RealTime Leak Diagnosis in Water Distribution Systems Based on a Bank of Observers and a Genetic Algorithm
Abstract
:1. Introduction
2. Preliminaries
2.1. Pipeline Dynamical Model
2.2. Solution of Governing Equations through the Method of Characteristics (MOC)
2.2.1. Convergence and Stability Conditions
2.2.2. Special Boundary Conditions
2.3. Discrete Time Extended Kalman Filter
2.4. Genetic Algorithms
3. LDI Scheme in a Branched Pipeline WDN
3.1. General Branched Pipeline LDI System Design Principles
3.2. Leak Detection and Isolation Process
3.2.1. Leak Detection
3.2.2. Branch Identification
3.2.3. Leak Isolation
3.2.4. LDI Pseudo Code
Algorithm 1 LDI Scheme 

4. Tuxtla Gutiérrez Pilot Plant: A Case Study
4.1. Pilot Pipeline Description
4.2. Pilot Plant Modeling
4.3. Experimental Results
4.4. Some Final Remarks
 (1)
 The algorithm can hardly identify the parameters of a leak with a rate greater than 10 % of the nominal flow since this event can be considered as a catastrophic failure instead of a simple fault, this is because the assumptions to obtain a modeling of the system could not be fulfilled correctly. Moreover the smallest leak that can be detected depends directly on the accuracy of the flow rate sensors (noise variance).
 (2)
 To obtain moving average values of the input and output measurements, they are filtered with the equation [31]:$${\varsigma}_{F}\left(k\right)=\frac{1}{2N+1}(\varsigma (K+N)+\varsigma (k+N1)+...+\varsigma (kN))$$
 (3)
 The initial conditions of the observer, ${\mathbf{X}}_{0}$ are fixed as follows: ${H}_{{4}_{0}}$, ${Q}_{{4}_{0}}$, ${H}_{{5}_{0}}$, ${Q}_{{5}_{0}}$, ${H}_{{6}_{0}}$ and ${Q}_{{6}_{0}}$ are equal to the mean values of the measured outputs in a steadystate leakfree condition.
 (4)
 (5)
 On the other hand, the inner flowrate initial conditions. ${Q}_{{2}_{0}}$, ${Q}_{{2}_{0}}^{\prime}$, ${Q}_{{2}_{0}}^{\u2033}$, ${Q}_{{3}_{0}}$, ${Q}_{{3}_{0}}^{\prime}$, ${Q}_{{3}_{0}}^{\u2033}$, are computed using the law of conservation of mass:$${Q}_{{i}_{0}}={Q}_{{i}_{0}}^{\prime}+{Q}_{{i}_{0}}^{\u2033}$$
 (6)
 As is well known, the friction factor, $\tau $ in Equation (1), radically changes with the flow velocity in smooth pipes (pipes with a relative roughness usually lower than $1\times {10}^{3}$). That is why in the present work, the friction factor is calculated by using the SwameeJain [15]:$$\tau \left(Q\right)=\frac{0.25}{{\left(\right)}^{{log}_{10}}}2$$
5. Conclusions and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
 OECD. Water Governance in Cities; OECD Studies on Water; OECD Publishing: Paris, France, 2016; p. 140. [Google Scholar] [CrossRef]
 SantosRuiz, I.; LópezEstrada, F.R.; Puig, V.; ValenciaPalomo, G.; Hernández, H.R. Pressure Sensor Placement for Leak Localization in Water Distribution Networks Using Information Theory. Sensors 2022, 22, 443. [Google Scholar] [CrossRef] [PubMed]
 MoralesGonzález, I.O.; SantosRuiz, I.; LópezEstrada, F.R.; Puig, V. Pressure Sensor Placement for Leak Localization Using Simulated Annealing with Hyperparameter Optimization. In Proceedings of the 2021 5th International Conference on Control and FaultTolerant Systems (SysTol), SaintRaphaël, France, 29–30 September 2021; pp. 205–210. [Google Scholar] [CrossRef]
 Perez, R.; Sanz, G.; Puig, V.; Quevedo, J.; Cuguero Escofet, M.A.; Nejjari, F.; Meseguer, J.; Cembrano, G.; Mirats Tur, J.M.; Sarrate, R. Leak Localization in Water Networks: A ModelBased Methodology Using Pressure Sensors Applied to a Real Network in Barcelona [Applications of Control]. IEEE Control Syst. Mag. 2014, 34, 24–36. [Google Scholar] [CrossRef] [Green Version]
