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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
171

Modeling and uncertainty quantification in the nonlinear stochastic dynamics of horizontal drillstrings / Modélisation et quantification des incertitudes en dynamique stochastique non linéaire des tubes de forage horizontaux

Barbosa Da Cunha Junior, Americo 11 March 2015 (has links)
Prospection de pétrole utilise un équipement appelé tube de forage pour forer le sol jusqu'au le niveau du réservoir. Cet équipement est une longue colonne rotative, composée par une série de tiges de forage interconnectées et les équipements auxiliaires. La dynamique de cette colonne est très complexe parce que dans des conditions opérationnelles normales, elle est soumise à des vibrations longitudinales, latérales et de torsion, qui présentent un couplage non linéaire. En outre, cette structure est soumise à effets de frottement et à des chocs dûs aux contacts mécaniques entre les paires tête de forage/sol et tube de forage/sol. Ce travail présente un modèle mécanique-mathématique pour analyser un tube de forage en configuration horizontale. Ce modèle utilise la théorie des poutres qui utilise l'inertie de rotation, la déformation de cisaillement et le couplage non linéaire entre les trois mécanismes de vibration. Les équations du modèle sont discrétisées par la méthode des éléments finis. Les incertitudes des paramètres du modèle d'interaction tête de forage/sol sont prises en compte par l'approche probabiliste paramétrique, et les distributions de probabilité des paramètres aléatoires sont construits par le principe du maximum d'entropie. Des simulations numériques sont réalisées afin de caractériser le comportement dynamique non linéaire de la structure, et en particulier, de l'outil de forage. Des phénomènes dynamiques non linéaires par nature, comme le slick-slip et le bit-bounce, sont observés dans les simulations, ainsi que les chocs. Une analyse spectrale montre étonnamment que les phénomènes slick-slip et bit-bounce résultent du mécanisme de vibration latérale, et ce phénomène de choc vient de la vibration de torsion. Cherchant à améliorer l'efficacité de l'opération de forage, un problème d'optimisation qui cherche à maximiser la vitesse de pénétration de la colonne dans le sol, sur ses limites structurelles, est proposé et résolu / Oil prospecting uses an equipment called drillstring to drill the soil until the reservoir level. This equipment is a long column under rotation, composed by a sequence of connected drill-pipes and auxiliary equipment. The dynamics of this column is very complex because, under normal operational conditions, it is subjected to longitudinal, lateral, and torsional vibrations, which presents a nonlinear coupling. Also, this structure is subjected to friction and shocks effects due to the mechanical contacts between the pairs drill-bit/soil and drill-pipes/borehole. This work presents a mechanical-mathematical model to analyze a drillstring in horizontal configuration. This model uses a beam theory which accounts rotatory inertia, shear deformation, and the nonlinear coupling between three mechanisms of vibration. The model equations are discretized using the finite element method. The uncertainties in bit-rock interaction model parameters are taken into account through a parametric probabilistic approach, and the random parameters probability distributions are constructed by means of maximum entropy principle. Numerical simulations are conducted in order to characterize the nonlinear dynamic behavior of the structure, specially, the drill-bit. Dynamical phenomena inherently nonlinear, such as slick-slip and bit-bounce, are observed in the simulations, as well as shocks. A spectral analysis shows, surprisingly, that slick-slip and bit-bounce phenomena result from the lateral vibration mechanism, and that shock phenomena comes from the torsional vibration. Seeking to increase the efficiency of the drilling process, an optimization problem that aims to maximize the rate of penetration of the column into the soil, respecting its structural limits, is proposed and solved
172

Développement d'une méthodologie de Quantification d'Incertitudes pour une analyse Mutli-Physique Best Estimate et application sur un Accident d’Éjection de Grappe dans un Réacteur à Eau Pressurisée / Development of an Uncertainty Quantification methodology for Multi-Physics Best Estimate analysis and application to the Rod Ejection Accident in a Pressurized Water Reactor

