Synchronization Optimization of Pipe Diameter and Operation Frequency in a Pressurized Irrigation Network Based on the Genetic Algorithm
Abstract
:1. Introduction
2. Materials and Methods
2.1. Problem Description and Generalization
2.2. Mathematical Models
2.2.1. Mathematical Model of Irrigation Cost
2.2.2. Constraint Conditions of the Model
- Irrigation period constraints
- Pipe diameter constraints
- Velocity constraints
- Hydrant outlet pressure constraints
- Pump outlet pressure constraints
- Pump efficiency constraints
2.3. Method of the Model Solving
2.3.1. Fitness Function Design of GA
2.3.2. Solution Process of the Model
3. Results
3.1. Basic Information
3.2. Optimization Results
3.2.1. Algorithm Results
3.2.2. Calculation Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Rotation irrigation sectoring number | 1 | 2 | 3 | 4 | 5 | N/2 | |
Branch pipe number | 1 | 3 | 5 | 7 | 9 | … | N−1 |
2 | 4 | 6 | 8 | 10 | … | N | |
The number of main pipe segments between branch and pump | 1 | 1 | 2 | 2 | 3 | … |
Branch Pipe Number | Branch Pipe Segment Number and the Corresponding Pipe Diameter (mm) | ||||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | |
1 | 160 | 200 | 250 | 250 | 315 | 315 | 315 |
2 | 160 | 200 | 250 | 250 | 315 | 315 | - |
3 | 160 | 200 | 250 | 250 | 315 | 315 | 315 |
4 | 160 | 200 | 250 | 250 | 315 | 315 | - |
5 | 160 | 200 | 250 | 250 | 315 | 315 | 315 |
6 | 160 | 200 | 250 | 250 | 315 | 315 | - |
7 | 160 | 200 | 250 | 250 | 315 | 315 | 315 |
8 | 160 | 200 | 250 | 250 | 315 | 315 | - |
9 | 160 | 200 | 250 | 250 | 315 | 315 | 315 |
10 | 160 | 200 | 250 | 250 | - | - | - |
Unplasticized Polyvinyl Chloride (U-PVC) Pipes (with a Pressure Capacity of 0.6 MPa) | ||||||
---|---|---|---|---|---|---|
Outside diameter (mm) | 140 | 160 | 200 | 250 | 315 | 400 |
Inner diameter (mm) | 132.1 | 152.6 | 190.8 | 236.4 | 302.6 | 380.4 |
Unit price (Yuan/m) | 28 | 37 | 56 | 90 | 142 | 232 |
Irrigation Sectoring (i) | Operation Frequency (f) | |||||||
---|---|---|---|---|---|---|---|---|
s | 50 | 49 | 48 | 47 | … | 42 | 41 | |
B | 1 | 21.1 | 20.26 | 19.45 | 18.64 | … | 14.89 | 14.19 |
2 | −0.004611 | −0.004519 | −0.004427 | −0.004334 | −0.003873 | −0.003781 | ||
3 | −8.467 × 10−6 | −8.467 × 10−6 | −8.467 × 10−6 | −8.467 × 10−6 | −8.467 × 10−6 | −8.467 × 10−6 | ||
4 | −1.329 × 10−22 | −4.025 × 10−17 | −7.911 × 10−18 | −1.066 × 10−17 | 3.556 × 10−17 | 7.502 × 10−17 | ||
C | 1 | −0.02273 | 0.02265 | −0.02257 | 0.02248 | 0.02206 | 0.02197 | |
2 | 0.002277 | 0.002316 | 0.002356 | 0.002397 | 0.002632 | 0.002685 | ||
3 | −1.919 × 10−6 | −1.919 × 10−6 | −2.068 × 10−6 | 2.149 × 10−6 | −2.64 × 10−6 | 2.758 × 10−6 | ||