 Levinas, D.; Perelman, G.; Ostfeld, A. Water Leak Localization Using HighResolution Pressure Sensors. Water 2021, 13, 591. [Google Scholar] [CrossRef]
 Sun, C.; Parellada, B.; Puig, V.; Cembrano, G. Leak Localization in Water Distribution Networks Using Pressure and DataDriven Classifier Approach. Water 2020, 12, 54. [Google Scholar] [CrossRef] [Green Version]
 DelgadoAguiñaga, J.; Besançon, G. EKFbased leak diagnosis schemes for pipeline networks. IFACPapersOnLine 2018, 51, 723–729. [Google Scholar] [CrossRef]
 Torres, L.; Verde, C.; Molina, L. Leak diagnosis for pipelines with multiple branches based on model similarity. J. Process Control 2021, 99, 41–53. [Google Scholar] [CrossRef]
 DelgadoAguiñaga, J.; SantosRuiz, I.; Besançon, G.; LópezEstrada, F.; Puig, V. EKFbased observers for multileak diagnosis in branched pipeline systems. Mech. Syst. Signal Process. 2022, 178, 109198. [Google Scholar] [CrossRef]
 Pan, B.; Capponi, C.; Meniconi, S.; Brunone, B.; Duan, H.F. Efficient leak detection in single and branched polymeric pipeline systems by transient wave analysis. Mech. Syst. Signal Process. 2022, 162, 108084. [Google Scholar] [CrossRef]
 Liao, Z.; Yan, H.; Tang, Z.; Chu, X.; Tao, T. Deep learning identifies leak in water pipeline system using transient frequency response. Process Saf. Environ. Prot. 2021, 155, 355–365. [Google Scholar] [CrossRef]
 Chaudhry, M.H. Transientflow equations. In Applied Hydraulic Transients; Springer: Berlin/Heidelberg, Germany, 2014; pp. 35–64. [Google Scholar]
 Streeter, V.L.; Lai, C. Waterhammer analysis including fluid friction. Trans. Am. Soc. Civ. Eng. 1963, 128, 1491–1524. [Google Scholar] [CrossRef]
 Srbislava, G.; Ivana, A.; Petara, K.; Markob, J.; Nikolab, B.; Vojislavc, G. A review of explicit approximations of Colebrook’s equation. FME Trans. 2011, 39, 67–71. [Google Scholar]
 Abdulameer, L.S.; Dzhumagulova, N.; Algretawee, H.; Zhuravleva, L.; Alshammari, M.H. Comparison between HazenWilliams and DarcyWeisbach Equations to Calculate Head Loss through Conveyancing Treated Wastewater in Kerbala City, Iraq. East.Eur. J. Enterp. Technol. 2022, 1, 115. [Google Scholar] [CrossRef]
 Dulhoste, J.F.; Besançon, G.; Ortiz, F.L.T.; Begovich, O.; Navarro, A. About friction modeling for observerbased leak estimation in pipelines. In Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, USA, 12–15 December 2011; pp. 4413–4418. [Google Scholar]
 Carlsson, J. Water Hammer Phenomenon Analysis Using the Method of Characteristics and Direct Measurements Using a “Stripped” Electromagnetic Flow Meter. Master’s Thesis, Royal Institute of Technology, Stockholm, Sweden, 2016. [Google Scholar]
 O’Brien, G.G.; Hyman, M.A.; Kaplan, S. A Study of the Numerical Solution of Partial Differential Equations. J. Math. Phys. 1950, 29, 223–251. [Google Scholar] [CrossRef]
 Simon, D. Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches; John Wiley & Sons: Hoboken, NJ, USA, 2006. [Google Scholar]
 Fujii, K.; The ACDASimJ Group. Extended Kalman Filter. Reference Manual. 2013, pp. 14–22. Available online: https://wwwjlc.kek.jp/2004sep/subg/offl/kaltest/doc/ReferenceManual.pdf (accessed on 3 May 2022).
 Katoch, S.; Chauhan, S.S.; Kumar, V. A review on genetic algorithm: Past, present, and future. Multimed. Tools Appl. 2021, 80, 8091–8126. [Google Scholar] [CrossRef] [PubMed]
 Kumar, M.; Husain, M.; Upreti, N.; Gupta, D. Genetic Algorithm: Review and Application (1 December 2010). Available online: https://ssrn.com/abstract=3529843 (accessed on 16 April 2022).
 Mathew, T.V. Genetic Algorithm. Report Submitted at IIT Bombay 2012. Indian Institute of Technology, Bombay, Mumbai. Available online: http://datajobstest.com/datasciencerepo/GeneticAlgorithmGuide[TomMathew].pdf (accessed on 16 April 2022).
