# Early Detection and Identification of Damage in In-Service Waterworks Pipelines Based on Frequency-Domain Kurtosis and Time-Shift Coherence

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## Abstract

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## 1. Introduction

## 2. Source Localization of Impact Damage

#### 2.1. Conventional Source Location of Leaks in Fluid-Filled Pipelines

_{f}, B

_{f}, a, E, ρ, h, and ω denote the longitudinal wave speed of a fluid in free space, the bulk modulus of the internal fluid, the mean pipe radius, which is calculated based on the outer and inner diameter of a pipe, Young’s modulus of the pipe, the density of the pipe material, the pipe thickness, and the angular frequency, respectively.

#### 2.2. Source Location of Impact Damage in Fluid-Filled Buried Pipelines

## 3. Experiments

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Virtual measurement signal: (

**a**) virtual measurement signal x(t) and (

**b**) virtual measurement signal y(t).

**Figure 5.**Frequency response calculated by the virtual measurement signal: (

**a**) frequency response calculated by virtual measurement signal x(t) and (

**b**) frequency response calculated by virtual measurement signal y(t).

**Figure 7.**Results of FDK: (

**a**) FDK using virtual measurement signal x(t) and (

**b**) FDK using virtual measurement signal y(t).

**Figure 9.**Time signal obtained after the optimal bandpass filter process: (

**a**) using signal x(t) and (

**b**) using signal y(t).

**Figure 17.**Time-domain signal obtained after the optimal bandpass filter process: (

**a**) sensor 1 and (

**b**) sensor 2.

**Figure 19.**Time-domain signals obtained from each sensor including a ground-borne wave: (

**a**) propagation distance of 60 m and (

**b**) propagation distance of 80 m.

**Figure 20.**Excavation signals obtained at various points: (

**a**) results of the excavation test at 60 m, (

**b**) results of the excavation test at 80 m, (

**c**) results of the excavation test at 100 m, (

**d**) results of the excavation test at 120 m, (

**e**) results of the excavation test at 150 m, and (

**f**) results of the excavation test at 180 m.

**Figure 21.**Results of source location comparisons of raw signal and filtered signal: (

**a**) results of the excavation test at 60 m, (

**b**) results of the excavation test at 80 m, (

**c**) results of the excavation test at 100 m, (

**d**) results of the excavation test at 120 m, (

**e**) results of the excavation test at 150 m, and (

**f**) results of the excavation test at 180 m.

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**MDPI and ACS Style**

Lee, S.-H.; Park, C.-S.; Yoon, D.-J.
Early Detection and Identification of Damage in In-Service Waterworks Pipelines Based on Frequency-Domain Kurtosis and Time-Shift Coherence. *Water* **2023**, *15*, 1189.
https://doi.org/10.3390/w15061189

**AMA Style**

Lee S-H, Park C-S, Yoon D-J.
Early Detection and Identification of Damage in In-Service Waterworks Pipelines Based on Frequency-Domain Kurtosis and Time-Shift Coherence. *Water*. 2023; 15(6):1189.
https://doi.org/10.3390/w15061189

**Chicago/Turabian Style**

Lee, Sun-Ho, Choon-Su Park, and Dong-Jin Yoon.
2023. "Early Detection and Identification of Damage in In-Service Waterworks Pipelines Based on Frequency-Domain Kurtosis and Time-Shift Coherence" *Water* 15, no. 6: 1189.
https://doi.org/10.3390/w15061189