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Leak Localization in open water Channels

Leak Localization in open water Channels. Workshop on irrigation channels and related problems. N.Bedjaoui, E.Weyer and G. Bastin. Nadia Bedjaoui. Outline. Problem statement Objective of this work Leak localization methods Application Conclusion. Outline. Problem statement

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Leak Localization in open water Channels

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

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

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

  4. Outline • Problem statement • Objective • Methods • Application Problem statement • 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

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

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

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

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

  9. Outline • Problem statement • Objective • Methods • Application Problem statement 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

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

  11. Outline • Problem statement • Objective • Methods • Application 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 DifferentialEquations PDE • Method (1) bank of Nonlinear Saint-Venant models • Method (2) bank of Nonlinear Observers

  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. Outline • Problem statement • Objective • Methods (1) • Application • Conclusion Method (1): Modelling Q(t,0) Y(t,0) Y(t,L) Q(t,L) P0(t) Pool PL(t) Upstream Gate w xl Leak Downstream Gate L x x=0 x=L

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

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

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

  17. Outline • Problem statement • Objective • Methods (2) • Application • Conclusion 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

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

  19. Outline • Problem statement • Objective • Methods (2) • Application • Conclusion Method (2):Observer 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

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

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

  22. Outline • Problem statement • Objective • Methods (2) • Application • Conclusion Method (2):Observer 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

  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. observer design based on characteristic method

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

  26. Localization scheme • Method 1 • Method 2

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

  29. Scenario yx0 qx0 yxL qxL px0 Pool 5 pxL Gate 4 dxL Gate 5 Offtake Section=35

  30. Application on simulated data • Scenario yx0 qx0 yxL qxL px0 Pool 5 pxL Gate 4 dxL Gate 5 Offtake Section=35

  31. Observer convergence: using different gains

  32. Observer convergence from different initial conditions

  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. Localization scheme (method 1)

  35. Localization scheme (method 2)

  36. Results on simulated data H1 H2

  37. Localization results on simulated data

  38. Subject to a variation of 50% of n

  39. Application on real data • Scenario yx0 qx0 yxL qxL px0 Pool 5 pxL Gate 4 dxL Gate 5 Offtake

  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. Results on Real data

  42. Localization scheme • Method 1 • Method 2

  43. Results on simulated data

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

  46. Conclusion (2/2) 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

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