Delipei, Gregory 04 October 2019 (has links)
Durant les dernières décennies, l’évolution de la puissance de calcul a conduit au développement de codes de simulation en physique des réacteurs de plus en plus prédictifs pour la modélisation du comportement d’un réacteur nucléaire en situation de fonctionnement normal et accidentel. Un cadre d’analyse d’incertitudes cohérent avec l’utilisation de modélisations Best Estimate (BE) a été développé. On parle d’approche Best Estimate Plus Uncertain-ties (BEPU) et cette approche donne lieu `a de nombreux travaux de R&D à l’international en simulation numérique. Dans cette thèse, on étudie la quantification d’incertitudes multi-physiques dans le cas d’un transitoire d’ éjection de Grappe de contrôle (REA- Rod Ejection Accident) dans un Réacteur à Eau Pressurisée (REP). La modélisation BE actuellement disponible au CEA est réalisée en couplant les codes APOLLO3 R (netronique) et FLICA4 (thermohydraulique-thermique du combustible) dans l’environnement SALOME/CORPUS. Dans la première partie de la thèse, on examine différents outils statistiques disponibles dans la littérature scientifique dont la réduction de dimension, l’analyse de sensibilité globale, des modèles de substitution et la construction de plans d’expérience. On utilise ces outils pour développer une méthodologie de quantification d’incertitudes. Dans la deuxième partie de la thèse, on améliore la modélisation du comportement du combustible. Un couplage Best Effort pour la simulation d’un transitoire REA est disponible au CEA. Il comprend le code ALCYONE V1.4 qui permet une modélisation fine du comportement thermomécanique du combustible. Cependant, l’utilisation d’une telle modélisation conduit à une augmentation significative du temps de calcul ce qui rend actuellement difficile la réalisation d’une analyse d’incertitudes. Pour cela, une méthodologie de calibrage d’un modèle analytique simplifié pour le transfert de chaleur pastille-gaine basé sur des calculs ALCYONE V1.4 découplés a été développée. Le modèle calibré est finalement intégré dans la modélisation BE pour améliorer sa prédictivité. Ces deux méthodologies sont maquettées initialement sur un cœur de petite échelle représentatif d’un REP puis appliquées sur un cœur REP à l’échelle 1 dans le cadre d’une analyse multi-physique d’un transitoire REA. / The computational advancements of the last decades lead to the development of numerical codes for simulating the reactor physics with increa-sing predictivity allowing the modeling of the beha-vior of a nuclear reactor under both normal and acci-dental conditions. An uncertainty analysis framework consistent with Best Estimate (BE) codes was develo-ped in order to take into account the different sources of uncertainties. This framework is called Best Esti-mate Plus Uncertainties (BEPU) and is currently a field of increasing research internationally. In this the-sis we study the multi-physics uncertainty quantifi-cation for Rod Ejection Accident (REA) in Pressuri-zed Water Reactors (PWR). The BE modeling avai-lable in CEA is used with a coupling of APOLLO3 (neutronics) and FLICA4 (thermal-hydraulics and fuel-thermal) in the framework of SALOME/CORPUS tool. In the first part of the thesis, we explore different statistical tools available in the scientific literature including: dimension reduction, global sensitivity analy-sis, surrogate modeling and design of experiments. We then use them in order to develop an uncer-tainty quantification methodology. In the second part of the thesis, we improve the BE modeling in terms of its uncertainty representation. A Best Effort coupling scheme for REA analysis is available at CEA. This in-cludes ALCYONE V1.4 code for a detailed modeling of fuel-thermomechanics behavior. However, the use of such modeling increases significantly the compu-tational cost for a REA transient rendering the uncer-tainty analysis prohibited. To this purpose, we deve-lop a methodology for calibrating a simplified analytic gap heat transfer model using decoupled ALCYONE V1.4 REA calculations. The calibrated model is finally used to improve the previous BE modeling. Both de-veloped methodologies are tested initially on a small scale core representative of a PWR and then applied on a large scale PWR core.
173

Schémas aux résidus distribués et méthodes à propagation des ondes pour la simulation d’écoulements compressibles diphasiques avec transfert de chaleur et de masse / Residual distribution schemes and wave propagation methods for the simulation of two-phase compressible flows with heat and mass transfer

Carlier, Julien 06 December 2019 (has links)
Ce travail a pour thème la simulation numérique d’écoulements diphasiques dans un contexte industriel. En effet, la simulation d’écoulements diphasiques est un domaine qui présente de nombreux défis, en raison de phénomènes complexes qui surviennent, comme la cavitation et autres transferts entre les phases. En outre, ces écoulements se déroulent généralement dans des géométries complexes rendant difficile une résolution efficiente. Les modèles que nous considérons font partie de la catégorie des modèles à interfaces diffuses et permettent de prendre en compte aisément les différents transferts entre les phases. Cette classe de modèles inclut une hiérarchie de sous-modèles pouvant simuler plus ou moins d’interactions entre les phases. Pour mener à bien cette étude nous avons en premier lieu comparé les modèles diphasiques dits à quatre équations et six équations, en incluant les effets de transfert de masse. Nous avons ensuite choisi de nous concentrer sur le modèle à quatre équations. L’objectif majeur de notre travail a alors été d’étendre les méthodes aux résidus distribués à ce modèle. Dans le contexte des méthodes de résolution numérique, il est courant d’utiliser la forme conservative des équations de bilan. En effet, la résolution sous forme non-conservative conduit à une mauvaise résolution du problème. Cependant, résoudre les équations sous forme non-conservative peut s’avérer plus intéressant d’un point de vue industriel. Dans ce but, nous utilisons une approche développée récemment permettant d’assurer la conservation en résolvant un système sous forme non-conservative, à condition que la forme conservative soit connue. Nous validons ensuite notre méthode et l’appliquons à des problèmes en géométries complexes. Finalement, la dernière partie de notre travail est dédiée à étudier la validité des modèles à interfaces diffuses pour des applications à des problèmes industriels réels. On cherche alors, en utilisant des méthodes de quantification d’incertitude, à obtenir les paramètres rendant nos simulations les plus vraisemblables et cibler les éventuels développements pouvant rendre nos simulations plus réalistes. / The topic of this thesis is the numerical simulation of two-phase flows in an industrial framework. Two-phase flows modelling is a challenging domain to explore, mainly because of the complex phenomena involved, such as cavitation and other transfer processes between phases. Furthermore, these flows occur generally in complex geometries, which makes difficult the development of efficient resolution methods. The models that we consider belong to the class of diffuse interface models, and they allow an easy modelling of transfers between phases. The considered class of models includes a hierarchy of sub-models, which take into account different levels of interactions between phases. To pursue our studies, first we have compared the so-called four-equation and six-equation two-phase flow models, including the effects of mass transfer processes. We have then chosen to focus on the four-equation model. One of the main objective of our work has been to extend residual distribution schemes to this model. In the context of numerical solution methods, it is common to use the conservative form of the balance law. In fact, the solution of the equations under a non-conservative form may lead to a wrong solution to the problem. Nonetheless, solving the equations in non-conservative form may be more interesting from an industrial point of view. To this aim, we employ a recent approach, which allows us to ensure conservation while solving a non-conservative system, at the condition of knowing its conservative form. We then validate our method and apply it to problems with complex geometry. Finally, the last part of our work is dedicated to the evaluation of the validity of the considered diffuse interface model for applications to real industrial problems. By using uncertainty quantification methods, the objective is to get parameters that make our simulations the most plausible, and to target the possible extensions that can make our simulations more realistic.
174

