# An Efficient Burst Detection and Isolation Monitoring System for Water Distribution Networks Using Multivariate Statistical Techniques

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Framework

#### 2.2. Burst Monitoring System

^{2}chart of the PCA model according to the weighted average values ${z}_{i}$.

#### 2.2.1. Standardized Exponential Weighted Moving Average (Standardized EWMA)

#### 2.2.2. Principal Component Analysis

#### 2.3. Optimal Pressure Sensor Placement

#### 2.3.1. K-Means Clustering Approach

#### 2.3.2. Sensitivity Analysis

#### 2.4. Burst Identification

## 3. Results and discussion

#### 3.1. Simulation of a Water Distribution Network

^{3}/day (0.9954 l/s) and 173 m

^{3}/day (2.0023 l/s). The total water demand of the network was supplied from a fixed head reservoir at 250 m altitude.

#### 3.2. Monitoring of Burst Occurrence in the WDN

^{3}/day to 100 m

^{3}/day, and the burst location, occurrence time, and duration were randomly selected. The burst events occurred two times in the first and the second 24 h during the simulation at the same time interval. As an instance, the burst appeared at 384 min (in the first 24 h) and 1824 min (in the second 24 h) in scenario 6. Table 3 shows the three monitoring and detection systems applied in this study, as described in Section 2. System 1 employed CUSUM and a sensitivity analysis, as detailed in [10]. The sensitivity analysis was used to measure a perturbation in demand changes at each node, and the most sensitive node was selected as the location of the burst sensor. In system 1, the burst was detected by the CUSUM charts using time series data sets. The CUSUM chart detected demand fluctuations in the water distribution network. In system 2, k-means clustering and a sensitivity analysis were employed to determine the sensor location, and standardized EWMA charts were used to detect burst occurrence. The standardized EWMA diagnosed the burst using the upper and lower control limits of the algorithm. In system 3, the PCA was used, and the results were compared to system 2. The PCA was applied to pre-treat the data used for sensor location and to monitor the burst according to the data converted by the standardized EWMA. System 3 was compared to systems 1 and 2 in terms of efficiency and robustness. Performance evaluation involved detection and isolation of burst occurrence, and the robustness was evaluated by allocating the signal and noise ratios.

^{3}/day, 384 min, and 4 min at N4, respectively. Figure 4a,b show the variations in flowrate and unit head loss at the entrances of the WDN. The unit head loss was used instead of pressure at the entrance because the entrance was directly linked to the reservoir, and the pressure was not changed. Two small peaks, highlighted by circles in Figure 4a,b, show the variations of flowrate and unit loss. However, it is hard to identify these two peaks (which are induced by the burst at N4) in the measured data set due to the considerable variations in the daily pattern and the noise of the flowrate and unit head loss. This shows that a method to remove strong diurnal patterns in the WDN is necessary to identify the burst in the measured data set. Therefore, a mean trajectory removal technique was implemented prior to applying the monitoring system to remove the periodic pattern from the measurements. Figure 4c,d show the data set on which mean trajectory filtering was implemented. This data was input to the monitoring system.

^{3}/day) and S2(20 m

^{3}/day) was not detected by the CUSUM chart system. Moreover, the system 2 could not detect the burst in S2. This indicates that the systems 1 and 2 have limitations in detecting small burst flow rate despite of fast detection time. In addition, the detection time of the CUSUM and standardized EWMA systems increased as the burst size decreased from 100 m

^{3}/day in S10 to 10 m

^{3}/day in S1. This means that the univariate statistical monitoring systems were not efficient in detecting small bursts, and their monitoring performance was affected by noise, which hid small bursts. On the other hand, the standardized EWMA-PCA could detect bursts in all generated scenarios of which burst flowrates were from 10 m

^{3}/day to 100 m

^{3}/day, and the detection time was relatively fast, even for small bursts. This is because the detection performance of the proposed system improved by considering unit head loss alongside flowrate.

#### 3.3. Robustness of the Three Monitoring Systems

#### 3.4. Optimal Sensor Placement

^{3}/day, and the burst occurred on an individual node at a time interval. The sensitivity analysis was performed under steady state conditions. The results of cumulative sensitivity of all candidate nodes were obtained and are summarized in Table 5. The cumulative sensitivity varied in a range between 5.16 $\times $ 10

^{−7}and 1.10 $\times $ 10

^{−5}. The most and the least sensitive sections in the WDN were, respectively, N2 and N1 according to variation in pressure drop. Having conducted the sensitivity analysis in all nodes, the clustering algorithm was implemented to classify the nodes according to hydraulic similarities. Thus, the optimal sensor location was obtained in a node that had the highest sensitivity among all nodes in the same cluster.

