# Leakage Detection in Water Distribution Networks Based on Multi-Feature Extraction from High-Frequency Pressure Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}per year, which causes a financial cost of USD 39 billion per year [3]. Leakage is one of the most common and harmful failures, as it causes huge water waste and poses big challenges to the daily operations and maintenance of systems. The World Bank estimated that the annual leakage volume in urban water distribution networks was close to 50 billion m

^{3}worldwide, which accounted for more than 15% of the total annual water supply volume [4]. Leakage events also cause socioeconomic losses due to disruption to production processes, damage to property, and increased energy costs for pumping and supplying water [2,5]. In addition, leakage may lead to the intrusion of pollutants into the pipeline, resulting in water-quality deterioration [6]. Therefore, leakage detection is of great significance for saving water resources, reducing economic loss, and ensuring the operational safety of WDNs.

## 2. Methodology

#### 2.1. Overview of the Proposed Method

- (1)
- Data Preprocessing

**s**was processed by the Butterworth band-stop filter for the removal of measurement noise. The filtered time series

_{00}**s**was obtained from time series

_{0}**s**, which was ready for the extraction of leakage characteristics. The multi-features of leakage are composed of instantaneous characteristics (ICs) and trend characteristics (TCs). IC refers to an instantaneous drop and the instantaneous increase in pressure caused by the negative pressure wave generated by a leakage [10]. TC means the increased flow caused by a leakage event which leads to a certain degree of trend pressure drop in a network.

_{00}- (2)
- Instantaneous Characteristic Diagnosis (IC Diagnosis)

**s**to extract the ICs and obtain the IC time series

_{0}**s**. Then, an appropriate threshold for ICs (

_{1}**thr**) was analyzed and set according to the instantaneous pressure drop levels of the background pressure fluctuations in the network environment. When there was a maximum point

_{ic}**p**in time series

**s**whose IC value exceeded

_{1}**thr**, a probable leakage event at point

_{ic}**p**was diagnosed.

- (3)
- Trend Characteristic Diagnosis (TC Diagnosis)

**p**with a probable leakage event, the trend time series

**s**was obtained with a smoothing process from the time series

_{2,p}**s**. CWT was performed on time series

_{0}**s**to extract the TCs and obtain the TC time series

_{2,p}**s**. An appropriate threshold for TCs (

_{3,p}**thr**) was analyzed and set according to the trend pressure drop levels of the background pressure fluctuations in the network environment. When the maximum in the time series

_{tc}**s**exceeded

_{3,p}**thr**, it was diagnosed that a leakage event had occurred at point

_{tc}**p**, and the leakage alarm was triggered for further analysis.

- (4)
- Leakage Degree Prediction

#### 2.2. Data Preprocessing

**s**was filtered by the Butterworth band-stop filter in this paper. The Butterworth band-stop filter uses the Fourier transform to convert the signal from the time domain to the frequency domain. According to the frequency characteristics of the signal, the noise signal is removed, and the effective signal is retained. The transfer function of the Butterworth band-stop filter is given in Equation (1):

_{00}**n**is the order of the filter,

**f**is the frequency, and

**f**is the cut-off frequency. The pressure fluctuation of the high-frequency signal becomes clear after filtering, as shown by time series

_{c}**s**in Figure 1.

_{0}#### 2.3. IC Diagnosis

#### 2.3.1. IC Extraction

**s**to obtain the IC time series

_{0}**s**. The formula of CWT is shown in Equation (2):

_{1}**W**is called the wavelet transform coefficient, which is the inner product of the mother wavelet and the time series in scale

_{f}(α,τ)**α**and displacement

**τ**, reflecting the similarity between the time series and the mother wavelet at the scale

**α**and displacement

**τ**. Since the wavelet has the characteristic of rapid decay, it reflects the properties of the time series near the displacement

**τ**.

**s**. The wavelet transform coefficient of each point obtained by CWT means the IC value at the point and reflects the instantaneous pressure drop amplitude at the point in time series

_{0}**s**.

