# Simpler Is Better—Calibration of Pipe Roughness in Water Distribution Systems

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## 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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**Figure 2.**Case study system (the location of the system was generated with Google Maps [66], and the layout of the network was provided by LMW).

**Figure 5.**Optimization results—4 different decision variable set formulations under 3 optimization methods.

**Figure 6.**Comparison of the observed and modeled HGL at: (

**a**) RTU1; (

**b**) RTU5 during the calibration period.

**Figure 7.**(

**a**) Comparison of the observed and modeled system total flow during the validation period; (

**b**–

**f**): Comparison of the observed and modeled HGL at RTU1 to RTU5 during the validation period.

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 | $N$ | 400 | 50 | 100 | 350 |

${p}_{c}$ | 0.7 | 0.7 | 0.7 | 0.7 | |

${p}_{m}$ | 0.01 | 0.01 | 0.01 | 0.03 | |

DE | $N$ | 400 | 100 | 100 | 340 |

$CR$ | 0.9 | 0.9 | 0.9 | 0.9 | |

Initial $F$ | 0.8 | 0.8 | 0.8 | 0.8 |

^{1}DVs = decision variables.

**Table 3.**Optimization results obtained from three optimization methods and four decision variable set formulations.

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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## Share and Cite

**MDPI and ACS Style**

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

**AMA Style**

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 Style**

Zhao, 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