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Table of contents
1 Introduction
1.1 Context of the research
1.2 Position of the research
1.3 Objectives of the research
1.4 Strategy of the research
1.5 Manuscript layout
2 Classical reduced-order model
2.1 Reference computational model
2.2 Classical nominal reduced-order model
2.3 Classical stochastic reduced-order model
3 Global-displacements reduced-order model
3.1 Reduced kinematics for the kinetic energy
3.1.1 Construction of the polynomial basis
3.1.2 Reduced-kinematics mass matrix
3.2 Global-displacements reduced-order basis
3.3 Numerical implementation
3.4 Local-displacements reduced-order basis
4 Multilevel reduced-order model
4.1 Formulation of the multilevel reduced-order model
4.2 Implementation of the multilevel nominal reduced-order model
4.2.1 Numerical procedure
4.2.2 Construction of the reduced-order bases
4.2.3 Construction of the reduced-order models
4.3 Multilevel stochastic reduced-order model
5 Statistical inverse identication of the multilevel stochastic reduced- order model: application to an automobile
5.1 Problem denition
5.1.1 Experimental measurements (excitation force and observation points) and frequency band of analysis
5.1.2 Computational model
5.1.3 Modal density characterizing the dynamics and denition of the LF, MF, and HF bands
5.1.4 Damping model for the automobile
5.1.5 Denition of the observations
5.1.6 Dening the objective function used for the convergence analyses of the deterministic computational ROMs
5.1.7 Dening the objective function used for the identication of the stochastic computational ROMs
5.2 Classical nominal ROM and classical stochastic ROM
5.2.1 First step: C-NROM
5.2.2 Second step: C-SROM
5.3 Multilevel nominal ROM and multilevel stochastic ROM
5.3.1 First step: ML-NROM
5.3.2 Second step: ML-SROM
5.4 Complementary results
5.4.1 Deterministic analysis of the contribution of each of the ROBs
5.4.2 Stochastic sensitivity analysis
6 Conclusions and future prospects
Bibliography
