49 research outputs found

    Fast model updating coupling Bayesian inference and PGD model reduction

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    International audienceThe paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example

    A goal-oriented finite element method and its extension to pgd reduced-order modeling

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    RÉSUMÉ: Nous proposons une méthode éléments finis formulée pour des quantités d’intérêt. L’objectif est d’accroître la précision des solutions numériques pour ces quantités, choisies par l’utilisateur, sans pour autant perdre en précision globale. Les approches traditionnelles visant à contrôler l’erreur en quantité d’intérêt utilisent habituellement la solution d’un problème adjoint pour: (i) estimer l’erreur en quantité d’intérêt; et (ii) savoir comment adapter la discrétisation afin d’obtenir un espace éléments finis capable de mieux représenter les quantités d’intérêt de la solution. Ces approches s’inscrivent donc dans un procédé itératif de prédictions-corrections. Nous proposons d’utiliser cette même solution adjointe conjointement avec un probleme primal modifié, tel que sa solution soit ajustée à une valeur plus précise de la quantité d’intérêt. Ainsi, nous résolvons dans un espace qui est déjà adapté à la quantité d’intérêt. L’originalité de la présente approche consiste à utiliser la solution du problème adjoint non pas en tant que substitut de la solution exacte/référence pour l’estimation d’erreur et l’adaptation, mais en extrayant de celle-ci des valeurs des quantités d’intérêt extrêmement précises. Ces valeurs sont ensuite utilisées dans une minimisation sous contrainte de l’énergie (problème primal contraint) afin d’obtenir une solution plus précise en quantité d’intérêt. Ensuite, nous étendons cette approche en quantité d’intérêt à un contexte de réduction de modèles en utilisant la PGD. Ces méthodes reposent généralement sur des représentations spectrales, et sont de plus en plus utilisées pour simuler des problèmes en haute dimension. En ne considérant que les principaux modes propres de la solution, ces méthodes déjouent la malédiction de la dimensionnalité et rendent possibles des simulations auparavant inenvisageables.----------ABSTRACT: We present a finite element formulation of boundary-value problems that aims at constructing approximations specifically tailored for the estimation of quantities of interest of the solution, hence the name goal-oriented finite element method. The main idea is to formulate the problem as a constrained minimization problem that includes refined information in the goal functionals, so that the resulting model is capable of delivering enhanced predictions of the quantities of interest. This paradigm constitutes a departure from classical goal-oriented approaches in which one computes first the finite element solution and subsequently adapts the mesh via a greedy approach, by controlling error estimates measured in terms of quantities of interest using a posteriori dual-based error estimates. The formulation is then extended to the so-called Proper Generalized Decomposition method, an instance of model order reduction methods, with the aim of constructing reduced-order models tailored for the approximation of quantities of interest. Model order reduction methods aim at circumventing the curse of dimensionality arising from the high number of parameters of a given problem, by uncovering and/or exploiting lower dimensional structures present in the model or in the solution. Numerical examples are disseminated throughout the dissertation. They appear at the end of each of the three main chapters and Chapter 5 consists of an application example, namely a parametrized electrostatic cracked composite material

    Snapshot-Based Methods and Algorithms

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    An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

    Model Order Reduction

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    An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

    Perspectives on European Earthquake Engineering and Seismology: Volume 2

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    Geotechnical Engineering & Applied Earth Science

    PB-JFT-23

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    Proceedings of the 1st International Workshop on Resilience

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    Built environment constitutes the fundamental layer for many services and functions of our society. Many physical infrastructures are vulnerable to natural hazards (e.g. earthquakes, floods, tornados) as well as man-made hazards, and the risk of catastrophic damage due to hazardous events continues to increase worldwide. Considerable progress has been made towards risk management and mitigation, however, in particular the earthquake engineering community still faces many new challenges. Focusing principally on seismic resilience, the objectives of the workshop have centred on (i) how we use resilience-based engineering to steward our built environment and make it safer, resilient and sustainable, and (ii) how to assess and develop strategies to improve community resilience against a major disruptive event. The workshop has comprised presentations and discussion sessions. The state of knowledge regarding disaster resilience has first been examined in the light of the lessons learnt from recent major earthquakes. Then the views and approaches were solicited with contributions from Japan, Asia, Europe, North and South America on the new directions for Resilience-Based Design (RBD) in an effort towards catalysing and elaborating a comprehensive, collective and integrated approach to resilience. Currently running research projects on resilience, funded by the EU, were also presented.JRC.E.4-Safety and Security of Building
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