System identification of linear vibrating structures

Abstract

Methods of dynamic modelling and analysis of structures, for example the finite element method, are well developed. However, it is generally agreed that accurate modelling of complex structures is difficult and for critical applications it is necessary to validate or update the theoretical models using data measured from actual structures. The techniques of identifying the parameters of linear dynamic models using Vibration test data have attracted considerable interest recently. However, no method has received a general acceptance due to a number of difficulties. These difficulties are mainly due to (i) Incomplete number of Vibration modes that can be excited and measured, (ii) Incomplete number of coordinates that can be measured, (iii) Inaccuracy in the experimental data (iv) Inaccuracy in the model structure. This thesis reports on a new approach to update the parameters of a finite element model as well as a lumped parameter model with a diagonal mass matrix. The structure and its theoretical model are equally perturbed by adding mass or stiffness and the incomplete number of eigen-data is measured. The parameters are then identified by an iterative updating of the initial estimates, by sensitivity analysis, using eigenvalues or both eigenvalues and eigenvectors of the structure before and after perturbation. It is shown that with a suitable choice of the perturbing coordinates exact parameters can be identified if the data and the model structure are exact. The theoretical basis of the technique is presented. To cope with measurement errors and possible inaccuracies in the model structure, a well known Bayesian approach is used to minimize the least squares difference between the updated and the initial parameters. The eigen-data of the structure with added mass or stiffness is also determined using the frequency response data of the unmodified structure by a structural modification technique. Thus, mass or stiffness do not have to be added physically. The mass-stiffness addition technique is demonstrated by simulation examples and Laboratory experiments on beams and an H-frame.