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Table of contents
Introduction and general overview
EDF’s industrial need
Considered methods
Overview of the thesis
I Introduction to Error in Constitutive Relation and Data Assimilation methods
1 Identification methods and Error in Constitutive Relation
1.1 Reference Problem
1.2 Energy-based functionals. Introduction to the Error in Constitutive Relation
1.3 Conclusions
2 Data Assimilation
2.1 Introduction
2.2 Concepts and classic notation in data assimilation
2.3 Sequential and variational formalisms: Kalman filter and 4D-Var
2.3.1 Variational formalism: 4D-Var
2.3.2 Sequential formalism: The Kalman filter
2.4 Example of nonlinear identification by means of the Unscented KF
2.5 Conclusions
II Towards a combined use of Kalman filtering and Error in Constitutive Relation
3 A Kalman filter and ECR strategy for structural dynamics model identification
3.1 Purpose
3.2 Improving a priori knowledge with the ECR
3.3 Introducing the ECR functionals into Kalman Filtering
3.4 Solving the identification problem by using ECR – UKF coupled method
3.5 Numerical example of structural parameter identification
3.6 Conclusions
4 ECR and UKF for model enhancement in problems of industrial relevance
4.1 Damage identification through the ECR-UKF strategy for high DOF models
4.1.1 Case of evolving parameters
4.2 Identifying incorrect modelling of boundary conditions
4.2.1 A time-domain approach for the identification of mis-modeled boundaries
4.3 Comparison of ECR and BLUE methods for structural field reconstruction
4.4 Conclusions
5 Improvements of the ECR-UKF algorithm
5.1 Introducing algebraic constraints in the Unscented Kalman Filter
5.2 Parametric study of ECR-UKF parameter error covariance matrix
5.3 Conclusions
III Applications
6 ECR in civil structures assessment: application to the SMART benchmark
6.1 Introduction
6.2 Main results
6.3 Conclusions and further work on the SMART benchmark
7 Study of a reinforced concrete beam with strong boundary coupling
7.1 Experimental setup and problem description
7.2 Boundary impedances identification
7.2.1 A new approach to identify boundary conditions based in ECR functionals
7.3 Study of the evolving structural damage
7.4 Conclusions
Conclusions and future research
Appendices
A Stochastic interpolation: the BLUE formalism
B Minimization of the ECR functional and first order derivatives in a FE framework.
C The Unscented Kalman filter
D Implementation within Code Aster FE software
E Application of the ECR to the SMART benchmark
Bibliography
