Ensemble Kalman Filters (EnKF) and geometric characterization of sensitivity spaces for Uncertainty Quantification in optimization - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2015

Ensemble Kalman Filters (EnKF) and geometric characterization of sensitivity spaces for Uncertainty Quantification in optimization

Résumé

We present an original framework for uncertainty quantification (UQ) in optimization. It is based on a cascade of ingredients with growing computational complexity for both forward and reverse uncertainty propagation. The approach is merely geometric. It starts with a complexity-based splitting of the independent variables and the definition of a parametric optimization problem. Geometric characterization of global sensitivity spaces through their dimensions and relative positions by the principal angles between global search subspaces bring a first set of information on the impact of uncertainties on the functioning parameters on the optimal solution. Joining the multi-point descent direction and the quantiles on the optimization parameters permits to define the notion of Directional Extreme Scenarios (DES) without sampling of large dimension design spaces. One goes beyond DES with Ensemble Kalman Filters (EnKF) after the multi-point optimization algorithm is cast into an ensemble simulation environment. This formulation accounts for the variability in large dimension. The UQ cascade ends with the joint application of the EnKF and DES leading to the concept of Ensemble Directional Extreme Scenarios (EDES) which provides more exhaustive possible extreme scenarios knowing the Probability Density Function of our optimization parameters. A final interest of the approach is that it provides an indication of the size of the ensemble which must be considered in the EnKF. These ingredients are illustrated on an history matching problem.
Fichier principal
Vignette du fichier
paper_opt_enkf.pdf (2.67 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01138181 , version 1 (01-04-2015)

Identifiants

Citer

Bijan Mohammadi. Ensemble Kalman Filters (EnKF) and geometric characterization of sensitivity spaces for Uncertainty Quantification in optimization. Computer Methods in Applied Mechanics and Engineering, 2015, 290, pp.228-249. ⟨10.1016/j.cma.2015.03.006⟩. ⟨hal-01138181⟩
98 Consultations
218 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More