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Hiroto WAKITA Department of Civil Engineering, Chuo University,

～ Load to Korea ～. Estimation of Water Flow at Watarase Retardation Pond Using Kalman Filter Finite Element Method. Hiroto WAKITA Department of Civil Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, Japan. danger. Introduction. Japan. many mountains,

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Hiroto WAKITA Department of Civil Engineering, Chuo University,

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  1. ～Load to Korea～ Estimation of Water Flow at Watarase Retardation Pond Using Kalman Filter Finite Element Method Hiroto WAKITA Department of Civil Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, Japan

  2. danger Introduction Japan many mountains, small valley area rainy season, typhoon flood Watarase Retardation Pond

  3. Kalman Filter Finite Element Method Problems The basic equation used for numerical analysis cannot express an actual problem. The observation data obtained by actual observation includes mechanical and individual errors. It is economically and physically very difficult to set many observation points. It is difficult to dispose boundary condition.

  4. Kalman Filter estimation value time direction Image of Kalman Filter observation data

  5. time direction space direction Kalman Filter FEM + estimation value Image of Kalman Filter observation data

  6. Finite Element Matrix ：observation value ：state value ：observation matrix ：state transition matrix ：driving matrix ：system noise ：observation noise Basic Equation ＜System Equation＞ ＜Observation Equation＞

  7. Linear Shallow Water Equation Basic equation <momentum equation> Y <continuity equation>

  8. Discretization Galerkin method with liner triangular Spatial discretization Temporal discretization Explicit Euler method

  9. Finite Element Matrix Finite element matrix in FEM State transition matrix in KF-FEM

  10. Algorithm 1. 2. 3. Off-line 4. 5. if then Go To 6 else Go To 2 6. On-line 7.

  11. Numerical Example Tokyo Watarase Retardation Pond

  12. Finite Element Mesh nodes 400 elements 682

  13. Situation Filled water Watarase Retardation Pond

  14. Altitude of Riverbed

  15. Point 2 Point 3 Point 1 Point 5 Observation and Estimation Points observation point estimation point

  16. Observation Data Normal Flood ( 2001/8/21～26)

  17. Observation Data of Discharge Point 1 Ｄｉｓｃｈａｒｇｅ Point 2 Point 3 Ｄｉｓｃｈａｒｇｅ Ｄｉｓｃｈａｒｇｅ

  18. Observation Data of Water Elevation Point 1 Ｗａｔｅｒ　Ｅｌｅｖａｔｉｏｎ Point 2 Point 3 Ｗａｔｅｒ　Ｅｌｅｖａｔｉｏｎ Ｗａｔｅｒ　Ｅｌｅｖａｔｉｏｎ

  19. Parameter ＤＡＴＡ ＶＡＬＵＥ total time (day) 5 Δt (sec) 1 lamping parameter : e 0.9 gravitational acceleration : g (m/sec ) 9.8 2 water depth : h (m) 5.0 coefficient of kinematic eddy viscosity : Al(m /sec) 0.01

  20. Result of Water Flow

  21. Result of Water Elevation Ｗａｔｅｒ　Ｅｌｅｖａｔｉｏｎ

  22. Result of Discharge Ｄｉｓｃｈａｒｇｅ

  23. Conclusion KF-FEM is applied to the Watarase Retardation Pond and estimated water flow. As estimation of water elevation could get good result, KF-FEM is useful method for estimation problem and the analysis considering observation.

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