Analysis of Elastic Body using Kalman Filter Finite Element Method

This research is the estimation of elastic body using the Kalman Filter Finite Element Method. The ground is always continuing a minute vibration. And it is very difficult to identify data about production of any actions. The Kalman Filter is the method of estimating unknown parameter using observation data distorted by noise. The Kalman Filter is the filtering algorithm presented by Kalman and Bucy in 1960’s, which is based on the stochastic process theory of the state space model and the orthogonal projection for the linear system. In the Kalman Filter, the system and observation noise are included. The system noise is error that arises in approximating basic equation. The state space model is consisted by system model equation and the observation equation. The system model equation can be expressed state of phenomena. And the observation equation is denoting relation between the actual observation data and the state value. The Kalman Filter is a calculation algorithm is estimation problem it is divided in three workspace shown as followed, (

1

) Prediction is the problem calculated optimal estimated values in the future, (

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) Filtering is calculated it at the present, (

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) Smoothing is calculated it in the past. The Kalman Filter can estimate the state value in time direction. However, the Kalman Filter cannot estimate the state value in space direction. If combine the advantage of the Kalman Filter and Finite Element Method, it can estimate not only in time but also in space direction. And it is the Kalman Filter Finite Element Method. For the temporal discretaization, the Newmark β method is used. And For the spatial discretaization, the Galerkin method is applied. As the numerical analysis, it is presented that the estimation of the quarry. The quarry is Futatsuisi-mountain in Miyagi Japan. The actual data is used from September 20

th

in 2005.