Latent Space-Based Likelihood Estimation Using a Single Observation for Bayesian Updating of a Nonlinear Hysteretic Model
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910644931919872 |
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| author | Lee, Sangwon Yaoyama, Taro Matsumoto, Yuma Hida, Takenori Itoi, Tatsuya |
| author_facet | Lee, Sangwon Yaoyama, Taro Matsumoto, Yuma Hida, Takenori Itoi, Tatsuya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Latent Space-Based Likelihood Estimation Using a Single Observation for Bayesian Updating of a Nonlinear Hysteretic Model Lee, Sangwon Yaoyama, Taro Matsumoto, Yuma Hida, Takenori Itoi, Tatsuya Applications 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. |
| title | Latent Space-Based Likelihood Estimation Using a Single Observation for Bayesian Updating of a Nonlinear Hysteretic Model |
| topic | Applications |
| url | https://arxiv.org/abs/2404.03871 |