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：本研究提出了一种量化贝叶斯模型更新中不确定性的新方法，该方法在稀疏或单一观测条件下依然有效。传统的基于欧几里得距离与巴氏距离的不确定性量化指标在观测数据充足时具有潜力，但在数据不足的情况下（特别是对于像屈服后行为这类非线性响应）其验证效果有限。我们的方法通过利用变分自编码器（VAE）这一生成模型的潜空间来解决这一挑战，该模型支持非参数似然评估。该方法对于基于结构非线性地震响应更新模型参数具有重要价值，而此类场景中数据稀缺是常见难题。数值实验证实了所提方法能够利用有限观测数据准确更新参数并量化不确定性。此外，这些数值实验揭示了关于非线性行为的信息增加会降低估计不确定性的趋势。本研究为具有显著不确定性的场景提供了稳健的不确定性量化工具，从而拓展了贝叶斯更新方法在数据受限环境中的适用性。