# On Image Fusion of Ground Surface Vibration for Mapping and Locating Underground Pipeline Leakage: An Experimental Investigation

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Search of Connected Subgraphs

_{1}, V

_{2}> from vertex V

_{1}to vertex V

_{2}, and then V

_{1}and V

_{2}are considered to be connected. If any two vertices V

_{i}and V

_{j}(V

_{i}, V

_{j}∈Vertex) are connected, then the undirected graph G is a connected graph. As illustrated in Figure 1, the undirected graph is a connected graph, whereas the undirected graph in Figure 2 is a non-connected graph, despite the existence of three connected components. Here, the terminology “connected component” [21,24,25] refers to the maximum connected subgraph in an undirected graph.

_{1}, V

_{2}> in the undirected graph G represents the position and adjacency between vertices. In a directed graph, however, this adjacency represents a path, and the path edges <V

_{1}, V

_{2}> and <V

_{2}, V

_{1}> are different paths, representing different ways of linkage, thereby leading to different search paths. In the undirected graph, however, the path edge <V

_{1}, V

_{2}> is a relative concept, because there is no direction defined in the undirected graph. Therefore, this adjacent edge can point either from V

_{1}to V

_{2}, or from V

_{2}to V

_{1}. By definition, with respect to the logical structure of the whole graph, there is no total order relationship between the vertices of an undirected graph. Thus, it is impossible to arrange the vertices in the graph into a unique and fixed linear sequence, in that each vertex can be treated as the starting vertex. When sorting the points adjacent to a particular vertex, there may be multiple sorting results without a special order of sequence for the nodes in the sorting.

_{3}along the edge (V

_{5}, V

_{3}) after accessing V

_{1}, V

_{2}, V

_{3}, V

_{4}, and V

_{5}because of the presence of loop. Generally, there are two paths of graph traversal including the depth-first search and the breadth-first search, which are both applicable to undirected graphs.

#### 2.2. Moment Estimation

_{0}and y

_{0}are the centroid coordinates selected in the current round of calculation. The normalized central moment of the (p + q)-th order is given by

## 3. Initial Experiments on Test Rig

#### 3.1. Experimental Set-Up

#### 3.2. Determination of the Frequency Range for Leakage Detection

## 4. Image Analysis

#### 4.1. Contour Image Analysis

#### 4.2. Image Fusion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Imaging Fusion on the Application of Pipe Location

