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

This study presents a novel approach to quantify uncertainties in Bayesian model updating, which is effective for sparse or single observations. Conventional uncertainty quantification methods are limited in situations with insufficient data, particularly for nonlinear responses like postyield behavior. Our method addresses this challenge using the latent space of a variational autoencoder (VAE), a generative model that enables nonparametric likelihood evaluation. This approach is valuable in updating model parameters based on nonlinear seismic responses of a structure, wherein data scarcity is a common challenge. Our numerical experiments confirmed the ability of the proposed method to accurately update parameters and quantify uncertainties using a single observation. Additionally, the numerical experiments revealed that increased information about nonlinear behavior tends 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 approximate Bayesian updating methods in data-constrained environments.