_{0}#### 2.3.2. IC Threshold Analysis

**s**was calculated based on fluctuations in pressure over a very short period. On the same time scale, both leakage events and the background pressure fluctuations caused by noise in the network may produce a similar shape of instantaneous pressure drop. Therefore, it is necessary to set an appropriate threshold for ICs to distinguish background pressure fluctuations and leakage events effectively. The leakage-free time series data set was used to evaluate the instantaneous pressure drop levels of the background pressure fluctuations and determine the threshold for ICs. The threshold for ICs was calculated as follows:

_{1}**thr**is the threshold for ICs,

_{ic}**mean**and

_{ic}**σ**are the mean and the standard deviation of the leakage-free time series data set, and

_{ic}**α**is the threshold coefficient for ICs, which is used to adjust the strictness of the diagnosis of ICs. The IC value of the maximum point

_{ic}**p**in time series

**s**was compared with

_{1}**thr**. When the IC value of point

_{ic}**p**exceeded

**thr**, this meant that the instantaneous pressure drop at point

_{ic}**p**was most likely not caused by the background pressure fluctuations in the network. Hence, it was diagnosed that there was a probable leakage event at point

**p**.

#### 2.4. TC Diagnosis

#### 2.4.1. TC Extraction

**thr**in Section 2.3, the pressure data of the length

_{ic}**l**before and after the point

**p**in time series

**s**was taken to obtain the time series

_{0}**s**and the time series

_{0,p,before}**s**, respectively, as shown in Equations (6) and (7):

_{0,p,after}**s**and

_{2,p,before}**s**were obtained from

_{2,p,after}**s**and

_{0,p,before}**s**and concatenated into the trend time series

_{0,p,after}**s**, which reflected the average pressure level before and after point

_{2,p}**p**. The sliding time window theory was used to calculate the average pressure value of each point in the smoothing process [31]. The formulas of the smoothing process are as follows:

**cl**is the window length, which is used to adjust the smoothness of the original signal. Time series

**s**obtained by the smoothing process can more clearly show the trend change characteristics of pressure. The TC time series

_{2,p}**s**was obtained by performing CWT on

_{3,p}**s**. The Haar wavelet was also chosen as the mother wavelet when performing CWT on time series

_{2,p}**s**. The maximum in the time series

_{2,p}**s**means the TC value at point

_{3,p}**p**and reflects the trend pressure drop amplitude at point

**p**in time series

**s**.

_{0}#### 2.4.2. TC Threshold Analysis

**thr**is the threshold for TCs,

_{tc}**mean**and

_{tc}**σ**are the mean and the standard deviation of the leakage-free time series data set, and

_{tc}**α**is the threshold coefficient for TCs, which is used to adjust the strictness of the diagnosis of TCs. When the maximum in the time series

_{tc}**s**exceeds

_{3,p}**thr**, this means that the trend pressure drop amplitude at point

_{tc}**p**exceeds the normal range of the background pressure fluctuations in the network. Then, it is diagnosed that a new leakage event occurs at point

**p**.

**thr**and

_{ic}**thr**were set based on leakage-free time series to comprehensively diagnose whether there existed leakage events in the network. In this paper, IC and TC were diagnosed in series rather than in parallel, the purpose of this being to reduce the computational cost of the process of TC extraction.

_{tc}#### 2.5. Leakage Degree Prediction

**X**and

**Y**are the two variables. PCC is in the range of −1 to 1. When PCC exceeds 0.8, it can be considered that

**X**and

**Y**are highly positively correlated. Then, the selected leakage characteristic and leakage flow were linearly fitted for leakage degree prediction. For a newly diagnosed leakage event, leakage flow is predicted with the extracted leakage characteristic value. Based on the predicted leakage flow, the detected leakage event is classified as severe leakage or small leakage and the predicted leakage degree is obtained, which provides a reference for the leakage repair response level of the water company.

