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 proceedingConference contributionpeer-review


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 languageEnglish
Title of host publicationModel Validation and Uncertainty Quantification, Volume 3 - Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
EditorsZhu Mao
Number of pages8
ISBN (Print)9783030487782
StatePublished - 2020
Event38th IMAC, A Conference and Exposition on Structural Dynamics, 2020 - Houston, United States
Duration: 10 Feb 202013 Feb 2020

Publication series

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


Conference38th IMAC, A Conference and Exposition on Structural Dynamics, 2020
Country/TerritoryUnited States

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.


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


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