Bayesian Approach of Model Updating of Structural Parameters with Simulated Modal Data

Abstract

The present study investigates the effectiveness of Bayesian approach of model updating of structure, using simulated modal data sets as evidence. The importance of the prediction of error implemented in the proposed Bayesian framework to assess its capability in sampling posterior values with improved accuracy has been highlighted. The natural frequencies and mode shapes of the structure are taken only as the evidence. The study highlighted the importance of the likelihood functions corresponding to the prediction of error between the experimental and predicted data. The study also implemented the likelihood functions corresponding to the prediction of error variances of natural frequencies only in sampling posterior values with higher accuracy. The efficacy of the proposed approach in dealing with the issue of incomplete data sets, that makes the problem typically ill-conditioned, is duly addressed. The present work also implemented model reduction technique to synthesise the mode shape ordinates at unmeasured degrees of freedom (DOF) from the reduced-order model. In addition, the efficiency of the proposed model reduction algorithm is explored by adding noises of varying percentages to the measured mode shape values. The proposed methodology is illustrated numerically to update the stiffness parameters of an eight-storey shear building model, considering simulated datasets contaminated by Gaussian error as evidence. Results with both incomplete and complete data sets using the proposed Markov Chain Monte Carlo approach are studied. The accuracy on the synthesis of mode shapes from unmeasured DOF using model reduction algorithm is also studied.