Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method.

Hamed Ebrahimian, Rodrigo Astroza, Joel P. Conte*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

105 Scopus citations


This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques are used jointly with the extended Kalman filter (EKF) to estimate time-invariant parameters associated to the nonlinear material constitutive models used in the FE model of the structural system of interest. The EKF as a parameter estimation tool requires the computation of structural FE response sensitivities (total partial derivatives) with respect to the material parameters to be estimated. Employing the direct differentiation method, which is a well-established procedure for FE response sensitivity analysis, facilitates the application of the EKF in the parameter estimation problem. To verify the proposed nonlinear FE model updating framework, two proof-of-concept examples are presented. For each example, the FE-simulated response of a realistic prototype structure to a set of earthquake ground motions of varying intensity is polluted with artificial measurement noise and used as structural response measurement to estimate the assumed unknown material parameters using the proposed nonlinear FE model updating framework. The first example consists of a cantilever steel bridge column with three unknown material parameters, while a three-story three-bay moment resisting steel frame with six unknown material parameters is used as second example. Both examples demonstrate the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise.

Original languageEnglish
Pages (from-to)1495-1522
Number of pages28
JournalEarthquake Engineering and Structural Dynamics
Issue number10
StatePublished - Aug 2015

Bibliographical note

Publisher Copyright:
Copyright © 2015 John Wiley & Sons, Ltd.


  • Kalman filter
  • direct differentiation method
  • finite element model updating
  • finite element response sensitivity
  • nonlinear finite element
  • parameter estimation
  • structural health monitoring


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