Latent Space-Based Likelihood Estimation Using a Single Observation for Bayesian Updating of a Nonlinear Hysteretic Model

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.