Structural modal identification and MCMC-based model updating by a Bayesian approach

Finite element analysis is one of the important methods to study the structural performance. Due to the simplification, discretization and error of structural parameters, numerical model errors always exist. Besides, structural characteristics may also change because of material aging, structural damage, etc., making the initial finite element model cannot simulate the operational response of the structure accurately. Based on Bayesian methods, the initial model can be updated to obtain a more accurate numerical model. This paper presents the work on the field test, modal identification and model updating of a Chinese reinforced concrete pagoda. Based on the ambient vibration test, the acceleration response of the structure under operational environment was collected. The first six translational modes of the structure were identified by the enhanced frequency domain decomposition method. The initial finite element model of the pagoda was established, and the elastic modulus of columns, beams and slabs were selected as model parameters to be updated. Assuming the error between the measured mode and the calculated one follows a Gaussian distribution, the posterior probability density function (PDF) of the parameter to be updated is obtained and the uncertainty is quantitatively evaluated based on the Bayesian statistical theory and the Metropolis-Hastings algorithm, and then the optimal values of model parameters can be obtained. The results show that the difference between the calculated frequency of the finite element model and the measured one is reduced, and the modal correlation of the mode shape is improved. The updated numerical model can be used to evaluate the safety of the structure as a benchmark model for structural health monitoring (SHM).