  A novel framework for Bayesian structural model updating is presented in this
study. The proposed method utilizes the surrogate unimodal encoders of a
multimodal variational autoencoder (VAE). The method facilitates an
approximation of the likelihood when dealing with a small number of
observations. It is particularly suitable for high-dimensional correlated
simultaneous observations applicable to various dynamic analysis models. The
proposed approach was benchmarked using a numerical model of a single-story
frame building with acceleration and dynamic strain measurements. Additionally,
an example involving a Bayesian update of nonlinear model parameters for a
three-degree-of-freedom lumped mass model demonstrates computational efficiency
when compared to using the original VAE, while maintaining adequate accuracy
for practical applications.