## 3. Results and Discussion

#### 3.1. Experimental Network Setup

^{2}, and the total length of the pipeline is 52 m. The network includes a tank, a water pump, 3 pipes of 100 mm diameter, 11 pipes of 50 mm diameter, and 1 pipe of 25 mm diameter. There are three monitoring points in the network, and each monitoring point is equipped with a high-frequency pressure sensor and an ultrasonic flowmeter. The sampling frequency of the pressure sensor is 10,000 Hz, and the sampling frequency of the flowmeter is 1 Hz. There are seven leakage simulators in the network to simulate leakage events. The opening status and opening range of each leakage simulator are controlled by a valve. The diameter of the leakage simulator A6 is 32 mm, and the diameters of the other leakage simulators are 15 mm. The water in the tank flows into the network after being pressurized by the pump and finally flows back into the tank through valves X1 and X2.

#### 3.2. Performance Indicators and Method Parameters

#### 3.2.1. Performance Indicators

**β**is used to adjust the weights of Precision and Recall in different tasks. When Precision is more important,

**β**can take a value greater than 1. Considering that the water company hoped to detect as many leakage events as possible in the actual leakage detection work,

**β**was taken as 2 in this paper to increase the weight of Recall. Precision, Recall, and F-Score were used to select the appropriate

**α**and

_{ic}**α**, while FAR and MAR were used to describe the leakage detection results for the time series data sets.

_{tc}#### 3.2.2. Parameters for Multi-Feature Extraction

**α**should be close to the total duration of the ICs of leakage events. The calculation of the total duration of an IC is defined in Figure 3. The instantaneous pressure drop duration, the instantaneous pressure increase duration, and the total duration of IC of leakages in 1065 time series in the steady-state time series data set were determined, as shown in Figure 4. The results show that the instantaneous pressure drop duration of 75.49% leakages was in the range of 500–1500, that the instantaneous pressure increase duration of 71.55% leakage was not more than 1000, and that the total duration of IC of 81.88% leakages was not more than 2500. Therefore,

**α**was taken as 2500 in the extraction of the IC.

**l**in Equations (6) and (7) was taken as 10,000, and

**cl**in Equation (8) was taken as 2000, which indicated that the pressure value of each time point in the time series

**s**reflected the average pressure level within 0.4 s around the point

_{2,p}**p**and avoided the influence of the noise. When CWT was performed on time series

**s**, the change in

_{2,p}**α**did not significantly affect the detection of TCs due to the elimination of ICs in the time series

**s**. Considering that the pressure fluctuations caused by variations in water consumption might have an impact on the calculation of the average pressure drop levels caused by leakage events,

_{2,p}**α**was taken as 1000 in the extraction of TCs.

#### 3.3. Results for Two Time Series Data Sets

#### 3.3.1. Leakage Detection Results

**α**and

_{ic}**α**, respectively. With increase in

_{tc}**α**and

_{ic}**α**,

_{tc}**thr**and

_{ic}**thr**increase correspondingly, the diagnostic criteria for ICs and TCs become stricter, and more background pressure fluctuations and small-degree leakage events are not detected as leakage events, resulting in an increase in Precision and a decrease in Recall. Hence, F-Scores were used to balance Precision and Recall and select the appropriate thresholds. Finally,

_{tc}**α**and

_{ic}**α**in the steady-state time series data set took 0 and 3 to obtain the maximum F-Score of 93.30%, and

_{tc}**α**and

_{ic}**α**in the water-consumption time series data set took 1 and 2 to obtain the maximum F-Score of 84.75%. Compared with the steady-state time series data set, the increase in

_{tc}**α**and

_{ic}**α**in the water-consumption time series data set had a more significant impact on Recall but roughly the same impact on Precision, which means that variations in water consumption create huge challenges in the diagnosis of small leakage events.

