Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

Mingming Song; Rodrigo Astroza; Hamed Ebrahimian; Babak Moaveni; Costas Papadimitriou

doi:10.1007/978-3-030-47638-0_31

Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

Mingming Song^*, Rodrigo Astroza, Hamed Ebrahimian, Babak Moaveni, Costas Papadimitriou

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper studies the performance of recursive and batch Bayesian methods for nonlinear model updating. Unscented Kalman filter (UKF) is selected to represent the recursive Bayesian method, and two UKF approaches are investigated and compared, i.e., non-adaptive UKF and adaptive UKF. The proposed new adaptive filter, forgetting factor adaptive UKF, estimates the model parameters and measurement noise covariance in an online manner. The forgetting factor adaptive UKF is based on the principle of matching the covariance of residuals to its theoretical values by updating the measurement noise covariance. The performance of non-adaptive UKF, adaptive UKF and batch Bayesian method are investigated when applied to a numerical nonlinear 3-story 3-bay steel frame structure for parameter estimation of material properties. Different types of modeling errors are considered in the 21 updating models to study the effects of modeling errors on model updating. It is found that adaptive UKF approach provides the most accurate parameter estimations, while batch Bayesian approach gives the smallest errors on response predictions.

Original language	English
Title of host publication	Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
Editors	Zhu Mao
Publisher	Springer
Pages	279-286
Number of pages	8
ISBN (Print)	9783030487782
DOIs	https://doi.org/10.1007/978-3-030-47638-0_31
State	Published - 2020
Event	38th IMAC, A Conference and Exposition on Structural Dynamics, 2020 - Houston, United States Duration: 10 Feb 2020 → 13 Feb 2020

Publication series

Name	Conference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)	2191-5644
ISSN (Electronic)	2191-5652

Conference

Conference	38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
Country/Territory	United States
City	Houston
Period	10/02/20 → 13/02/20

Bibliographical note

Funding Information:
The financial support of this study by the National Science Foundation Grants 1254338 and 1903972 is acknowledged. Rodrigo Astroza acknowledges the financial support from the Chilean National Commission for Scientific and Technological Research (CONICYT), FONDECYT project No. 11160009.

Publisher Copyright:
© 2020, The Society for Experimental Mechanics, Inc.

Keywords

Adaptive UKF
Bayesian model updating
Measurement noise covariance
Modeling errors
Unscented Kalman filter

Access to Document

10.1007/978-3-030-47638-0_31

Cite this

Song, M., Astroza, R., Ebrahimian, H., Moaveni, B., & Papadimitriou, C. (2020). Nonlinear Model Updating Using Recursive and Batch Bayesian Methods. In Z. Mao (Ed.), Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020 (pp. 279-286). (Conference Proceedings of the Society for Experimental Mechanics Series). Springer. https://doi.org/10.1007/978-3-030-47638-0_31

Song, Mingming ; Astroza, Rodrigo ; Ebrahimian, Hamed et al. / Nonlinear Model Updating Using Recursive and Batch Bayesian Methods. Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020. editor / Zhu Mao. Springer, 2020. pp. 279-286 (Conference Proceedings of the Society for Experimental Mechanics Series).

@inproceedings{fd0b0b1744824f188200a762554feae3,

title = "Nonlinear Model Updating Using Recursive and Batch Bayesian Methods",

abstract = "This paper studies the performance of recursive and batch Bayesian methods for nonlinear model updating. Unscented Kalman filter (UKF) is selected to represent the recursive Bayesian method, and two UKF approaches are investigated and compared, i.e., non-adaptive UKF and adaptive UKF. The proposed new adaptive filter, forgetting factor adaptive UKF, estimates the model parameters and measurement noise covariance in an online manner. The forgetting factor adaptive UKF is based on the principle of matching the covariance of residuals to its theoretical values by updating the measurement noise covariance. The performance of non-adaptive UKF, adaptive UKF and batch Bayesian method are investigated when applied to a numerical nonlinear 3-story 3-bay steel frame structure for parameter estimation of material properties. Different types of modeling errors are considered in the 21 updating models to study the effects of modeling errors on model updating. It is found that adaptive UKF approach provides the most accurate parameter estimations, while batch Bayesian approach gives the smallest errors on response predictions.",

keywords = "Adaptive UKF, Bayesian model updating, Measurement noise covariance, Modeling errors, Unscented Kalman filter",

author = "Mingming Song and Rodrigo Astroza and Hamed Ebrahimian and Babak Moaveni and Costas Papadimitriou",

note = "Funding Information: The financial support of this study by the National Science Foundation Grants 1254338 and 1903972 is acknowledged. Rodrigo Astroza acknowledges the financial support from the Chilean National Commission for Scientific and Technological Research (CONICYT), FONDECYT project No. 11160009. Publisher Copyright: {\textcopyright} 2020, The Society for Experimental Mechanics, Inc.; 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020 ; Conference date: 10-02-2020 Through 13-02-2020",