#### 3.5. Burst Isolation

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Periodic daily patterns at node 1: (

**a**) flowrate, (

**b**) noisy flowrate, (

**c**) pressure, and (

**d**) noisy pressure.

**Figure 4.**Variation of flowrate and pressure at the entrance over a 48 h period: (

**a**) Flowrate, (

**b**) unit head loss, (

**c**) flowrate without periodic pattern, and (

**d**) head loss without periodic pattern.

**Figure 5.**Burst detection at the entrance of the WDN according to S6 using (

**a**) CUSUM, (

**b**) standardized EWMA, and (

**c**) standardized EWMA-PCA.

**Figure 6.**A comparison of the three monitoring systems according to noise in flowrate and pressure considering (

**a**) detection time and (

**b**) detection ratio.

Node Number | Elevation (m) | Demand (m^{3}/day) | Link | Length (m) | Diameter (mm) |
---|---|---|---|---|---|

N1 | 125 | 86 | L1 | 1200 | 400 |

N2 | 120 | 130 | L2 | 1400 | 150 |

N3 | 121 | 86 | L3 | 500 | 150 |

N4 | 120 | 86 | L4 | 700 | 350 |

N5 | 110 | 173 | L5 | 400 | 150 |

N6 | 116 | 86 | L6 | 400 | 125 |

N7 | 117 | 86 | L7 | 600 | 350 |

N8 | 115 | 173 | L8 | 300 | 250 |

N9 | 110 | 173 | L9 | 400 | 200 |

N10 | 111 | 130 | L10 | 500 | 200 |

N11 | 114 | 173 | L11 | 400 | 200 |

N12 | 110 | 173 | L12 | 400 | 250 |

N13 | 105 | 173 | L13 | 350 | 200 |

N14 | 110 | 86 | L14 | 500 | 150 |

Scenario | Burst Flowrate (m^{3}/day) | Burst Location | Occurrence Time (min) | Duration (min) |
---|---|---|---|---|

S1 | 10 | N14 | 902 | 2 |

S2 | 20 | N6 | 685 | 5 |

S3 | 30 | N7 | 551 | 7 |

S4 | 40 | N10 | 62 | 8 |

S5 | 50 | N2 | 589 | 7 |

S6 | 60 | N4 | 384 | 4 |

S7 | 70 | N7 | 348 | 3 |

S8 | 70 | N14 | 540 | 7 |

S9 | 80 | N1 | 744 | 4 |

S10 | 100 | N7 | 980 | 5 |

System | Burst Monitoring Method | Sensor Placement Approach | Reference |
---|---|---|---|

System 1 | CUSUM chart | Sensitivity analysis | [9] |

System 2 | Standardized EWMA chart | k-means clustering and sensitivity analysis | This study |

System 3 | Standardized EWMA and PCA | PCA, k-means clustering, and sensitivity analysis | This study |

Scenario | CUSUM (system 1) | Standardized EWMA (system 2) | Standardized EWAM-PCA (system 3) |
---|---|---|---|

S1 | - | - | 0.88 s |

S2 | - | 47.72 s | 1.63 s |

S3 | 4.11 s | 30.27 s | 6.04 s |

S4 | 3.32 s | 35.52 s | 12.98 s |

S5 | 1.83 s | 20.87 s | 4.62 s |

S6 | 1.15 s | 27.51 s | 2.59 s |

S7 | 1.01 s | 25.99 s | 1.56 s |

S8 | 0.95 s | 25.36 s | 5.33 s |

S9 | 1.09 s | 17.41 s | 2.84 s |

S10 | 0.83 s | 25.84 s | 4.10 s |

Average | 1.79 s | 28.50 s | 4.26 s |

Node | N1 | N2 | N3 | N4 | N5 | N6 | N7 |

Cumulative sensitivity (${S}_{i}$) | $5.16\times {10}^{-7}$ | $1.10\times {10}^{-5}$ | $1.53\times {10}^{-6}$ | $1.88\times {10}^{-6}$ | $2.35\times {10}^{-6}$ | $3.78\times {10}^{-6}$ | $1.88\times {10}^{-6}$ |

Node | N8 | N9 | N10 | N11 | N12 | N13 | N14 |

Cumulative sensitivity (${S}_{i}$) | $2.12\times {10}^{-6}$ | $2.76\times {10}^{-6}$ | $4.14\times {10}^{-6}$ | $3.76\times {10}^{-6}$ | $2.48\times {10}^{-6}$ | $2.76\times {10}^{-6}$ | $4.09\times {10}^{-6}$ |

