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.

翻译：本研究提出了一种在贝叶斯模型更新中量化不确定性的新方法，该方法在稀疏观测或单观测场景下尤为有效。传统的基于欧氏距离和巴氏距离等指标的度量方法，在观测数据充足时具有潜力，但在数据不足（尤其是后屈服等非线性响应行为）时，其有效性受到限制。我们的方法通过利用变分自编码器（VAE）的潜空间——一种支持非参数似然评估的生成式模型——来解决这一挑战。该方法在基于结构非线性地震响应更新模型参数时具有重要价值，而此类场景中数据稀缺是常见难题。数值实验证实，所提方法能够仅凭有限观测数据准确更新参数并量化不确定性。此外，这些实验还表明，随着非线性行为信息的增加，估计结果的不确定性呈下降趋势。本研究为高度不确定性场景下的量化分析提供了稳健工具，从而拓展了贝叶斯更新方法在数据受限环境中的应用范围。