Construction of a stochastic model for a water supply network with hidden leaks and a method for detecting and calculating the leaks

Andrei Tevyashev, Olga Matviyenko, Glib Nikitenko


We have constructed a stochastic model of a water supply network with leaks, which, compared to the previously proposed models (excluding leaks), more adequately describes the processes of transportation and water distribution in water supply systems. Mathematical modeling of water supply networks is associated with difficulties related to the huge dimensionality of actual water supply networks, limited information resources and operational data, which does not make it possible to assess parameters of the technological equipment and structure of a water supply network adequately enough. Therefore, an equivalent scheme is built for an actual water supply network based on its dictation points, which is then used for subsequent calculations. The task on building a scheme for an equivalent water supply network consists of three problems: identification of the structure, parameters, and state of a water supply network. The proposed method for leaks detection is based on the comparison of change in the magnitude of head at pumping stations and at the dictation points of a water supply network. Based on the stochastic model of a water supply network with leaks, we have constructed a method for calculating the magnitude of leaks, which implies the following: by knowing the head of water at the nodes of an equivalent water supply network and the approximate diameters of leaks at nodes, new values of heads at nodes of the equivalent water supply network are calculated. Then we again compute the magnitude of a leak by knowing the new head at the node and the diameter of the leaks. Upon completion of several such iterations, a conclusion is drawn on that starting at a certain step the magnitude of leaks and the heads at the nodes of the equivalent water supply network stop changing. By knowing the magnitude of leaks and head at each node within the equivalent water supply network, we determine the actual diameter of fistulas at each node. The proposed method for calculating the magnitude of leaks does not require financial costs or the use of additional equipment; it could be used by water utilities to detect and calculate the magnitude of leaks


water supply network; leaks; equivalent water supply network; stochastic model; pumping station

Full Text:



Van Zyl, J. E., Cassa, A. M. (2014). Modeling Elastically Deforming Leaks in Water Distribution Pipes. Journal of Hydraulic Engineering, 140 (2), 182–189. doi:

Ostapkowicz, P. (2016). Leak detection in liquid transmission pipelines using simplified pressure analysis techniques employing a minimum of standard and non-standard measuring devices. Engineering Structures, 113, 194–205. doi:

Pérez, R., Puig, V., Pascual, J., Quevedo, J., Landeros, E., Peralta, A. (2011). Methodology for leakage isolation using pressure sensitivity analysis in water distribution networks. Control Engineering Practice, 19 (10), 1157–1167. doi:

Casillas Ponce, M. V., Garza Castañón, L. E., Cayuela, V. P. (2014). Model-based leak detection and location in water distribution networks considering an extended-horizon analysis of pressure sensitivities. Journal of Hydroinformatics, 16 (3), 649–670. doi:

Jiménez-Cabas, J., Romero-Fandiño, E., Torres, L., Sanjuan, M., López-Estrada, F. R. (2018). Localization of Leaks in Water Distribution Networks using Flow Readings. IFAC-PapersOnLine, 51 (24), 922–928. doi:

Amoatey, P. K., Bárdossy, A., Steinmetz, H. (2018). Inverse Optimization based Detection of Leaks from Simulated Pressure in Water Networks, Part 1: Analysis for a Single Leak. Journal of Water Management Modeling. doi:

Ishido, Y., Takahashi, S. (2014). A New Indicator for Real-time Leak Detection in Water Distribution Networks: Design and Simulation Validation. Procedia Engineering, 89, 411–417. doi:

Sousa, J., Ribeiro, L., Muranho, J., Marques, A. S. (2015). Locating Leaks in Water Distribution Networks with Simulated Annealing and Graph Theory. Procedia Engineering, 119, 63–71. doi:

Mashford, J., Silva, D. D., Marney, D., Burn, S. (2009). An Approach to Leak Detection in Pipe Networks Using Analysis of Monitored Pressure Values by Support Vector Machine. 2009 Third International Conference on Network and System Security. doi:

Jasper, M. N., Mahinthakumar, G. (Kumar), Ranjithan, S. (Ranji), Brill, E. D. (2013). A Sensitivity Analysis of Data Measurement Types for Leak Detection in Water Distribution Systems. World Environmental and Water Resources Congress 2013. doi:

Li, X., Li, G. (2010). Leak Detection of Municipal Water Supply Network Based on the Cluster-Analysis and Fuzzy Pattern Recognition. 2010 International Conference on E-Product E-Service and E-Entertainment. doi:

Evdokimov, A. G., Tevyashev, A. D. (1980). Operativnoe upravlenie potokoraspredeleniem v inzhenernyh setyah. Kharkiv: Vishcha shkola, 144.

Tevyashev, A. D., Kozyrenko, S. I., Nepochatova, V. D. (2015). Stohasticheskaya model' kvazistatsionarnyh rezhimov raboty sistem vodosnabzheniya i metod ee postroeniya dlya vodoprovodnyh setey s utechkami. Truboprovodnye sistemy energetiki. Metodicheskie i prikladnye problemy matematicheskogo modelirovaniya. Novosibirsk, 205–220.

Teviashev, A. D., Matvienko, O. I. (2014). About one approach to solve the problem of management of the development and operation of centralized water–supply systems. Econtechmod. An International Quarterly Journal, 3 (3), 61–76.

Tevyashev, A., Matviyenko, O. (2015). Mathematical Model and Method of Optimal Stochastic Control of the Modes of Operation of the Water Main. Eastern-European Journal of Enterprise Technologies, 6 (4 (78)), 45–53. doi:

GOST Style Citations

Copyright (c) 2019 Andrei Tevyashev, Olga Matviyenko, Glib Nikitenko

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN (print) 1729-3774, ISSN (on-line) 1729-4061