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Finite element (FE) model updating is often used to associate FE models with corresponding existing structures for
the condition assessment. FE model updating is an inverse problem and prone to be ill-posed and ill-conditioning when
there are many errors and uncertainties in both an FE model and its corresponding measurements. In this case, it is
important to quantify these uncertainties properly. Bayesian FE model updating is one of the well-known methods to
quantify parameter uncertainty by updating our prior belief on the parameters with the available measurements. In
Bayesian inference, likelihood plays a central role in summarizing the overall residuals between model predictions and
corresponding measurements. Therefore, likelihood should be carefully chosen to reflect the characteristics of the
residuals. It is generally known that very little or no information is available regarding the statistical characteristics of
the residuals. In most cases, the likelihood is assumed to be the independent identically distributed Gaussian distribution
with the zero mean and constant variance. However, this assumption may cause biased and over/underestimated
estimates of parameters, so that the uncertainty quantification and prediction are questionable. To alleviate the potential
misuse of the inadequate likelihood, this study introduced approximate Bayesian computation (i.e., likelihood-free
Bayesian inference), which relaxes the need for an explicit likelihood by analyzing the behavior similarities between
model predictions and measurements. We performed FE model updating based on likelihood-free Markov chain Monte
Carlo (MCMC) without using the likelihood. Based on the result of the numerical study, we observed that the
likelihood-free Bayesian computation can quantify the updating parameters correctly and its predictive capability for the
measurements, not used in calibrated, is also secured.
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