of undelivered demand.
- Pressure range (PR) evaluated as the variation of the nodal pressure out of the optimal operating range.
2.3. Network Simulation: Pressure-Driven Analysis
2.4. Benchmark Set-Up
2.5. Pareto Fronts and Solution Subset Selection
2.6. Operation Scenarios and Performance Assessment
- A 10% increase in the demand in all nodes;
- A 30% increase in the demand in 1/3 nodes of the network with the maximum demand;
- A 30% increase in the demand in 1/3 nodes of the network with the minimum demand.
3. Results and Discussion
3.1. Two-Loop Network
3.2. Hanoi Network
3.3. Balerma Irrigation Network
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Condition | Emitter Coefficient | Demand |
---|---|---|
Problem | Acronym | LC | WS | NP | NN |
---|---|---|---|---|---|
Two-loop network | TLN | 1 | 1 | 8 | 7 |
Hanoi network | HAN | 1 | 1 | 34 | 32 |
Balerma irrigation network | BIN | 1 | 4 | 454 | 443 |
Population Size | ||||
---|---|---|---|---|
Problem | NFEs | Group1 | Group2 | Group3 |
Two-loop network | 100,000 | 40 | 80 | 160 |
Hanoi network | 600,000 | 60 | 120 | 240 |
Balerma irrigation network | 2,000,000 | 200 | 400 | 800 |
Network | Diameter (mm) | Cost (USD × m) | Minimum Pressure (m) |
---|---|---|---|
Two-loop network | 25.4; 50.8; 76.2; 101.6; 152.4; 203.2; 254; 304.8; 355.6; 406.4; 457.2; 508; 558.8; 609.6 | 2; 5; 8; 11; 16; 23; 32; 50; 60; 90; 130; 170; 300; 550 | 30 |
Hanoi network | 304.8; 406.4; 508; 609.6; 762; 1016 | 45.72; 70.4; 98.38; 129.33; 180.74; 278.28 | 30 |
Balerma irrigation network | 113; 126.6; 144.6; 162.8; 180.8; 226.2; 285; 361.8; 452.2; 581.8 | 7.22; 9.1; 11.92; 14.84; 18.38; 28.6; 45.39; 76.32; 124.64; 215.85 | 20 |
Two-Loop Network | Hanoi Network | Balerma Irr Network | ||||||
---|---|---|---|---|---|---|---|---|
Sol | Cost | Resilience | Sol | Cost | Resilience | Sol | Cost | Resilience |
1 | 0.42 | 0.248 | 1 | 6.25 | 0.219 | 1 | 2.05 | 0.408 |
2 | 0.46 | 0.351 | 2 | 6.57 | 0.260 | 2 | 2.41 | 0.65 |
3 | 0.57 | 0.550 | 3 | 7.18 | 0.300 | 3 | 3.28 | 0.801 |
4 | 0.97 | 0.752 | 4 | 8.21 | 0.332 | 4 | 5.72 | 0.896 |
5 | 1.25 | 0.800 | 5 | 8.79 | 0.340 | 5 | 10.04 | 0.928 |
6 | 1.67 | 0.849 | 6 | 10.70 | 0.352 | 6 | 15.01 | 0.941 |
7 | 4.4 | 0.903 | 7 | 20.92 | 0.955 |
Network | TLN | HAN | BIN | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Pipe ID | 2 | 4 | 20 | 25 | 13 | 51 | 188 | 194 | 338 | 75 | 480 | 119 |
Length (m) | 1000 | 1000 | 2200 | 1300 | 800 | 2500 | 800 | 354 | 200 | 421 | 1450 | 314 |
Scenario | Setup |
---|---|
1 | 10% increase in the demands in all nodes; |
2 | 30% increase in the demands in 1/3 nodes with the maximum demand; |
3 | 30% increase in the demands in 1/3 nodes with the minimum demand; |
4 | Pipe failure; |
5 | 10% increase in the demands in all nodes + pipe failure; |
6 | 30% increase in the demands in 1/3 nodes with the maximum demand + pipe failure; |
7 | 30% increase in the demands in 1/3 nodes with the minimum demand + pipe failure. |
Two-Loop Network | Hanoi Network | Balerma Irr Network | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sol | Cost (×106 USD) | In (-) | Pmin (m) | Sol | Cost (×106 USD) | In (-) | Pmin (m) | Sol | Cost (×106 USD) | In (-) | Pmin (m) |
