Bayesian finite element model updating with a variational autoencoder and polynomial chaos expansion

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The quantification of uncertainty in civil structures poses a significant challenge in contemporary research due to the substantial computational demands involved. This study introduces an innovative approach for updating the finite element model (FEM) and quantifying uncertainties in civil structures through the synergistic use of variational autoencoder (VAE) and polynomial chaos expansion (PCE). Within this framework, the unknown parameters inherent to the structural FEM are represented as latent variables and can be effectively inferred through the VAE. These latent variables are modeled using a multivariate Gaussian distribution. In the proposed methodology, the PCE serves to approximate the log-likelihood function associated with the latent variables, facilitating the derivation of the analytic expression for the variational lower bound. By maximizing this variational lower bound, both the mean and standard deviation can be readily determined. To assess the accuracy and computational efficiency of the proposed technique, numerical analyses are performed on a cantilever beam and a steel pedestrian bridge. Furthermore, the effectiveness of the proposed approach is validated through its application to damage identification within a benchmark model. Significantly, the results indicate that the proposed method offers superior computational efficiency compared to the conventional VAE approach. Notably, the findings reveal that employing a high-order PCE is unnecessary; rather, a low-order PCE suffices for precise parameter identification. Consequently, the proposed methodology necessitates only a limited dataset for training to ascertain the PCE coefficients, thereby enhancing its practical applicability and efficiency.