Node | Parameters of Regression Model | Flow Rate | Pressure | ||||
---|---|---|---|---|---|---|---|

p_{1} | p_{2} | p_{3} | Mean | Standard Deviation | Mean | Standard Deviation | |

N1 | −1.94∙10^{−5} | −3.46∙10^{−4} | 225 | 88.6 | 35.34 | 224.79 | 0.11 |

N2 | −1.70∙10^{−5} | −5.73∙10^{−4} | 230 | 134.0 | 53.43 | 229.58 | 0.23 |

N3 | −2.26∙10^{−5} | −4.51∙10^{−4} | 229 | 88.6 | 35.34 | 228.75 | 0.13 |

N4 | −3.36∙10^{−5} | −8.12∙10^{−4} | 230 | 88.6 | 35.34 | 229.63 | 0.20 |

N5 | −1.09∙10^{−5} | −4.52∙10^{−4} | 225 | 178.3 | 71.10 | 239.52 | 0.26 |

N6 | −4.05∙10^{−5} | −8.83∙10^{−4} | 234 | 88.6 | 35.34 | 233.56 | 0.24 |

N7 | −4.21∙10^{−5} | −9.16∙10^{−4} | 233 | 88.6 | 35.34 | 232.54 | 0.25 |

N8 | −1.16∙10^{−5} | −4.45∙10^{−4} | 235 | 178.2 | 71.10 | 234.50 | 0.27 |

N9 | −1.20∙10^{−5} | −5.10∙10^{−4} | 240 | 178.3 | 71.10 | 239.47 | 0.28 |

N10 | −2.09∙10^{−5} | −6.85∙10^{−4} | 239 | 134.0 | 53.43 | 238.48 | 0.28 |

N11 | −1.10∙10^{−5} | −4.80∙10^{−4} | 236 | 178.3 | 71.10 | 235.51 | 0.26 |

N12 | −1.16∙10^{−5} | −4.67∙10^{−4} | 240 | 178.3 | 71.10 | 239.49 | 0.27 |

N13 | −1.20∙10^{−5} | −5.26∙10^{−4} | 245 | 178.3 | 71.10 | 244.47 | 0.28 |

N14 | −5.06∙10^{−5} | −9.67∙10^{−4} | 240 | 88.6 | 35.34 | 239.46 | 0.29 |

_{1}, p

_{2}, and p

_{3}indicate parameters in the second-order regression model expressed by Equation (7).

Number of Sensors | Number of Probable Configurations | Selected Measurement Points |
---|---|---|

1 | 14 | 2 |

2 | 91 | 2, 10 |

3 | 364 | 2, 10, 14 |

4 | 1001 | 2, 6, 10, 14 |

5 | 2002 | 2, 3, 6, 10, 14 |

6 | 3003 | 2, 3, 6, 9, 11, 14 |

7 | 3432 | 2, 3, 4, 9, 10, 11, 14 |

8 | 3003 | 2, 3, 4, 6, 9, 10, 11, 14 |

9 | 2002 | 2, 3, 4, 9, 10, 11, 12, 13, 14 |

10 | 1001 | 2, 3, 4, 5, 6, 9, 10, 11, 13, 14 |

11 | 364 | 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14 |

12 | 91 | 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14 |

13 | 14 | 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14 |

14 | 1 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 |

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## Share and Cite

**MDPI and ACS Style**

Nam, K.; Ifaei, P.; Heo, S.; Rhee, G.; Lee, S.; Yoo, C.
An Efficient Burst Detection and Isolation Monitoring System for Water Distribution Networks Using Multivariate Statistical Techniques. *Sustainability* **2019**, *11*, 2970.
https://doi.org/10.3390/su11102970

**AMA Style**

Nam K, Ifaei P, Heo S, Rhee G, Lee S, Yoo C.
An Efficient Burst Detection and Isolation Monitoring System for Water Distribution Networks Using Multivariate Statistical Techniques. *Sustainability*. 2019; 11(10):2970.
https://doi.org/10.3390/su11102970

**Chicago/Turabian Style**

Nam, KiJeon, Pouya Ifaei, Sungku Heo, Gahee Rhee, Seungchul Lee, and ChangKyoo Yoo.
2019. "An Efficient Burst Detection and Isolation Monitoring System for Water Distribution Networks Using Multivariate Statistical Techniques" *Sustainability* 11, no. 10: 2970.
https://doi.org/10.3390/su11102970