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Estimation of Tidal Current using Kalman Filter

Estimation of Tidal Current using Kalman Filter. Finite Element Method with AIC. Ryosuke SUGA. Chuo university. D EPARTMENT OF C IVIL E NGINEERING F ACULTY OF S CIENCE AND E NGINEERING. Second MIT Conference on Computational Fluid and Solid Mechanics. Introduction.

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Estimation of Tidal Current using Kalman Filter

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  1. Estimation of Tidal Current using Kalman Filter Finite Element Method with AIC Ryosuke SUGA Chuo university DEPARTMENT OF CIVIL ENGINEERING FACULTY OF SCIENCE AND ENGINEERING Second MIT Conference on Computational Fluid and Solid Mechanics

  2. Introduction In a seaside area, various structures are built in Japan. Important To grasp the state of the sea around a seaside area JAPAN The mechanical and the manual error are included in the observation data. (observation noise) A numerical model cannot express the physical phenomena completely. (system noise) It is difficult to set many observation points economically. Kalman filter finite element method Second MIT Conference on Computational Fluid and Solid Mechanics

  3. Observation data (+noise) Kalman filter Estimation value Kalman Filter To be presented by Kalman and Bucy in 1960’s the filtering algorithm based on stochastic process including noises Since the noise is taken into consideration, Kalman filter can remove the noise. It can estimate the state estimative value only in time series. aerospace science, control engineering and civil engineering Second MIT Conference on Computational Fluid and Solid Mechanics

  4. Kalman Filter Finite Element Method The conventional Kalman filter can not estimate the state values in space model. Kalman filter + finite element method It is possible to estimate the state estimative values not only in time series but also in space model. This method is possible even if it is a large-scale domain. Second MIT Conference on Computational Fluid and Solid Mechanics

  5. Purpose To present Kalman filter finite element method To estimate of tidal current using Kalman filter finite element method Second MIT Conference on Computational Fluid and Solid Mechanics

  6. Kalman Filter The state-space model of the Kalman filter <system equation> Applying the finite element equation <observation equation> : State vector at time k : State transition matrix : Driving matrix : System noise : Observation vector : Observation matrix : Observation noise Second MIT Conference on Computational Fluid and Solid Mechanics

  7. Algorithm 1. 2. 3. Off-line 4. 6 5. go to if then 2 go to else 6. On-line 7. Second MIT Conference on Computational Fluid and Solid Mechanics

  8. : Water velocity Basic Equation Shallow water equation h <momentum equation> <continuity equation> : Gravitational acceleration : Water elevation : Water depth Second MIT Conference on Computational Fluid and Solid Mechanics

  9. Finite Element Method The spatial discretization Galerkin method The temporal discretization BTD method Finite element equation Second MIT Conference on Computational Fluid and Solid Mechanics

  10. State transition matrix State vector Kalman Filter + Finite Element Method Finite element equation Finite element matrix Second MIT Conference on Computational Fluid and Solid Mechanics

  11. Algorithm 1. 2. 3. Off-line 4. 6 5. go to if then 2 go to else 6. On-line 7. Second MIT Conference on Computational Fluid and Solid Mechanics

  12. Akaike Information Criterion(AIC) AIC is the criterion of the selected one from the models which applied maximum log-likelihood method. Maximum log-likelihood method is the way to choose the value of mother group that has the possibility to produce observed sample larger than something else. Second MIT Conference on Computational Fluid and Solid Mechanics

  13. Numerical Example Estimation of tidal current using KF-FEM Onjuku coast The water pollution moves ahead with the inflow of pollution material. Second MIT Conference on Computational Fluid and Solid Mechanics

  14. Onjuku Coast Iwawada Port Onjuku Port No.5 No.2 No.3 No.4 No.1 Numerical Model Onjuku coast Second MIT Conference on Computational Fluid and Solid Mechanics

  15. Finite Element Mesh and Water Depth Node : 407 Element : 728 (m) Second MIT Conference on Computational Fluid and Solid Mechanics

  16. Observation Data at NO.1 Onjuku Coast Iwawada Port Onjuku Port No.5 No.2 No.3 No.4 No.1 Observation Estimation

  17. Result Onjuku Coast Iwawada Port Onjuku Port No.5 No.2 No.3 No.4 No.1 Observation Estimation

  18. Result Second MIT Conference on Computational Fluid and Solid Mechanics

  19. Conclusion KF-FEM has been presented. The tidal current was estimated using KF-FEM The tidal current at the Onjuku coast have been analyzed. KF-FEM is able to estimate a large-scale domain. Second MIT Conference on Computational Fluid and Solid Mechanics

  20. Second MIT Conference on Computational Fluid and Solid Mechanics

  21. Algorithm 1. 2. 3. Off-line 4. 6 5. go to if then 2 go to else 6. On-line 7. Second MIT Conference on Computational Fluid and Solid Mechanics

  22. Result Onjuku Coast Iwawada Port Onjuku Port No.5 No.2 No.3 No.4 No.1 Observation Estimation

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