Estimation Theory Applied to Improving Dynamic Structural Models

摘要

This paper presents a summary of key results from the field of estimation theory. In particular, results are given which are applicable to the problem of improving dynamic structural models to agree with test data. This problem is referred to as structural dynamics parameter identification or reconciliation of analytical models. Pertinent results from both parameter and state estimation are discussed as background information for the development of the iterated Extended Kalman Filter (EKF) for parameter estimation. The well-known Least Squares parameter estimation algorithms are presented for the cases of batch linear estimation, recursive linear estimation, and iterative batch nonlinear estimation. Included are a definition of related parameter estimation algorithms and a discussion of the conditions required for their commonality. Next, the linear Kalman Filter and Extended Kalman Filter equations for optimal state estimation are given, as well as a discussion of the additional generality introduced to obtain the iterated EKF equations. The structural dynamics parameter identification problem is then imbedded into the more general state estimation framework as a special simplified case. An extensive reference list is included. (ERA citation 10:010616)