_{tc}#### 3.3.2. Leakage Degree Prediction Results

#### 3.4. Discussion

#### 3.4.1. Adaptability Analysis of Threshold Setting

**α**took the value of 0 and

_{ic}**α**took the value of 3, which meant that the coincidence degree of ICs between the distributions of the leakage time series and the leakage-free time series was much higher than that of TCs in the network environment without variations in water consumption. Hence,

_{tc}**α**took the laxest value to decrease MAR and

_{ic}**α**took the strictest value to decrease FAR. With the addition of variations in water consumption, there was a small increase in the coincidence degree of ICs but a significant increase in the coincidence degree of TCs. Therefore,

_{tc}**α**should be reduced to avoid a steep increase in MAR. At this time,

_{tc}**α**should be increased to improve the overall performance of leakage detection. As a result,

_{ic}**α**took 1 and

_{ic}**α**took 2 in the water-consumption time series data set.

_{tc}**α**and

_{ic}**α**appropriately and improve adaptability to different network environments. For instance, when there are slight variations in water consumption in a network during the night, a low

_{tc}**α**and a high

_{ic}**α**is suggested, e.g., 0 and 3, and when variations in water consumption become greater during the daytime, a higher

_{tc}_{,}**α**and a lower

_{ic}**α**are needed.

_{tc}#### 3.4.2. Comparison of Three Methods for Leakage Detection

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Leakage detection performance for the steady-state time series data set under different threshold coefficients.

**Figure 6.**Leakage detection performance for the water-consumption time series data set under different threshold coefficients.

**Figure 7.**Relationships between characteristic values of leakage events and leakage flow in the steady-state time series data set.

**Figure 8.**Relationships between characteristic values of leakage events and leakage flow in the water-consumption time series data set.

**Figure 9.**Leakage degree prediction results: (

**a**) the steady-state time series data set; (

**b**) the water-consumption time series data set.

**Figure 10.**The distribution of pressure drop levels in leakage-free time series in two time series data sets.

**Figure 11.**The influence of the threshold coefficient on leakage detection performance in two time series data sets based on two methods: (

**a**) the single-feature-based method on the steady-state time series data set; (

**b**) the single-feature-based method on the water-consumption time series data set; (

**c**) the CUSUM method on the steady-state time series data set; (

**d**) the CUSUM method on the water-consumption time series data set.

Label | Output | |
---|---|---|

L | NL | |

L | TP | FN |

NL | FP | TN |

Time Series Data Set Name | FAR | MAR |
---|---|---|

Steady-State Time Series Data Set | 2.63% | 3.41% |

Water-Consumption Time Series Data Set | 4.97% | 10.26% |

Time Series Data Set Name | α_{ic} | α_{tc} |
---|---|---|

Steady-State Time Series Data Set | 0 | 3 |

Water-Consumption Time Series Data Set | 1 | 2 |

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## Share and Cite

**MDPI and ACS Style**

Wu, X.; Peng, S.; Zheng, G.; Fang, X.; Tian, Y.
Leakage Detection in Water Distribution Networks Based on Multi-Feature Extraction from High-Frequency Pressure Data. *Water* **2023**, *15*, 1187.
https://doi.org/10.3390/w15061187

**AMA Style**

Wu X, Peng S, Zheng G, Fang X, Tian Y.
Leakage Detection in Water Distribution Networks Based on Multi-Feature Extraction from High-Frequency Pressure Data. *Water*. 2023; 15(6):1187.
https://doi.org/10.3390/w15061187

**Chicago/Turabian Style**

Wu, Xingqi, Sen Peng, Guolei Zheng, Xu Fang, and Yimei Tian.
2023. "Leakage Detection in Water Distribution Networks Based on Multi-Feature Extraction from High-Frequency Pressure Data" *Water* 15, no. 6: 1187.
https://doi.org/10.3390/w15061187