4 | 3.97 × 10−10 | 4.203 × 10−10 | 4.455 × 10−10 | 4.729 × 10−10 | 6.493 × 10−10 | 6.95 × 10−10 |
Optimization Model | Irrigation Sectoring | Operating Frequency (Hz) | Pump Flow (m3/h) | Pump Head (m) | Pump Efficiency (%) | Irrigation Period (h) |
---|---|---|---|---|---|---|
PDM | 1 | 50 | 844 | 11.2 | 81.6 | 5.1 |
2 | 50 | 555 | 15.9 | 76.3 | 9.7 | |
3 | 50 | 626 | 14.9 | 79.4 | 8.3 | |
4 | 50 | 646 | 14.6 | 80 | 8.7 | |
5 | 50 | 673 | 14.2 | 80.7 | 6.1 | |
OFM | 1 | 42 | 593 | 9.6 | 79 | 8.4 |
2 | 41 | 636 | 8.3 | 79.3 | 8.1 | |
3 | 45 | 727 | 9.6 | 80.4 | 7.1 | |
4 | 41 | 612 | 8.7 | 79.2 | 9.3 | |
5 | 44 | 644 | 10.2 | 75.5 | 7.6 | |
SOM | 1 | 50 | 579 | 15.6 | 77.5 | 8.6 |
2 | 48 | 642 | 13.1 | 80.1 | 8.2 | |
3 | 43 | 581 | 10.4 | 78.8 | 8.2 | |
4 | 48 | 545 | 14.5 | 76.4 | 10.7 | |
5 | 43 | 593 | 12.3 | 79 | 6.5 |
Optimization Model | Branch Pipe Number | Branch Pipe Segment Number | ||||||
---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
PDM | 1 | 200 | 200 | 200 | 200 | 200 | 200 | 200 |
2 | 250 | 250 | 250 | 250 | 250 | 315 | - | |
3 | 315 | 315 | 315 | 315 | 315 | 315 | 315 | |
4 | 160 | 200 | 200 | 200 | 315 | 315 | - | |
5 | 200 | 200 | 200 | 200 | 200 | 200 | 250 | |
6 | 200 | 250 | 250 | 250 | 315 | 315 | - | |
7 | 200 | 200 | 250 | 250 | 315 | 315 | 315 | |
8 | 160 | 200 | 200 | 200 | 200 | 200 | - | |
9 | 315 | 315 | 315 | 315 | 315 | 315 | 315 | |
10 | 160 | 160 | 160 | 200 | - | - | - | |
SOM | 1 | 200 | 200 | 200 | 200 | 250 | 250 | 315 |
2 | 160 | 160 | 200 | 200 | 200 | 200 | - | |
3 | 160 | 160 | 160 | 200 | 250 | 250 | 315 | |
4 | 200 | 200 | 250 | 250 | 250 | 250 | - | |
5 | 200 | 200 | 200 | 315 | 315 | 315 | 315 | |
6 | 160 | 160 | 200 | 200 | 200 | 250 | - | |
7 | 160 | 160 | 160 | 160 | 250 | 250 | 2 | |
8 | 160 | 160 | 160 | 160 | 160 | 160 | - | |
9 | 160 | 160 | 200 | 250 | 315 | 315 | 315 | |
10 | 200 | 200 | 200 | 200 | - | - | - |
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Pang, Y.; Li, H.; Tang, P.; Chen, C. Synchronization Optimization of Pipe Diameter and Operation Frequency in a Pressurized Irrigation Network Based on the Genetic Algorithm. Agriculture 2022, 12, 673. https://doi.org/10.3390/agriculture12050673
Pang Y, Li H, Tang P, Chen C. Synchronization Optimization of Pipe Diameter and Operation Frequency in a Pressurized Irrigation Network Based on the Genetic Algorithm. Agriculture. 2022; 12(5):673. https://doi.org/10.3390/agriculture12050673
Chicago/Turabian StylePang, Yiyuan, Hong Li, Pan Tang, and Chao Chen. 2022. "Synchronization Optimization of Pipe Diameter and Operation Frequency in a Pressurized Irrigation Network Based on the Genetic Algorithm" Agriculture 12, no. 5: 673. https://doi.org/10.3390/agriculture12050673