Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems
Abstract
:1. Introduction
2. Methods
2.1. Calibration Process
2.2. Model Simplification
2.3. Optimization Problem Formulation
2.4. Decision Variable Formulations
2.5. Optimization Methods
2.6. Common Engineering Practice and Model Validation
3. Case Study System
3.1. System Overview
3.2. Existing Hydraulic Model
3.3. Data Collection and Processing
3.3.1. Data Monitoring
3.3.2. Selection of Calibration and Validation Period
3.3.3. Data Pre-Processing
3.4. Model Calibration
3.4.1. Calibration Process
3.4.2. Decision Variable Set Formulations
4. Results and Discussion
4.1. Model Calibration Results
4.1.1. Optimization Settings for Model Calibration
4.1.2. Model Calibration Results
4.2. Discussion of Model Calibration Results
4.3. Evaluation of Formulation 2 (4 DVs) Using Validation Data
5. Summary and Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Decision Variable Set Formulation No. | Basis for Grouping Pipes |
---|---|
Formulation 1 | Every pipe in the pruned network as an individual decision variable |
Formulation 2 | Pipe material |
Formulation 3 | Pipe material + Pipe diameter |
Formulation 4 | Pipe material + Pipe velocity under peak flows |
Parameters | Formulation 1 126 DVs 1 | Formulation 2 4 DVs | Formulation 3 10 DVs | Formulation 4 34 DVs | |
---|---|---|---|---|---|
GA | 400 | 50 | 100 | 350 | |
0.7 | 0.7 | 0.7 | 0.7 | ||
0.01 | 0.01 | 0.01 | 0.03 | ||
DE | 400 | 100 | 100 | 340 | |
0.9 | 0.9 | 0.9 | 0.9 | ||
Initial | 0.8 | 0.8 | 0.8 | 0.8 |
SLSQP | GA | DE | ||
---|---|---|---|---|
Avg. of 10 Runs | Avg. of 10 Runs | Avg. of 10 Runs | ||
Formulation 1: 126 DVs | Ave RMSE (m) | 1.333 | 1.322 | 1.384 |
Run Time (h) | 4.21 | 49.73 | 15.76 | |
No. of generations | 318 | 1155 | 250 | |
No. of evaluations | 39,980 | 462,000 | 100,000 | |
Formulation 2: 4 DVs | Ave RMSE (m) | 1.709 | 1.709 | 1.709 |
Run Time (h) | 0.02 | 0.68 | 0.88 | |
No. of generations | 27 | 126 | 85 | |
No. of evaluations | 147 | 6280 | 8500 | |
Formulation 3: 10 DVs | Ave RMSE (m) | 1.468 | 1.468 | 1.468 |
Run Time (h) | 0.08 | 4.38 | 2.38 | |
No. of generations | 69 | 406 | 224 | |
No. of evaluations | 770 | 40,550 | 22,400 | |
Formulation 4: 34 DVs | Ave RMSE (m) | 1.409 | 1.4 | 1.407 |
Run Time (h) | 0.51 | 21.33 | 10.47 | |
No. of generations | 138 | 562 | 295 | |
No. of evaluations | 4825 | 196,840 | 100,300 |
Decision Variable No. | DV1 | DV2 | DV3 | DV4 |
---|---|---|---|---|
Pipe Material | MSCL | DICL | GRP | mPVC |
Run No. | Roughness Values | |||
1 | 10.62 | 0.44 | 2.91 | 0.01 |
2 | 10.65 | 0.44 | 2.91 | 0.01 |
3 | 10.59 | 0.44 | 2.91 | 0.01 |
4 | 10.60 | 0.44 | 2.91 | 0.01 |
5 | 10.63 | 0.44 | 2.91 | 0.01 |
6 | 10.63 | 0.44 | 2.91 | 0.01 |
7 | 10.62 | 0.44 | 2.91 | 0.01 |
8 | 10.63 | 0.44 | 2.91 | 0.01 |
9 | 10.60 | 0.44 | 2.91 | 0.01 |
