Bayesian two-stage structural identification with equivalent formulation and EM algorithm
For structural model identification using a Bayesian two-stage approach, modal properties (e.g., natural frequencies) are first extracted from measured data in Stage I and then used for determining structural properties (e.g., stiffness) in Stage II. With sufficient data that allow the problem to be...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2024
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| Online Access: | https://hdl.handle.net/10356/173017 |
| _version_ | 1811695726116208640 |
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| author | Zhu, Jia-Xin Au, Siu-Kui |
| author2 | School of Civil and Environmental Engineering |
| author_facet | School of Civil and Environmental Engineering Zhu, Jia-Xin Au, Siu-Kui |
| author_sort | Zhu, Jia-Xin |
| collection | NTU |
| description | For structural model identification using a Bayesian two-stage approach, modal properties (e.g., natural frequencies) are first extracted from measured data in Stage I and then used for determining structural properties (e.g., stiffness) in Stage II. With sufficient data that allow the problem to be globally identifiable, the computational problem often reduces to optimizing a ‘measure-of-fit’ function to yield the ‘most probable value’ (MPV) that informs the ‘best estimate’, and determining the Hessian of the function to yield the posterior covariance matrix that informs the remaining uncertainty. Recent developments deal with the presence of model error, and the increasing complexity calls for proper computational strategy. In this spirit, assuming Gaussian model error, this work develops a hypothetical yet mathematically equivalent formulation for the two-stage problem, which facilitates development of effective algorithms for MPV using Expectation-Maximization techniques. By treating hypothetically the MPV of modal properties in Stage I as ‘data’ and model error as latent variables, the Q-function in the M−step can be expressed as a sum of two terms that can be optimized with respect to structural parameters and model error parameters. The optimization of structural parameters reduces to that of a Stage II problem without model error, for which existing algorithms can be applied. Analytical expressions are also derived for computing the posterior covariance matrix. The proposed methodology is investigated with synthetic data for model errors associated with sensor misalignment and model simplification, lab data for the effect of number of modes and measured degrees of freedom (DoFs), and field data for reality tests. |
| first_indexed | 2024-10-01T07:28:03Z |
| format | Journal Article |
| id | ntu-10356/173017 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:28:03Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1730172024-01-12T15:34:18Z Bayesian two-stage structural identification with equivalent formulation and EM algorithm Zhu, Jia-Xin Au, Siu-Kui School of Civil and Environmental Engineering Engineering::Civil engineering Bayesian Method Expectation–Maximization Technique Model Error System Identification Two-Stage Approach For structural model identification using a Bayesian two-stage approach, modal properties (e.g., natural frequencies) are first extracted from measured data in Stage I and then used for determining structural properties (e.g., stiffness) in Stage II. With sufficient data that allow the problem to be globally identifiable, the computational problem often reduces to optimizing a ‘measure-of-fit’ function to yield the ‘most probable value’ (MPV) that informs the ‘best estimate’, and determining the Hessian of the function to yield the posterior covariance matrix that informs the remaining uncertainty. Recent developments deal with the presence of model error, and the increasing complexity calls for proper computational strategy. In this spirit, assuming Gaussian model error, this work develops a hypothetical yet mathematically equivalent formulation for the two-stage problem, which facilitates development of effective algorithms for MPV using Expectation-Maximization techniques. By treating hypothetically the MPV of modal properties in Stage I as ‘data’ and model error as latent variables, the Q-function in the M−step can be expressed as a sum of two terms that can be optimized with respect to structural parameters and model error parameters. The optimization of structural parameters reduces to that of a Stage II problem without model error, for which existing algorithms can be applied. Analytical expressions are also derived for computing the posterior covariance matrix. The proposed methodology is investigated with synthetic data for model errors associated with sensor misalignment and model simplification, lab data for the effect of number of modes and measured degrees of freedom (DoFs), and field data for reality tests. Ministry of Education (MOE) Nanyang Technological University Submitted/Accepted version The research presented in this work is supported by Academic Research Fund Tier 1 (RG68/22) from the Ministry of Education, Singapore. 2024-01-10T01:39:33Z 2024-01-10T01:39:33Z 2024 Journal Article Zhu, J. & Au, S. (2024). Bayesian two-stage structural identification with equivalent formulation and EM algorithm. Mechanical Systems and Signal Processing, 209, 111025-. https://dx.doi.org/10.1016/j.ymssp.2023.111025 0888-3270 https://hdl.handle.net/10356/173017 10.1016/j.ymssp.2023.111025 209 111025 en RG68/22 Mechanical Systems and Signal Processing © 2023 Elsevier Ltd. All rights reserved. This article may be downloaded for personal use only. Any other use requires prior permission of the copyright holder. The Version of Record is available online at http://doi.org/10.1016/j.ymssp.2023.111025. application/pdf |
| spellingShingle | Engineering::Civil engineering Bayesian Method Expectation–Maximization Technique Model Error System Identification Two-Stage Approach Zhu, Jia-Xin Au, Siu-Kui Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title | Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title_full | Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title_fullStr | Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title_full_unstemmed | Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title_short | Bayesian two-stage structural identification with equivalent formulation and EM algorithm |
| title_sort | bayesian two stage structural identification with equivalent formulation and em algorithm |
| topic | Engineering::Civil engineering Bayesian Method Expectation–Maximization Technique Model Error System Identification Two-Stage Approach |
| url | https://hdl.handle.net/10356/173017 |
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