Fractal-Heuristic Method of Water Quality Sensor Locations in Water Supply Network
Abstract
:1. Introduction
2. Materials and Methods
2.1. Comparison of Placement Indications with the Results Obtained Using Other Heuristic Methods
2.2. Analyzed Water Network
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Water Demand of Maximum Detected | Q |
---|---|
0%–20% | 1 |
21%–40% | 2 |
41%–60% | 3 |
61%–80% | 4 |
81%–100% | 5 |
Type of recipient | a |
Housing estates | 1 |
Schools, office buildings, administration | 2 |
Department stores, shops | 3 |
Industry, restaurants, clinics | 4 |
Water-intensive industry, hospitals, fire department | 5 |
Type of buildings | b |
Warehouse and industrial premises | 1 |
Department stores, shops | 2 |
Housing estates, schools, office buildings, administration | 3 |
Restaurants | 4 |
Water-intensive industry, hospitals | 5 |
The Average Concentration of Free Chlorine—mgCl2/dm3: In a Subarea (First Stage) In a Junction—Except for the Hydrant Junctions (Second Stage) | c |
---|---|
0.25–0.30 | 1 |
0.19–0.24 | 2 |
0.13–0.18 | 3 |
0.07–0.12 | 4 |
0.00–0.06 | 5 |
Location | Number of Observed Data | Observed Mean | Computed Mean | Mean Error | RMS Error |
---|---|---|---|---|---|
Network | 425 | 0.14 | 0.13 | 0.017 | 0.033 |
Correlation between means: 0.874 |
A | B | C | D | E | F | G | H | I | J | K | L | M | N | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 19 | |||||||||||||
2 | 2 | |||||||||||||
3 | 92 | |||||||||||||
4 | 1 | |||||||||||||
5 | 12 | 94 | ||||||||||||
6 | 0 | 3 | 3 | |||||||||||
7 | 6 | 28 | ||||||||||||
8 | 26 | 17 | ||||||||||||
9 | 64 | |||||||||||||
10 | 112 | 2 | ||||||||||||
11 | 49 | 20 | 51 | 6 | ||||||||||
12 | 132 | 28 | 82 | 123 | 95 | 114 | 673 | 113 | ||||||
13 | 42 | 419 | 191 | 271 | 263 | 249 | 222 | 38 | 25 | |||||
14 | 8 | 239 | 120 | 103 | 60 | 262 | 301 | 53 | 22 | 21 | 8 | |||
15 | 13 | 5 | 51 | 37 | 40 | 513 | 106 | 33 | 23 | 28 | 17 | |||
16 | 6 | 45 | 66 | 79 | 7 | 9 | 13 | 14 | 85 | |||||
17 | 38 | 30 | 8 | |||||||||||
18 | 32 | 34 | ||||||||||||
19 | 14 | 50 | ||||||||||||
20 | 6 | 29 | 2 | |||||||||||
21 | 16 | 3 | ||||||||||||
22 | 3 | |||||||||||||
23 | 2 | 8 | ||||||||||||
24 | 29 |
Q Coefficient | a Coefficient | |||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | E | F | G | H | I | J | K | L | M | N | A | B | C | D | E | F | G | H | I | J | K | L | M | N | |
1 | 1 | 1 | ||||||||||||||||||||||||||
2 | 1 | 1 | ||||||||||||||||||||||||||
3 | 1 | 1 | ||||||||||||||||||||||||||
4 | 1 | 1 | ||||||||||||||||||||||||||
5 | 1 | 1 | 1 | 1 | 1 | |||||||||||||||||||||||
6 | 1 | 1 | 1 | 1 | 1 | 5 | 1 | |||||||||||||||||||||
7 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||||
8 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||||
9 | 1 | 1 | ||||||||||||||||||||||||||
10 | 1 | 1 | 2 | 1 | ||||||||||||||||||||||||
11 | 1 | 1 | 1 | 1 | 3 | 2 | 1 | 1 | ||||||||||||||||||||
12 | 2 | 1 | 1 | 1 | 1 | 1 | 5 | 1 | 3 | 2 | 2 | 1 | 5 | 2 | 1 | 1 | ||||||||||||
13 | 1 | 4 | 2 | 3 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 4 | 1 | 3 | 1 | 1 | 4 | ||||||||||
14 | 1 | 2 | 1 | 1 | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 3 | 3 | 2 | 1 | 3 | 2 | 4 | 4 | ||||||
15 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 5 | 1 | 1 | 2 | 1 | ||||||
16 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||||
17 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||
18 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||||
19 | 1 | 1 | 2 | 1 | ||||||||||||||||||||||||
20 | 1 | 1 | 1 | 1 | 4 | 1 | ||||||||||||||||||||||
21 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||||
