A combined Kalman Filter and Error in Constitutive Relation approach for system identification in structural dynamics.

Abstract : Error in Constitutive Relation (ECR) methods measure model error by evaluating the difference between admissible fields using an energy norm. This technique presents interesting features such as good ability to spatially localize erroneously modeled regions, strong robustness in presence of noisy data, and good regularity properties of cost functions. On the other hand, the Kalman filter (KF) is a prediction-correction algorithm for recursive system estimation. The KF is particularly suitable for studying evolutionary systems embedding noisy data from both model and observation. The main part of this work is devoted to establish and evaluate a general-purpose identification approach using ECR and KF. In order to achieve this goal, the ECR is initially used to improve the a priori knowledge of model errors. Furthermore, ECR functionals are introduced in a state-space description of the identification problem. Its resolution is performed by means of the Unscented Kalman Filter (UKF), a second-order, reduced-cost, Kalman filter. The adequacy of the ECR-UKF approach to address problems of industrial relevance is shown through different numerical examples and complex industrial cases, such as structural time-varying damage assessment, boundary conditions identification of in-operation structures and field reconstruction problems. Moreover, these examples are used to improve the performance of the ECR-UKF algorithm, particularly the introduction of algebraic constraints in the ECR-UKF algorithm and the influence of error covariance matrix design.
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Contributor : Albert Alarcon Cot <>
Submitted on : Wednesday, August 22, 2012 - 4:41:16 PM
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Albert Alarcon Cot. A combined Kalman Filter and Error in Constitutive Relation approach for system identification in structural dynamics.. Mechanics of the structures [physics.class-ph]. Ecole Polytechnique X, 2012. English. ⟨pastel-00724815⟩

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