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doi = "10.1007/978-3-030-47638-0_31",

language = "English",

isbn = "9783030487782",

series = "Conference Proceedings of the Society for Experimental Mechanics Series",

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Song, M, Astroza, R, Ebrahimian, H, Moaveni, B & Papadimitriou, C 2020, Nonlinear Model Updating Using Recursive and Batch Bayesian Methods. in Z Mao (ed.), Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020. Conference Proceedings of the Society for Experimental Mechanics Series, Springer, pp. 279-286, 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, Houston, United States, 10/02/20. https://doi.org/10.1007/978-3-030-47638-0_31

Nonlinear Model Updating Using Recursive and Batch Bayesian Methods. / Song, Mingming; Astroza, Rodrigo; Ebrahimian, Hamed et al.
Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020. ed. / Zhu Mao. Springer, 2020. p. 279-286 (Conference Proceedings of the Society for Experimental Mechanics Series).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

AU - Song, Mingming

AU - Astroza, Rodrigo

AU - Ebrahimian, Hamed

AU - Moaveni, Babak

AU - Papadimitriou, Costas

N1 - Funding Information: The financial support of this study by the National Science Foundation Grants 1254338 and 1903972 is acknowledged. Rodrigo Astroza acknowledges the financial support from the Chilean National Commission for Scientific and Technological Research (CONICYT), FONDECYT project No. 11160009. Publisher Copyright: © 2020, The Society for Experimental Mechanics, Inc.

PY - 2020

Y1 - 2020

N2 - This paper studies the performance of recursive and batch Bayesian methods for nonlinear model updating. Unscented Kalman filter (UKF) is selected to represent the recursive Bayesian method, and two UKF approaches are investigated and compared, i.e., non-adaptive UKF and adaptive UKF. The proposed new adaptive filter, forgetting factor adaptive UKF, estimates the model parameters and measurement noise covariance in an online manner. The forgetting factor adaptive UKF is based on the principle of matching the covariance of residuals to its theoretical values by updating the measurement noise covariance. The performance of non-adaptive UKF, adaptive UKF and batch Bayesian method are investigated when applied to a numerical nonlinear 3-story 3-bay steel frame structure for parameter estimation of material properties. Different types of modeling errors are considered in the 21 updating models to study the effects of modeling errors on model updating. It is found that adaptive UKF approach provides the most accurate parameter estimations, while batch Bayesian approach gives the smallest errors on response predictions.

AB - This paper studies the performance of recursive and batch Bayesian methods for nonlinear model updating. Unscented Kalman filter (UKF) is selected to represent the recursive Bayesian method, and two UKF approaches are investigated and compared, i.e., non-adaptive UKF and adaptive UKF. The proposed new adaptive filter, forgetting factor adaptive UKF, estimates the model parameters and measurement noise covariance in an online manner. The forgetting factor adaptive UKF is based on the principle of matching the covariance of residuals to its theoretical values by updating the measurement noise covariance. The performance of non-adaptive UKF, adaptive UKF and batch Bayesian method are investigated when applied to a numerical nonlinear 3-story 3-bay steel frame structure for parameter estimation of material properties. Different types of modeling errors are considered in the 21 updating models to study the effects of modeling errors on model updating. It is found that adaptive UKF approach provides the most accurate parameter estimations, while batch Bayesian approach gives the smallest errors on response predictions.

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T3 - Conference Proceedings of the Society for Experimental Mechanics Series

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BT - Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020

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Song M, Astroza R, Ebrahimian H, Moaveni B, Papadimitriou C. Nonlinear Model Updating Using Recursive and Batch Bayesian Methods. In Mao Z, editor, Model Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020. Springer. 2020. p. 279-286. (Conference Proceedings of the Society for Experimental Mechanics Series). doi: 10.1007/978-3-030-47638-0_31

Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

Abstract

Publication series

Conference

Bibliographical note

Keywords

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