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Latent variable model and its application to Bayesian operational modal analysis
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Wei ZHU1, Bin-bin LI1, 2, 3, Yan-long XIE4, Xiao-yu CHEN1
Journal of Vibration Engineering | 2024, 37(9) : 1476 - 1484
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Journal of Vibration Engineering | 2024, 37(9): 1476-1484
Latent variable model and its application to Bayesian operational modal analysis
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Wei ZHU1, Bin-bin LI1, 2, 3, Yan-long XIE4, Xiao-yu CHEN1
Affiliations
  • 1ZJU-UIUC Institute, Zhejiang University, Haining 314400, China
  • 2Center for Balance Architecture, Zhejiang University, Hangzhou 310058, China
  • 3The Architectural Design and Research Institute of Zhejiang University Co., Ltd., Hangzhou 310058, China
  • 4College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
Published: 2024-09-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.09.004
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As a method for operational modal analysis （OMA），the Bayesian FFT algorithm has garnerd significant attention for its high accuracy and efficiency，as well as its ability of uncertainty quantification. However，different cases of OMA （e.g. well-separated mode，closely-spaced modes，and multi-setup OMA） require different optimization strategy，and it is tedious in computer coding. A new framework is proposed in this paper to unify the above-mentioned cases of OMA，and the implement is simplified as a consequence. Regarding the structural modal response as a latent variable，the single-setup and multi-setup Bayesian OMA is cast as latent variable models，which have been deeply investigated in statistics. An expectation-maximization （EM） algorithm is developed for both single-setup and multi-setup OMA. The introduction of latent variables decouples the parameter optimization in EM，and Louis identity is employed to calculate the Hessian matrix. Two field tests are applied to verify the performance of the proposed approach，with a comparison to the existing algorithm. Consistent results are obtained，and a great advantage in efficiency is observed in the case of closely-spaced modes. The proposed latent variable model unifies the cases of Bayesian OMA，with the advantage of simplified implementation and fast computation. It also paves a way for a further improvement of Bayesian OMA，e.g. with the approach of variational Bayes or Gibbs sampling.

operational modal analysis  /  parameter identification  /  latent variable model  /  expectation maximization  /  uncertainty
Wei ZHU, Bin-bin LI, Yan-long XIE, Xiao-yu CHEN. Latent variable model and its application to Bayesian operational modal analysis[J]. Journal of Vibration Engineering, 2024 , 37 (9) : 1476 -1484 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.09.004
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Article Info
doi: 10.16385/j.cnki.issn.1004-4523.2024.09.004
  • Receive Date：2022-10-09
  • Online Date：2026-02-12
  • Published：2024-09-28
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  • Received：2022-10-09
  • Revised：2022-12-09
Funding
Affiliations
    1ZJU-UIUC Institute, Zhejiang University, Haining 314400, China
    2Center for Balance Architecture, Zhejiang University, Hangzhou 310058, China
    3The Architectural Design and Research Institute of Zhejiang University Co., Ltd., Hangzhou 310058, China
    4College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
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