  This study presents a novel approach to quantifying uncertainties in Bayesian
model updating, which is effective in sparse or single observations.
Conventional uncertainty quantification metrics such as the Euclidean and
Bhattacharyya distance-based metrics are potential in scenarios with ample
observations. However, their validation is limited in situations with
insufficient data, particularly for nonlinear responses like post-yield
behavior. Our method addresses this challenge by using the latent space of a
Variational Auto-encoder (VAE), a generative model that enables nonparametric
likelihood evaluation. This approach is valuable in updating model parameters
based on nonlinear seismic responses of structure, wherein data scarcity is a
common challenge. Our numerical experiments confirm the ability of the proposed
method to accurately update parameters and quantify uncertainties using limited
observations. Additionally, these numerical experiments reveal a tendency for
increased information about nonlinear behavior to result in decreased
uncertainty in terms of estimations. This study provides a robust tool for
quantifying uncertainty in scenarios characterized by considerable uncertainty,
thereby expanding the applicability of Bayesian updating methods in
data-constrained environments.
