Application of the Reduced Kalman Filter Finite Element Method to the Ground

Abstract

The purpose of this study is to investigate estimation of acceleration of the ground using the Kalman filter finite element method. From data of acceleration observed in the site, arbitrary data of acceleration is estimated. In this paper, as the state equation, the equilibrium of stress equation, the strain - displacement equation, and the stress - strain equation are used. For spatial discretization, the finite element method and the Galerkin method is used as an interpolation method. For temporal discrezation, the Newmark � method is applied. the Kalman filter finite element method is the combination of the Kalman filter and the finite element method. This method can estimate from noisy observation in the site. However, long computational time is required for computation by the method. Then, to reduce the computational time, the computational domain is divided into two parts, the main domain and the subsidiary domain. In the main domain, filtering procedures are carried out, whereas only deterministic process is taken for the variables in the subsidiary domain. Eliminating the state variables in the subsidiary domain, the drastically efficient computation is carried out. In this paper, this method is called the Reduced Kalman Filter Finite Element Method. As the numerical study, this method is applied to Ohyorogi tunnnel site. The site is located in Mt.Ohyorogi in Hiroshima prefecture, Japan. The blasting examination was carried out on August 26th, 2009. Then accelerations are measured at two points by the accelerometer. These obtained data are used as observation and reference data. The acceleration is estimated by the presented method using observation data. The estimation value is compared with reference data at estimation point.