Model reduction technique for Bayesian model updating of structural parameters using simulated modal data

An attempt has been made to study the effectiveness of model reduction technique for Bayesian approach of model updating with incomplete modal data sets. The inverse problems in system identification require the solution of a family of plausible values of model parameters based on available data. Specifically, an iterative model reduction algorithm is proposed based on a non-linear optimization method to solve the transformation parameter such that no prior choices of response parameters are required. The modal ordinates synthesized at the unmeasured degrees of freedom (DOF) from the reduced order model are used for a better estimate of likelihood functions. The reduced-order model is subsequently implemented for updating of unknown structural parameters. The present study also synthesizes the mode shape ordinates at unmeasured DOF from the reduced order model. The efficiency of the proposed model reduction algorithm is further studied by adding noises of varying percentages to the measured modal data sets. The proposed methodology is illustrated numerically to update the stiffness parameters of an eight-story shear building model considering simulated datasets contaminated by Gaussian error as evidence. The capability of the proposed model reduction algorithm coupled with Markov Chain Monte Carlo (MCMC) algorithm is compared with the case where only MCMC algorithm is used to investigate their effectiveness in updating model parameters. The numerical study focuses on the effect of reduced number of measurements for various measurement configurations in estimating the variation of errors in determining the modal data. Subsequently, its effects in reducing the uncertainty of model updating parameters are investigated. The effectiveness of the proposed model reduction algorithm is tested for number of modes equal to the number of master DOFs and gradually decrease of mode numbers from the number of master DOFs.