Eigen structure assignment based finite element model updating

International Conference on Computer Aided Engineering (CAE-2013)

Subhamoy Sen, & Baidurya Bhattacharya

2013-01-01

Mathematical models deviate from real structures owing to assumptions regarding boundary conditions, model order selection, material and geometric parameters and numerical errors, all of which may lead to incorrect prediction of structural response. The objective of model updating is therefore to adjust the mathematical model so that it can predict the actual response with better accuracy. In this paper, control theory based Eigen Structure Assignment (ESA) technique is used to update the finite element model (FEM). ESA uses state feedback to update existing system matrices. One of the benefits of using feedback in a closed loop system is its ability to alter system’s transient response. In order to alter transient response, the eigenstructure of the system must be changed, which is accomplished in ESA based model updating methods through feedback control. This simultaneous assignment of eigenvalue-vector pairs in FEM generated system matrix is done by using a controller or gain matrix. However, unlike general control technique which uses active forces to control the system, here feedback force is fictitious and control is achieved through virtual forces that update the system matrix to match system eigenstructure to the desired one. In this paper, we extend the ESA based model updating by adopting state space identification to match the eigenstructure of model state matrix to the eigenstructure of the identified state matrix. FEM of an Euler-Bernoulli type beam and a transmission tower have been used to validate this method. The systems have been identified using their response histories at selected degrees of freedom applying stochastic state space algorithm. Eigen structure of the identified state matrix is then used for updating the model.