An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes
The Bayesian FFT method has gained attention in operational modal analysis of civil engineering structures. Not only the most probable value (MPV) of modal parameters can be computed efficiently, but also the identification uncertainty can be rigorously quantified in terms of posterior covariance ma...
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sg-ntu-dr.10356-1499832021-05-19T07:28:18Z An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes Li, Binbin Au, Siu-Kui School of Civil and Environmental Engineering Engineering::Civil engineering Operational Modal Analysis Bayesian Inference The Bayesian FFT method has gained attention in operational modal analysis of civil engineering structures. Not only the most probable value (MPV) of modal parameters can be computed efficiently, but also the identification uncertainty can be rigorously quantified in terms of posterior covariance matrix. A recently developed fast algorithm for general multiple (possibly close) modes was found to work well in most cases, but convergence could be slow or even fail in challenging situations. The algorithm is also tedious to computer-code. Aiming at resolving these issues, an expectation-maximization (EM) algorithm is developed by viewing the modal response as a latent variable. The parameter-expansion EM and the parabolic-extrapolation EM are further adopted, allowing mode shape norm constraints to be incorporated and accelerating convergence, respectively. A robust implementation is provided based on the QR and Cholesky decompositions, so that the computation can be done efficiently and reliably. Empirical studies verify the performance of the proposed EM algorithm. It offers a more efficient and robust (in terms of convergence) alternative that can be especially useful when the existing algorithm has difficulty to converge. In addition, it opens a way to compute the MPV in the Bayesian FFT method for other unexplored cases, e.g., multi-mode multi-setup problem. Accepted version The financial support from the UK Engineering and Physical Sciences Research Council, United Kingdom (EP/N017897/1) is gratefully acknowledged. The start-up fund from Zhejiang University (130000- 171207704/018) is also acknowledged. 2021-05-19T07:28:18Z 2021-05-19T07:28:18Z 2019 Journal Article Li, B. & Au, S. (2019). An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes. Mechanical Systems and Signal Processing, 132, 490-511. https://dx.doi.org/10.1016/j.ymssp.2019.06.036 0888-3270 0000-0003-4479-3359 0000-0002-0228-1796 https://hdl.handle.net/10356/149983 10.1016/j.ymssp.2019.06.036 2-s2.0-85068864863 132 490 511 en Mechanical Systems and Signal Processing © 2019 Elsevier Ltd. All rights reserved. This paper was published in Mechanical Systems and Signal Processing and is made available with permission of Elsevier Ltd. application/pdf |
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Engineering::Civil engineering Operational Modal Analysis Bayesian Inference Li, Binbin Au, Siu-Kui An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
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The Bayesian FFT method has gained attention in operational modal analysis of civil engineering structures. Not only the most probable value (MPV) of modal parameters can be computed efficiently, but also the identification uncertainty can be rigorously quantified in terms of posterior covariance matrix. A recently developed fast algorithm for general multiple (possibly close) modes was found to work well in most cases, but convergence could be slow or even fail in challenging situations. The algorithm is also tedious to computer-code. Aiming at resolving these issues, an expectation-maximization (EM) algorithm is developed by viewing the modal response as a latent variable. The parameter-expansion EM and the parabolic-extrapolation EM are further adopted, allowing mode shape norm constraints to be incorporated and accelerating convergence, respectively. A robust implementation is provided based on the QR and Cholesky decompositions, so that the computation can be done efficiently and reliably. Empirical studies verify the performance of the proposed EM algorithm. It offers a more efficient and robust (in terms of convergence) alternative that can be especially useful when the existing algorithm has difficulty to converge. In addition, it opens a way to compute the MPV in the Bayesian FFT method for other unexplored cases, e.g., multi-mode multi-setup problem. |
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School of Civil and Environmental Engineering |
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School of Civil and Environmental Engineering Li, Binbin Au, Siu-Kui |
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Article |
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Li, Binbin Au, Siu-Kui |
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Li, Binbin |
title |
An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
title_short |
An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
title_full |
An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
title_fullStr |
An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
title_full_unstemmed |
An expectation-maximization algorithm for Bayesian operational modal analysis with multiple (possibly close) modes |
title_sort |
expectation-maximization algorithm for bayesian operational modal analysis with multiple (possibly close) modes |
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2021 |
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https://hdl.handle.net/10356/149983 |
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1701270538273423360 |