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

TL;DR

This paper introduces a novel Bayesian updating method using a Variational Auto-encoder's latent space to accurately quantify uncertainties from limited or single observations, especially for nonlinear seismic responses.

Contribution

The study develops a nonparametric likelihood evaluation approach in latent space, enhancing Bayesian model updating under data scarcity for nonlinear structural responses.

Findings

Accurately updates parameters with limited data

Quantifies uncertainties effectively in sparse observation scenarios

Decreases uncertainty with increased nonlinear information

Abstract

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.