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

Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joseph Le

doi:10.1002/eqe.2532

Cited by 108 publications

(61 citation statements)

References 42 publications

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“…Figure 4 summarizes the algorithm to update the nonlinear FE model using the UKF. More information on the nonlinear FE model updating using the EKF and UKF can be found in [8] and [7], respectively. It is noted that in Figures 2, 3, and 4…”

Section: -P2mentioning

confidence: 99%

“…However, such models are not commonly used in state-of-the-art mechanics-based structural FE modeling because they cannot adequately simulate the actual nonlinear behavior of civil structures. Recently, the problem of updating mechanics-based nonlinear FE models of structures using input-output data recorded during damage-inducing events has been investigated [6][7][8]. The main benefit of using advanced FE models is that they are able to capture the damage mechanisms to be detected and identified in the structural system and therefore can provide accurate information about presence, location, type, and extent of damage in the structure.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Methods for Nonlinear System Identification of Civil Structures

Conte

Astroza

Ebrahimian

2015

MATEC Web of Conferences

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Abstract. This paper presents a new framework for the identification of mechanics-based nonlinear finite element (FE) models of civil structures using Bayesian methods. In this approach, recursive Bayesian estimation methods are utilized to update an advanced nonlinear FE model of the structure using the input-output dynamic data recorded during an earthquake event. Capable of capturing the complex damage mechanisms and failure modes of the structural system, the updated nonlinear FE model can be used to evaluate the state of health of the structure after a damage-inducing event. To update the unknown time-invariant parameters of the FE model, three alternative stochastic filtering methods are used: the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the iterated extended Kalman filter (IEKF). For those estimation methods that require the computation of structural FE response sensitivities with respect to the unknown modeling parameters (EKF and IEKF), the accurate and computationally efficient direct differentiation method (DDM) is used. A three-dimensional five-story two-by-one bay reinforced concrete (RC) frame is used to illustrate the performance of the framework and compare the performance of the different filters in terms of convergence, accuracy, and robustness. Excellent estimation results are obtained with the UKF, EKF, and IEKF. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the modeling parameters are observed when using these filters. The UKF slightly outperforms the EKF and IEKF.

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Section: -P2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian Methods for Nonlinear System Identification of Civil Structures

Conte

Astroza

Ebrahimian

2015

MATEC Web of Conferences

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“…Using nonlinear finite element (FE) model updating in time domain has emerged as one of the powerful system identification methods for structural systems 4,5,6,7,8 . Astroza et al 9 and Ebrahimian et al 10 have proposed the use of high-fidelity mechanics-based nonlinear FE models with stochastic filtering methods as an advanced SHM and DID framework capable of real-world applications. In another study, Ebrahimian et al 11 has proposed an alternative estimation and uncertainty quantification approach for nonlinear FE model updating based on a batch Bayesian estimation method.…”

Section: Introductionmentioning

confidence: 99%

Output-only identification of civil structures using nonlinear finite element model updating

2015

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This paper presents a novel approach for output-only nonlinear system identification of structures using data recorded during earthquake events. In this approach, state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with Bayesian Inference method to estimate (i) time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure, and (ii) the time history of the earthquake ground motion. To validate the performance of the proposed framework, the simulated responses of a bridge pier to an earthquake ground motion is polluted with artificial output measurement noise and used to jointly estimate the unknown material parameters and the time history of the earthquake ground motion. This proof-of-concept example illustrates the successful performance of the proposed approach even in the presence of high measurement noise.

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“…Different frameworks for mechanics‐based nonlinear FE model updating have been developed recently . These frameworks provide an advanced approach for system and damage ID and SHM of civil structures, which overcome the important shortcomings of the damage ID methods based on linear modal ID.…”

Section: Introductionmentioning

confidence: 99%

Bayesian optimal estimation for output-only nonlinear system and damage identification of civil structures

Ebrahimian

Astroza

Conte

et al. 2018

Struct Control Health Monit

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Summary This paper presents a new framework for output‐only nonlinear system and damage identification of civil structures. This framework is based on nonlinear finite element (FE) model updating in the time‐domain, using only the sparsely measured structural response to unmeasured or partially measured earthquake excitation. The proposed framework provides a computationally feasible approach for structural health monitoring and damage identification of civil structures when accurate measurement of the input seismic excitations is challenging (e.g., buildings with significant foundation rocking and bridges with piers in deep water) or the measured seismic excitations are erroneous and/or distorted by significant measurement error (e.g., malfunctioning sensors). Grounded on Bayesian inference, the proposed framework estimates the unknown FE model parameters and the ground acceleration time histories simultaneously, using the sparse measured dynamic response of the structure. Two approaches are presented in this study to solve the joint structural system parameter and input identification problem: (a) a sequential maximum likelihood estimation approach, which reduces to a sequential nonlinear constrained optimization method, and (b) a sequential maximum a posteriori estimation approach, which reduces to a sequential iterative extended Kalman filtering method. Both approaches require the computation of FE response sensitivities with respect to the unknown FE model parameters and the values of base acceleration at each time step. The FE response sensitivities are computed efficiently using the direct differentiation method. The two proposed approaches are validated using the seismic response of a 5‐story reinforced concrete building structure, numerically simulated using a state‐of‐the‐art mechanics‐based nonlinear structural FE modeling technique. The simulated absolute acceleration response time histories of 3 floors and the relative (to the base) roof displacement response time histories of the building to a bidirectional horizontal seismic excitation are polluted with artificial measurement noise. The noisy responses of the structure are then used to estimate the unknown FE model parameters characterizing the nonlinear material constitutive laws of the concrete and reinforcing steel and the (assumed) unknown time history of the ground acceleration in the longitudinal direction of the building. The same nonlinear FE model of the structure is used to simulate the structural response and to estimate the dynamic input and system parameters. Thus, modeling uncertainty is not considered in this paper. Although the validation study demonstrates the estimation accuracy of both approaches, the sequential maximum a posteriori estimation approach is shown to be significantly more efficient computationally than the sequential maximum likelihood estimation approach.

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

Cited by 108 publications

References 42 publications

Bayesian Methods for Nonlinear System Identification of Civil Structures

Bayesian Methods for Nonlinear System Identification of Civil Structures

Output-only identification of civil structures using nonlinear finite element model updating

Bayesian optimal estimation for output-only nonlinear system and damage identification of civil structures

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