**Figure A1.**Grid of measurement points in [20].

**Figure A2.**Magnitude contour image of ground surface vibration measurements at different frequencies.

## References

- Cao, X.; Ruan, C. Compilation of investigation on water loss rate of water supply pipelines in global major cities. Water Purif. Technol.
**2017**, 36, 6–14. [Google Scholar] - Mojgan, G.; Raymond, K.W.; Fang, C.; Yang, W.; Simon, F. Effective Local Metric Learning for Water Pipe Assessment. In Pacific-Asia Conference on Knowledge Discovery and Data Mining; Springer International Publishing: Auckland, New Zealand, 2016. [Google Scholar]
- Farley, M.; Wyeth, G.; Ghazali, Z.B.M.; Istandar, A.; Singh, S.; Dijk, N.; Raksakulthai, V.; Kirkwood, E. The Manager’s Non-Revenue Water Handbook: A Guide to Understanding Water Losses; Ranhill Utilities Berhad and the United States Agency for International Development: Bangkok, Thailand, 2008. [Google Scholar]
- Dutta, R.; Cohn, A.G.; Muggleton, J.M. 3D mapping of buried underworld infrastructure using dynamic Bayesian network based multi-sensory image data fusion. J. Appl. Geophys.
**2013**, 92, 8–19. [Google Scholar] [CrossRef] - Gao, Y.; Brennan, M.J.; Joseph, P.F.; Muggleton, J.M.; Hunaidi, O. On the selection of acoustic/vibration sensors for leak detection in plastic water pipes. J. Sound Vib.
**2005**, 283, 927–941. [Google Scholar] [CrossRef] - Gao, Y.; Sui, F.; Muggleton, J.M.; Yang, J. Simplified dispersion relationships for fluid-dominated axisymmetric wave motion in buried fluid-filled pipes. J. Sound Vib.
**2016**, 375, 386–402. [Google Scholar] [CrossRef] - Muggleton, J.M.; Brennan, M.J. The design and instrumentation of an experimental rig to investigate acoustic methods for the detection and location of underground piping systems. Appl. Acoust.
**2008**, 69, 1101–1107. [Google Scholar] [CrossRef] - Pan, S.; Xu, Z.; Li, D.; Lu, D. Research on detection and location of fluid-filled pipeline leakage based on acoustic emission technology. Sensors
**2018**, 18, 3628. [Google Scholar] [CrossRef][Green Version] - Choi, J.; Shin, J.; Song, C.; Han, S.; Park, D.I. Leak detection and location of water pipes using vibration sensors and modified ML prefilter. Sensors
**2017**, 17, 2104. [Google Scholar] [CrossRef] [PubMed][Green Version] - Casillas, M.V.; Puig, V.; Garza-Castañón, L.E.; Rosich, A. Optimal sensor placement for leak location in water distribution networks using genetic algorithms. Sensors
**2013**, 13, 14984–15005. [Google Scholar] [CrossRef] [PubMed][Green Version] - Us, S.; Mysorewala, N.M.F.; Cheded, L. A Multiscale Approach to Leak Detection and Localization in Water Pipeline Network. Water Resour. Manag.
**2017**, 31, 3829–3842. [Google Scholar] - Ng, K.S.; Chen, P.Y.; Tseng, Y.C. A design of automatic water leak detection device. In Proceedings of the 2017 2nd International Conference on Opto-Electronic Information Processing (ICOIP), Singapore, 7–9 July 2017; pp. 70–73. [Google Scholar]
- Kirby, R.; Duan, W.; Karimi, M.; Brennan, M.; Kessissoglou, N. Detecting sound waves generated by leaks in buried water distribution pipes. In Proceedings of the ACOUSTICS 2017 Perth: Sound, Science and Society—2017 Annual Conference of the Australian Acoustical Society (AAS); Centre for Marine Science and Technology, Curtin University: Perth, Australia, 2017; pp. 1–9. [Google Scholar]
- Gao, Y.; Liu, Y.; Muggleton, J.M. Axisymmetric fluid-dominated wave in fluid-filled plastic pipes: Loading effects of surrounding elastic medium. Appl. Acoust.
**2017**, 116, 43–49. [Google Scholar] [CrossRef] - Elliott, J.; Fletcher, R.; Wrigglesworth, M. Seeking the hidden threat: Applications of a new approach in pipeline leak detection. In Proceedings of the Society of Petroleum Engineers—13th Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC), Abu Dhabi, Arab, 3–6 November 2008; Volume 3, pp. 1258–1267. [Google Scholar]
- Ma, Y.; Gao, Y.; Cui, X.; Brennan, M.J.; Almeida, F.C.L.; Yang, J. Adaptive phase transform method for pipeline leakage detection. Sensors
**2019**, 19, 310. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gao, Y.; Liu, Y.; Ma, Y.; Cheng, X.; Yang, J. Application of the differentiation process into the correlation-based leak detection in urban pipeline networks. Mech. Syst. Signal Process.
**2018**, 112, 251–264. [Google Scholar] [CrossRef] - Hennigar, G.W. Water Leakage Control and Sonic Detection. Can. Water Resour. J.
**1984**, 9, 51–57. [Google Scholar] [CrossRef] - Gao, Y.; Muggleton, J.M.; Liu, Y.; Rustighi, E. An analytical model of ground surface vibration due to axisymmetric wave motion in buried fluid-filled pipes. J. Sound Vib.
**2017**, 395, 142–159. [Google Scholar] [CrossRef][Green Version] - Muggleton, J.M.; Brennan, M.J.; Gao, Y. Determining the location of buried plastic water pipes from measurements of ground surface vibration. J. Appl. Geophys.
**2011**, 75, 54–61. [Google Scholar] [CrossRef] - Ma, X.; Wu, B.; Jin, X. Edge-disjoint spanning trees and the number of maximum state circles of a graph. J. Comb. Optim.
**2018**, 35, 997–1008. [Google Scholar] [CrossRef] - Miyoshi, T.; Nagasaki, T.; Shinjo, H. Moment-based character-normalization methods using a contour image combined with an original image. In Proceedings of the International Conference on Document Analysis and Recognition (ICDAR), Washington, DC, USA, 25–28 August 2013; pp. 1066–1070. [Google Scholar]
- Jin, C.; Xu, K. Estimation and application of the watermark embedding strength. In Proceedings of the 11th Joint International Computer Conference, JICC 2005; World Scientific Publishing: Hong Kong, China, 2005. [Google Scholar]
- Zhang, Y.; Zhao, S.; Meng, J. Edge fault tolerance of graphs with respect to lambda(2)-optimal property. Theor. Comput. Sci.
**2019**, 783, 95–104. [Google Scholar] [CrossRef] - Wang, S.; Zhang, G. Edge fault tolerance of regular graphs on super 3-restricted edge connectivity. Ars Comb.
**2019**, 144, 55–80. [Google Scholar]

**Figure 3.**Pipe rig layout: (

**a**) photograph showing the test rig under construction; (

**b**) schematic of three test pipes.

**Figure 5.**Ground surface vibration measurement using the sensor array at the distance of 1.5 m from the leak.

**Figure 6.**Ground surface vibration measurement using the sensor array at the distance of 1 m from the leak.

**Figure 7.**Ground surface vibration measurement using the sensor array at the distance of 0.5 m from the leak.

**Figure 8.**Frequency domain vibrational velocity on the ground measured at the distances from the leak of (

**a**) 0.5 m, (

**b**) 1 m, and (

**c**) 1.5 m.

**Figure 9.**Frequency domain vibrational velocity on the ground measured at the burial depth of (

**a**) 0.5 m, (

**b**) 1 m, and (

**c**) 1.5 m.

**Figure 11.**Steps for the mapping and locating the pipe leakage based on ground surface vibration measurements.

**Figure 13.**Contour image based on CobMode for Figure 12.

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## Share and Cite

**MDPI and ACS Style**

Yan, S.; Yuan, H.; Gao, Y.; Jin, B.; Muggleton, J.M.; Deng, L.
On Image Fusion of Ground Surface Vibration for Mapping and Locating Underground Pipeline Leakage: An Experimental Investigation. *Sensors* **2020**, *20*, 1896.
https://doi.org/10.3390/s20071896

**AMA Style**

Yan S, Yuan H, Gao Y, Jin B, Muggleton JM, Deng L.
On Image Fusion of Ground Surface Vibration for Mapping and Locating Underground Pipeline Leakage: An Experimental Investigation. *Sensors*. 2020; 20(7):1896.
https://doi.org/10.3390/s20071896

**Chicago/Turabian Style**

Yan, Shuan, Hongyong Yuan, Yan Gao, Boao Jin, Jennifer M. Muggleton, and Lizheng Deng.
2020. "On Image Fusion of Ground Surface Vibration for Mapping and Locating Underground Pipeline Leakage: An Experimental Investigation" *Sensors* 20, no. 7: 1896.
https://doi.org/10.3390/s20071896