10 | 10.60 | 0.44 | 2.90 | 0.01 |
Avg. | 10.62 | 0.44 | 2.91 | 0.01 |
Decision Variable No. | DV1 | DV2 | DV3 | DV4 | DV5 | DV6 | DV7 | DV8 | DV9 | DV10 |
---|---|---|---|---|---|---|---|---|---|---|
Pipe Material | mPVC | mPVC | DICL | DICL | DICL | DICL | DICL | GRP | MSCL | GRP |
Nominal Diameter (mm) | 300 | 375 | 375 | 450 | 500 | 600 | 750 | 1000 | 1200 | 1400 |
Run No. | Roughness Values | |||||||||
1 | 0.01 | 20.00 | 0.01 | 0.01 | 12.54 | 4.47 | 0.01 | 1.98 | 11.02 | 1.56 |
2 | 0.01 | 20.00 | 0.01 | 0.01 | 17.08 | 4.43 | 0.01 | 1.41 | 11.31 | 1.56 |
3 | 0.01 | 20.00 | 0.01 | 0.01 | 18.84 | 4.46 | 0.01 | 1.28 | 10.96 | 1.56 |
4 | 0.01 | 20.00 | 0.01 | 0.01 | 13.71 | 4.48 | 0.01 | 1.82 | 10.87 | 1.57 |
5 | 0.01 | 20.00 | 0.01 | 0.01 | 17.03 | 4.46 | 0.01 | 1.44 | 10.87 | 1.58 |
6 | 0.01 | 20.00 | 0.01 | 0.01 | 14.59 | 4.48 | 0.01 | 1.71 | 10.94 | 1.57 |
7 | 0.01 | 20.00 | 0.01 | 0.01 | 12.81 | 4.49 | 0.01 | 1.93 | 11.01 | 1.57 |
8 | 0.01 | 20.00 | 0.01 | 0.01 | 15.03 | 4.46 | 0.01 | 1.65 | 11.07 | 1.56 |
9 | 0.01 | 20.00 | 0.01 | 0.01 | 14.44 | 4.47 | 0.01 | 1.74 | 10.93 | 1.56 |
10 | 0.01 | 20.00 | 0.01 | 0.01 | 13.20 | 4.46 | 0.01 | 1.89 | 11.04 | 1.55 |
Avg. | 0.01 | 20.00 | 0.01 | 0.01 | 14.93 | 4.47 | 0.01 | 1.68 | 11.00 | 1.56 |
Pressure Monitoring Sites | |||||||
---|---|---|---|---|---|---|---|
Pressure monitoring site | Average observed HGL (m) | Average modeled HGL (m) | Average observed pressure (m) | Average modeled pressure (m) | Average difference (m) | Percentage difference in pressures | RMSE (m) |
RTU1 | 145.80 | 145.55 | 75.06 | 74.81 | 0.26 | 0.34% | 0.508 |
RTU2 | 139.98 | 138.01 | 70.95 | 68.98 | 1.47 | 2.77% | 2.196 |
RTU3 | 128.27 | 127.23 | 66.36 | 65.32 | 1.04 | 1.57% | 3.646 |
RTU4 | 137.60 | 137.66 | 74.86 | 74.92 | −0.06 | −0.08% | 1.809 |
RTU5 | 128.77 | 128.03 | 59.15 | 58.41 | 0.74 | 1.24% | 1.585 |
Avg. | 1.949 | ||||||
Flow monitoring site | |||||||
Flow monitoring site | Average observed flow (L/s) | Average modeled flow (L/s) | Average difference (L/s) | Percentage difference | RMSE (L/s) | ||
Sys_Flow | 3374 | 3379 | −5 | 0.16% | 31 |
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Zhao, Q.; Wu, W.; Simpson, A.R.; Willis, A. Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems. Water 2022, 14, 3276. https://doi.org/10.3390/w14203276
Zhao Q, Wu W, Simpson AR, Willis A. Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems. Water. 2022; 14(20):3276. https://doi.org/10.3390/w14203276
Chicago/Turabian StyleZhao, Qi, Wenyan Wu, Angus R. Simpson, and Ailsa Willis. 2022. "Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems" Water 14, no. 20: 3276. https://doi.org/10.3390/w14203276
APA StyleZhao, Q., Wu, W., Simpson, A. R., & Willis, A. (2022). Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems. Water, 14(20), 3276. https://doi.org/10.3390/w14203276