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

Summary 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 con...

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Veröffentlicht in:	Earthquake engineering & structural dynamics Jg. 44; H. 10; S. 1495 - 1522
Hauptverfasser:	Ebrahimian, Hamed, Astroza, Rodrigo, Conte, Joel P.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Bognor Regis Blackwell Publishing Ltd 01.08.2015 Wiley Subscription Services, Inc
Schlagworte:	direct differentiation method Estimates Finite element method finite element model updating finite element response sensitivity Kalman filter Mathematical models Model updating Noise measurement nonlinear finite element Nonlinearity Parameter estimation Seismic phenomena structural health monitoring
ISSN:	0098-8847, 1096-9845
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Abstract	Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.
AbstractList	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. 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. Copyright © 2015 John Wiley & Sons, Ltd. Summary 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. Copyright © 2015 John Wiley & Sons, Ltd. Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.
Author	Conte, Joel P. Astroza, Rodrigo Ebrahimian, Hamed
Author_xml	– sequence: 1 givenname: Hamed surname: Ebrahimian fullname: Ebrahimian, Hamed organization: Department of Structural Engineering, University of California, CA,, San Diego, USA – sequence: 2 givenname: Rodrigo surname: Astroza fullname: Astroza, Rodrigo organization: Department of Structural Engineering, University of California, San Diego, CA,, USA – sequence: 3 givenname: Joel P. surname: Conte fullname: Conte, Joel P. email: Correspondence to: Joel P. Conte, Department of Structural Engineering, University of California, San Diego, CA, USA., jpconte@ucsd.edu organization: Department of Structural Engineering, University of California, CA,, San Diego, USA
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Snippet	Summary This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis... This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques... Summary This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis...
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SubjectTerms	direct differentiation method Estimates Finite element method finite element model updating finite element response sensitivity Kalman filter Mathematical models Model updating Noise measurement nonlinear finite element Nonlinearity Parameter estimation Seismic phenomena structural health monitoring
Title	Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method
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