1. Leak Localization in open water Channels Nadia Bedjaoui Workshop on irrigation channels and related problems N.Bedjaoui, E.Weyer and G. Bastin

2. 2 Outline Problem statement Objective of this work Leak localization methods Application Conclusion

3. 3 Outline Problem statement Objective of this work Leak localization methods Application Conclusion

4. 4 Irrigation channel = supply water to users for irrigation purposes Supply done with less water losses possible Manual control  large water losses Automatic control  minimizes these losses Additional water losses due to the presence of leaks Leak =wasted water left definitively from the channel Problem statement Outline Problem statement Objective Methods Application

5. 5 Outline Problem statement Objective Methods Application Types of leaks in irrigation channels Problem statement Failures in the civil engineering: Affect the walls of the channel

6. 6 Failures in the civil engineering:Affect an escape gate Outline Problem statement Objective Methods Application Types of leaks in irrigation channels Problem statement

7. 7 Types of leaks in irrigation channels Unpredicted offtakes Affect the farmer offtakes Outline Problem statement Objective Methods Application Problem statement

8. 8 Important to –Detect the presence of the leak –Estimate the size of the leak –Localize the position of the leak Outline Problem statement Objective Methods Application Problem statement

9. 9 Leak Detection + Estimation(E. Weyer& G. Bastin 2008) –Based on mass-balance model –Idea :Do the measurements check the model? –CUSUM algorithm: quick detection+ no faulse alarm –Impossible leak localization Problem statement Outline Problem statement Objective Methods Application

10. 10 Outline Problem statement Objective of this work Leak localization methods Application Conclusion

11. 11 Objective of this work Interest: leak localization –Leak is already detected and estimated by CUSUM algorithm (Weyer & Bastin 2008) Investigatation of two methods –Model used: Saint Venant model as Hyperbolic Partial Differential Equations PDE –Method (1) bank of Nonlinear Saint-Venant models –Method (2) bank of Nonlinear Observers Outline Problem statement Objective Methods Application

12. 12 Outline Problem statement Objective of this work Leak localization methods –Method (1) using a bank of pure models Modelling: Saint Venant is hyperbolic PDE –Method (2) using a bank on observers Observer objective Observer structure Observer Design Application Conclusion

13. 13 Method (1): Modelling Outline Problem statement Objective Methods (1) Application Conclusion x=Lx=0 Pool Upstream Gate Downstream Gate P L (t) Y(t,L) Leak Q(t,0) P 0 (t) Q(t,L) Y(t,0) w x L xl

14. 14 Method (1): Modelling Saint Venant Equations Boundary conditions (x=0 & x=L)(=Gate equations) Overshot gate Offtake Outline Problem statement Objective Methods (1) Application Conclusion

15. 15 Method (1):Modelling Two coupled quasi-linear Hyperbolic PDE subcritical flow Outline Problem statement Objective Methods (1) Application Conclusion

16. 16 Initial Conditions (in t=0) Boundary Conditions (in x=0 & x=L) Outline Problem statement Objective Methods (1) Application Conclusion Method (1):Modelling

17. 17 Method (2):Observer Method (2): using a bank of Observers Objective of the observer: From any Initial Conditions (t=0) Using the only measurements Y(t,0) & Y(t,L) The estimation error converges to zero Outline Problem statement Objective Methods (2) Application Conclusion

18. 18 Method (2): using a bank of Observers Observer structure Boundary conditions Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

19. 19 Method (2): using a bank of Observers Observer design 1) Linearized model 2) Formulating the estimation problem as a control problem 3) Using the results on boundary control to determine the boundary conditions of the observer that achieves good estimation Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

20. 20 Observer design 1) Linearized model around an equilibrium - Deviations from the equilibrium -Linearized model Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

21. 21 Observer design 1) Linearized observer around an equilibrium - Deviations from the equilibrium -Linearized observer Estimation error Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

22. 22 2) Formulating the estimation problem as a control problem - Control objective: regulate the deviations to 0 using boundary inputs -Estimation problem: regulate the estimation error to 0 using the boundary output errors Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

23. 23 Summary on boundary control of Saint Venant equations -Linear case + non-homogenous terms -Linear case +non-homogenous terms [ Bastin et al 2008] small enough for Saint Venant Subcritical flow -Quasi-linear case +non-homogenous terms [ Prieur et al 2008] small enough & sufficiently small

24. 24 observer design based on characteristic method

25. 25 Method (2): using a bank of Observers Initial Conditions (t=0) Boundary Conditions (x=0 & x=L) Outline Problem statement Objective Methods (2) Application Conclusion Method (2):Observer

26. 26 Localization scheme Method 1 Method 2

27. 27 Outline Introduction –Problem statement –Objective of this work Leak localization methods –Method based on models –Method based on observers Application of the 2 methods –Description of the system of application –Results and observations with Simulated data Real data Conclusion

28. 28 Application of the 2 methods Description of the system of application Gate 6Gate 5Gate 4Gate 3Gate 2Gate 1 Topview of Coly 6 Farm L=943m, delay=5mn, Silde slope=2 Bottom width=1.80m Gate width=1.91m

29. 29 Scenario Pool 5 Gate 4 Gate 5 p xL y xL Offtake q x0 p x0 q xL y x0 d xL Section=35

30. 30 Scenario Application on simulated data Pool 5 Gate 4 Gate 5 p xL y xL Offtake q x0 p x0 q xL y x0 d xL Section=35

31. 31 Observer convergence: using different gains

32. 32 Observer convergence from different initial conditions

33. 33 Outline Introduction –Problem statement –Objective of this work Leak localization methods –Method based on models –Method based on observers Application of the 2 methods –Description of the system of application –Results and observations with Simulated data Real data Conclusion

34. 34 Localization scheme (method 1)

35. 35 Localization scheme (method 2)

36. 36 Results on simulated data H1 H2

37. 37 Localization results on simulated data

38. 38 Subject to a variation of 50% of n

39. 39 Scenario Application on real data Pool 5 Gate 4 Gate 5 p xL y xL Offtake q x0 p x0 q xL y x0 d xL

40. 40 Outline Introduction –Problem statement –Objective of this work Leak localization methods –Method based on models –Method based on observers Application of the 2 methods –Description of the system of application –Results and observations with Simulated data Real data Conclusion

41. 41 Results on Real data

42. 42 Localization scheme Method 1 Method 2

43. 43 Results on simulated data

44. 44 Conclusion Objective: Leak localization Investigate two methods for leak localization Method (1) based on pure models Method (2) based on observers Design of observer: - Characteristic method - The estimation problem is written as boundary control problem for the linearized system -Convergence of the observer can be fixed by the gains

45. 45 Conclusion (2/2) Both methods give similar results Leak localization is too sensitive: Model uncertainty Offset on measurments Time Starting detection Feedback control

46. 46 2) Réconciliation de données globale Appliquée à un bief avec retards discrétisés : Filtre de Kalman  détection de prélèvements+défauts Combinaison locale -globale  Distinction défaut - prélèvement 3) Observateurs à entrées inconnues et H  Cas général des systèmes à retards Retards dans l’état et les entrées Retards variants dans le temps  Méthode testée avec succès sur le canal de Gignac Conclusion (2/2)