 Isermann, R. FaultDiagnosis Systems: An Introduction from Fault Detection to Fault Tolerance; Springer: Berlin/Heidelberg, Germany, 2005. [Google Scholar]
 Gertler, J.J. Fault Detection and Diagnosis in Engineering Systems; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar]
 Boaz, L.; Kaijage, S.; Sinde, R. An overview of pipeline leak detection and location systems. In Proceedings of the 2nd Pan African International Conference on Science, Computing and Telecommunications (PACT 2014), Arusha, Tanzania, 14–18 July 2014; pp. 133–137. [Google Scholar]
 Soldevila, A.; Boracchi, G.; Roveri, M.; TornilSin, S.; Puig, V. Leak detection and localization in water distribution networks by combining expert knowledge and datadriven models. Neural Comput. Appl. 2022, 34, 4759–4779. [Google Scholar] [CrossRef]
 Navarro, A.; DelgadoAguiñaga, J.A.; SánchezTorres, J.D.; Begovich, O.; Besançon, G. Evolutionary Observer Ensemble for Leak Diagnosis in Water Pipelines. Processes 2019, 7, 913. [Google Scholar] [CrossRef] [Green Version]
 Lindstrom, L.; Gracy, S.; Magnusson, S.; Sandberg, H. Leakage Localization in Water Distribution Networks: A ModelBased Approach. arXiv 2022, arXiv:2204.00050. [Google Scholar]
 SantosRuiz, I.; Bermúdez, J.; LópezEstrada, F.; Puig, V.; Torres, L.; DelgadoAguiñaga, J. Online leak diagnosis in pipelines using an EKFbased and steadystate mixed approach. Control Eng. Pract. 2018, 81, 55–64. [Google Scholar] [CrossRef]
 DelgadoAguiñaga, J.; Begovich, O. Water leak diagnosis in pressurized pipelines: A real case study. In Modeling and Monitoring of Pipelines and Networks; Verde, C., Torres, L., Eds.; Springer International Publishing: Berlin/Heidelberg, Germany, 2017; pp. 235–262. [Google Scholar]
Parameter  Symbol  Value  Dimension 

Inner diameter  $\varphi $  $4.86\times {10}^{2}$  $\mathrm{m}$ 
Wave speed  b  $422.75$  $\mathrm{m}/\mathrm{s}$ 
Relative roughness  ${\u03f5}_{r}$  $3.47\times {10}^{4}$  − 
Fluid kinematic viscosity  $\nu $  $8.03\times {10}^{7}$  ${\mathrm{m}}^{2}/\mathrm{s}$ 
Fluid density  $\rho $  $996.59$  $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ 
Acceleration due to gravity  g  $9.79$  $\mathrm{m}/{\mathrm{s}}^{2}$ 
Case  $\parallel {\mathit{e}}_{\mathit{z}{}_{\mathit{l}}}\parallel $ GA [m]  $\parallel {\mathit{e}}_{\mathit{z}{}_{\mathit{l}}}\parallel $ EKF [m] 

Experiment 1  $1.29\times {10}^{2}$  $2.98\times {10}^{2}$ 
Experiment 2  $1.53\times {10}^{2}$  $4.46\times {10}^{2}$ 
Experiment 3  $1.08\times {10}^{2}$  $0.98\times {10}^{2}$ 
Branch Number  Symbol  Value 

1  ${\tau}_{1}$  $2.40\times {10}^{2}$ 
2  ${\tau}_{2}$  $2.68\times {10}^{2}$ 
3  ${\tau}_{3}$  $3.67\times {10}^{2}$ 
4  ${\tau}_{4}$  $5.95\times {10}^{2}$ 
5  ${\tau}_{5}$  $3.76\times {10}^{2}$ 
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NavarroDíaz, A.; DelgadoAguiñaga, J.A.; SantosRuiz, I.; Puig, V. RealTime Leak Diagnosis in Water Distribution Systems Based on a Bank of Observers and a Genetic Algorithm. Water 2022, 14, 3289. https://doi.org/10.3390/w14203289
NavarroDíaz A, DelgadoAguiñaga JA, SantosRuiz I, Puig V. RealTime Leak Diagnosis in Water Distribution Systems Based on a Bank of Observers and a Genetic Algorithm. Water. 2022; 14(20):3289. https://doi.org/10.3390/w14203289
Chicago/Turabian StyleNavarroDíaz, Adrián, Jorge Alejandro DelgadoAguiñaga, Ildeberto SantosRuiz, and Vicenç Puig. 2022. "RealTime Leak Diagnosis in Water Distribution Systems Based on a Bank of Observers and a Genetic Algorithm" Water 14, no. 20: 3289. https://doi.org/10.3390/w14203289