Hierarchical Bayesian Model Updating Using Modal Data Based on Dynamic Condensation

PurposeThere is inherent variability of the structural parameters due to various changing environmental conditions, such as ambient temperature, wind speed, traffic load, etc. in an updating procedure. This concept is considered in this paper, where a Finite Element (FE) model updating methodology in a Hierarchical Bayesian framework using the modal data is presented. The modal data consists of multiple sets of Most Probable Values (MPVs) and covariance matrices of the modal parameters obtained at different instances.MethodsThe dynamic condensation technique is utilized to avoid direct matching between the experimental and analytical modes while solving the Eigen equation. The system eigenvalues and partial system mode shapes corresponding to the measured Degrees of Freedom (DOFs) are incorporated into the reduced-order Eigen equation to establish the relation between the modal data and the structural parameters. The Metropolis-within-Gibbs (MWG) sampler is proposed to sample from the posterior PDF. Another solution methodology is also presented to obtain the Maximum a Posteriori (MAP) estimate of the uncertain parameters.ResultsTwo numerical examples are presented to demonstrate the effectiveness of the proposed approach. The effectiveness of the proposed approach is also validated using an experimental example based on a laboratory structure. Both the MWG sampler and the estimation of MAP using the optimization method are utilized while updating the two structures and almost similar results are obtained from both methods.ConclusionAlthough similar results were obtained using both the methods, the simplified approach for MAP estimation is found to be more computationally efficient than the MWG sampler. Besides, it has been observed that the updating performance has been much better in case of the second numerical example as compared with the first numerical example and the laboratory example. This is due to the higher modeling error in case of the first numerical example and significant modeling and measurement errors associated with the updating exercise of the experimental example.