Moreover, it is built upon rigorous probabilistic framework that can directly incorporate various sources of uncertainties in the model parameters to be updated.
In recent years, the Bayesian inference has seen increasing usage in a variety of engineering problems.
To facilitate the entire model updating process with automation, the algorithm is implemented under Finite element analyses are widely used to predict the structural dynamic responses.
The result from a finite element analysis, however, oftentimes is different from the experimental measurement from an actual structure.
Then, by introducing measured response data, the assumed prior PDF is updated to the so-called posterior PDF that will then be analyzed to yield the optimal model parameters.
This actually avoids the abovementioned drawback of matrix inversion, since the Bayesian model updating is facilitated through finite element forward analyses under certain model parameter sample.
To alleviate the computational cost, Metropolis–Hastings Markov chain Monte Carlo (MH MCMC) is adopted to reduce the size of samples required for repeated finite element modal analyses.
Soize presented a nonparametric probabilistic approach based on random matrix theory to model the structural uncertainties and estimate the dispersion parameters . developed a perturbation scheme to analyze the statistical moments of updated parameters from measured variability in structural modal responses .
It is worth noting that the Bayesian inference-type of methods has recently attracted significant attention due to some intrinsic advantages [14–16].
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Finite element model updating has emerged in the 1990s as a subject of immense importance to the design, construction and maintenance of mechanical systems and civil engineering structures.
This discrepancy is due to a number of factors, ranging from the noise in measurement, normal variation of the structure, to the error in the finite element model itself.