A two-stage approach to stochastic finite element model updating using FRF data

Abstract

Stochastic model updating techniques are used to update an FE model of a structure so that the updated model can predict the mean as well as the variability of the structure's dynamic characteristics. Most of the current approaches and studies employ modal data to update the uncertain parameters related to the mass and stiffness matrices. Model updating using FRFs has an advantage over modal data that it avoids modal analysis errors and can be used to update the damping matrix. There is limited work on using FRFs for stochastic model updating and on identifying variability of the damping matrix. The existing methods simultaneously update the parameters related to the mass, stiffness, and damping matrices. These methods may encounter numerical challenges due to large differences in the order of magnitude of these matrices. In some situations, only the mass and stiffness matrices are to be updated to accurately predict the undamped dynamics of the structure and hence the damping identification is not necessary. In these situations, the existing methods cannot be used to update only the mass and stiffness matrices because the modelling and identification of the damping are necessary for updating with FRF-based methods. To address these limitations, this paper proposes a two-stage approach to stochastic model updating using normal FRFs. Normal FRFs represent the estimates of the FRFs, excluding the effect of the damping in the structures. Stage-I updates the mean and variability of the uncertain parameters related to the mass and stiffness matrices using normal FRFs. Stage-II updates the mean and variability of the uncertain parameters related to the damping matrix using the difference between the complex and normal FRFs. Separating updating of the damping matrix from updating of the mass and stiffness matrices improves the conditioning of the sensitivity matrices and eliminates the numerical challenges associated with updating the matrices with different orders of magnitude. For the situations where the variability in the undamped dynamics only needs to be predicted, stage-I of the proposed method can be used. Numerical studies on a damped cantilever beam and an aeroplane model (DLR-AIRMOD structure) are presented to validate the method. Experimental validation of the proposed method is carried out using nominally identical samples of a damped acrylic beam. The performance of the method is also compared with an existing complex FRF based method to highlight the effectiveness of the proposed method.