22 | 1 | 1 | ||||||||||||||||||||||||||
23 | 1 | 1 | 1 | 1 | ||||||||||||||||||||||||
24 | 1 | 1 | ||||||||||||||||||||||||||
b Coefficient | c Coefficient | |||||||||||||||||||||||||||
1 | 1 | 3 | ||||||||||||||||||||||||||
2 | 1 | 3 | ||||||||||||||||||||||||||
3 | 1 | 3 | ||||||||||||||||||||||||||
4 | 1 | 3 | ||||||||||||||||||||||||||
5 | 1 | 1 | 1 | 3 | 3 | 1 | ||||||||||||||||||||||
6 | 1 | 1 | 4 | 1 | 3 | 3 | 1 | 1 | ||||||||||||||||||||
7 | 1 | 1 | 3 | 3 | ||||||||||||||||||||||||
8 | 1 | 1 | 3 | 3 | ||||||||||||||||||||||||
9 | 2 | 3 | ||||||||||||||||||||||||||
10 | 2 | 1 | 3 | 3 | ||||||||||||||||||||||||
11 | 2 | 2 | 2 | 1 | 3 | 3 | 3 | 3 | ||||||||||||||||||||
12 | 2 | 2 | 2 | 1 | 5 | 2 | 2 | 1 | 3 | 3 | 3 | 3 | 3 | 2 | 3 | 3 | ||||||||||||
13 | 2 | 2 | 2 | 4 | 2 | 2 | 2 | 1 | 2 | 3 | 3 | 3 | 3 | 2 | 2 | 3 | 3 | 3 | ||||||||||
14 | 2 | 2 | 2 | 3 | 2 | 3 | 2 | 4 | 2 | 4 | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 3 | ||||||
15 | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 1 | 1 | 2 | 1 | 3 | 3 | 3 | 2 | 1 | 1 | 1 | 3 | 3 | 3 | 3 | ||||||
16 | 2 | 3 | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 3 | 3 | 3 | 3 | 3 | ||||||||||
17 | 2 | 1 | 1 | 1 | 1 | 3 | ||||||||||||||||||||||
18 | 1 | 1 | 1 | 1 | 0 | |||||||||||||||||||||||
19 | 1 | 1 | 2 | 2 | 0 | |||||||||||||||||||||||
20 | 1 | 4 | 1 | 2 | 3 | 3 | ||||||||||||||||||||||
21 | 1 | 1 | 2 | 3 | ||||||||||||||||||||||||
22 | 1 | 2 | ||||||||||||||||||||||||||
23 | 1 | 1 | 2 | 2 | ||||||||||||||||||||||||
24 | 1 | 2 |
A | B | C | D | E | F | G | H | I | J | K | L | M | N | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 3 | |||||||||||||
2 | 3 | |||||||||||||
3 | 3 | |||||||||||||
4 | 3 | |||||||||||||
5 | 3 | 3 | ||||||||||||
6 | 3 | 3 | 20 | |||||||||||
7 | 3 | 3 | ||||||||||||
8 | 3 | 3 | ||||||||||||
9 | 6 | |||||||||||||
10 | 12 | 3 | ||||||||||||
11 | 18 | 12 | 6 | 3 | ||||||||||
12 | 36 | 12 | 12 | 3 | 75 | 8 | 30 | 3 | ||||||
13 | 6 | 48 | 24 | 144 | 8 | 24 | 12 | 3 | 24 | |||||
14 | 6 | 24 | 18 | 18 | 12 | 24 | 18 | 36 | 12 | 48 | 48 | |||
15 | 3 | 6 | 6 | 8 | 6 | 12 | 15 | 3 | 3 | 12 | 3 | |||
16 | 8 | 6 | 3 | 6 | 3 | 3 | 3 | 3 | 3 | |||||
17 | 2 | 1 | 3 | |||||||||||
18 | 1 | 1 | ||||||||||||
19 | 4 | 2 | ||||||||||||
20 | 2 | 48 | 3 | |||||||||||
21 | 2 | 3 | ||||||||||||
22 | 2 | |||||||||||||
23 | 2 | 2 | ||||||||||||
24 | 2 |
Sensor Placement, Ranking Position | W Index Method | Maximum Water Demand Method | Maximum Water Age Method |
---|---|---|---|
1 | F13 | I12 | F5 |
2 | G12 | G15 | L14 |
3 | D13 | D13 | J24 |
4 | H20 | G14 | J10 |
5 | L14 | D14 | L16 |
Method | Number of Residents Outside Monitoring, M | Maximum Water Age, h |
---|---|---|
Significance index W | 12,433 | 26.0 |
According to base demand | 15,800 | 11.0 |
According to water age | 3406 | 96.0 |
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Beata, K.; Dariusz, K.; Ewa, H. Fractal-Heuristic Method of Water Quality Sensor Locations in Water Supply Network. Water 2020, 12, 832. https://doi.org/10.3390/w12030832
Beata K, Dariusz K, Ewa H. Fractal-Heuristic Method of Water Quality Sensor Locations in Water Supply Network. Water. 2020; 12(3):832. https://doi.org/10.3390/w12030832
Chicago/Turabian StyleBeata, Kowalska, Kowalski Dariusz, and Hołota Ewa. 2020. "Fractal-Heuristic Method of Water Quality Sensor Locations in Water Supply Network" Water 12, no. 3: 832. https://doi.org/10.3390/w12030832
APA StyleBeata, K., Dariusz, K., & Ewa, H. (2020). Fractal-Heuristic Method of Water Quality Sensor Locations in Water Supply Network. Water, 12(3), 832. https://doi.org/10.3390/w12030832