1 | 0.42 | 0.248 | 30.06 | 1 | 6.25 | 0.219 | 30.05 | 1 | 2.05 | 0.408 | 20.02 |
2 | 0.46 | 0.351 | 31.51 | 2 | 6.57 | 0.260 | 30.12 | 2 | 2.41 | 0.65 | 20.27 |
3 | 0.57 | 0.550 | 35.68 | 3 | 7.18 | 0.300 | 31.65 | 3 | 3.28 | 0.801 | 22.39 |
4 | 0.97 | 0.752 | 39.92 | 4 | 8.21 | 0.332 | 42.63 | 4 | 5.72 | 0.896 | 22.81 |
5 | 1.25 | 0.800 | 40.50 | 5 | 8.79 | 0.340 | 47.06 | 5 | 10.04 | 0.928 | 22.82 |
6 | 1.67 | 0.849 | 41.85 | 6 | 10.70 | 0.352 | 49.66 | 6 | 15.01 | 0.941 | 22.81 |
7 | 4.4 | 0.903 | 42.73 | 7 | 20.92 | 0.955 | 22.82 |
Network | Sol | Average In (-) | Average PR* (-) | Average Pmin (m) | Average DD* (%) | IC (%) |
---|---|---|---|---|---|---|
1 | 0.216 | 0.045 | 28.11 | 2.74 | 36.36 | |
2 | 0.251 | 0.075 | 24.73 | 11.49 | 27.27 | |
3 | 0.358 | - | 27.96 | - | - | |
TLN | 4 | 0.658 | - | 34.73 | - | - |
5 | 0.716 | - | 35.31 | - | - | |
6 | 0.789 | - | 37.05 | - | - | |
7 | 0.867 | - | 38.39 | - | - |
Network | Sol | Average In (-) | Average PR* (-) | Average Pmin (m) | Average DD* (%) | IC (%) |
---|---|---|---|---|---|---|
1 | 0.184 | 0.176 | 20.93 | 18.54 | 60 | |
2 | 0.179 | 0.075 | 22.40 | 9.37 | 26.66 | |
HAN | 3 | 0.199 | 0.055 | 23.68 | 9.59 | 26.66 |
4 | 0.214 | 0.067 | 31.26 | 4.21 | 26.66 | |
5 | 0.217 | 0.023 | 36.62 | 1.48 | 26.66 | |
6 | 0.326 | 0.022 | 36.26 | 1.99 | 6.66 |
Sol | Scenario | Pipe ID Failure | In | Pmin (m) |
---|---|---|---|---|
188 | - | Infeasible | ||
194 | - | Infeasible | ||
5 | 480 | 0.947 | 22.78 | |
51 | - | Infeasible | ||
119 | 0.938 | 22.78 | ||
75 | 0.935 | 22.78 | ||
338 | - | Infeasible | ||
188 | - | Infeasible | ||
194 | - | Infeasible | ||
7 | 6 | 480 | 0.946 | 22.82 |
51 | - | Infeasible | ||
119 | 0.949 | 22.82 | ||
75 | 0.948 | 22.82 | ||
338 | - | Infeasible | ||
188 | - | Infeasible | ||
194 | - | Infeasible | ||
7 | 480 | 0.948 | 22.72 | |
51 | - | Infeasible | ||
119 | 0.950 | 22.72 | ||
75 | 0.949 | 22.72 | ||
338 | - | Infeasible |
Network | Sol | Average In (-) | Average PR* (-) | Average Pmin (m) | Average DD* (%) | IC (%) |
---|---|---|---|---|---|---|
1 | 0.338 | 0.093 | 13.87 | 39.4 | 44.44 | |
2 | 0.599 | 0.073 | 17.66 | 9.52 | 44.44 | |
3 | 0.774 | 0.167 | 21.94 | - | 44.44 | |
BIN | 4 | 0.888 | 0.229 | 22.79 | - | 44.44 |
5 | 0.918 | 0.222 | 22.78 | - | 44.44 | |
6 | 0.935 | 0.237 | 22.78 | - | 44.44 | |
7 | 0.948 | 0.237 | 22.78 | - | 44.44 |
Sol | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Pmax [m] | 75.46 | 93.70 | 104.95 | 110.53 | 111.93 | 112.66 | 113.18 |
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Fuso, F.; Cunha, M.C.; Becciu, G. Functional Feasibility in Optimal Evaluation of Water Distribution Network Performances. Water 2020, 12, 3404. https://doi.org/10.3390/w12123404
Fuso F, Cunha MC, Becciu G. Functional Feasibility in Optimal Evaluation of Water Distribution Network Performances. Water. 2020; 12(12):3404. https://doi.org/10.3390/w12123404
Chicago/Turabian StyleFuso, Flavia, Maria C. Cunha, and Gianfranco Becciu. 2020. "Functional Feasibility in Optimal Evaluation of Water Distribution Network Performances" Water 12, no. 12: 3404. https://doi.org/10.3390/w12123404