Three essays on unveiling complex urban phenomena: toward improved understanding

Lym, Youngbin 13 November 2020 (has links)
No description available.
175

Robust damage detection in uncertain nonlinear systems /

Villani, Luis Gustavo Giacon. January 2019 (has links)
Orientador: Samuel da Silva / Abstract: Structural Health Monitoring (SHM) methodologies aim to develop techniques able to detect, localize, quantify and predict the progress of damages in civil, aerospatial and mechanical structures. In the hierarchical process, the damage detection is the first and most important step. Despite the existence of numerous methods of damage detection based on vibration signals, two main problems can complicate the application of classical approaches: the nonlinear phenomena and the uncertainties. This thesis demonstrates the importance of the use of a stochastic nonlinear model in the damage detection problem considering the intrinsically nonlinear behavior of mechanical structures and the measured data variation. A new stochastic version of the Volterra series combined with random Kautz functions is proposed to predict the behavior of nonlinear systems, considering the presence of uncertainties. The stochastic model proposed is used in the damage detection process based on hypothesis tests. Firstly, the method is applied in a simulated study assuming a random Duffing oscillator exposed to the presence of a breathing crack modeled as a bilinear oscillator. Then, an experimental application considering a nonlinear beam subjected to the presence of damage with linear characteristics (loss of mass in a bolted connection) is performed, with the direct comparison between the results obtained using a deterministic and a stochastic model. Finally, an experimental application considering a n... (Complete abstract click electronic access below) / Resumo: As metodologias de Monitoramento da Integridade Estrutural (SHM) visam desenvolver técnicas capazes de detectar, localizar, quantificar e prever o progresso de danos em estruturas civis, aeroespaciais e mecânicas. Nesse processo hierárquico, a detecção de danos é o primeiro e mais importante passo. Apesar da existência de inúmeros métodos de detecção de danos baseados em sinais de vibração, dois problemas principais podem complicar a aplicação de abordagens clássicas: os fenômenos não lineares e as incertezas. Esta tese demonstra a importância do uso de um modelo não linear estocástico no problema de detecção de danos, considerando o comportamento intrinsecamente não linear de estruturas mecânicas e a variação dos dados medidos. Uma nova versão estocástica das séries de Volterra, combinada com funções aleatórias de Kautz, é proposta para prever o comportamento de sistemas não lineares, considerando a presença de incertezas. O modelo estocástico proposto é utilizado no processo de detecção de danos com base em testes de hipótese. Primeiramente, o método é aplicado em um estudo simulado, assumindo um oscilador Duffing aleatório exposto à presença de uma trinca respiratória modelada como um oscilador bilinear. Em seguida, uma aplicação experimental é realizada considerando uma viga não linear sujeita à presença de um dano com características lineares (perda de massa em uma conexão parafusada), com a comparação direta entre os resultados obtidos utilizando um modelo determinístic... (Resumo completo, clicar acesso eletrônico abaixo) / Doutor
176

Stochastic finite element method with simple random elements

Starkloff, Hans-Jörg 19 May 2008 (has links)
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
177

Towards multifidelity uncertainty quantification for multiobjective structural design

Lebon, Jérémy 12 December 2013 (has links)
This thesis aims at Multi-Objective Optimization under Uncertainty in structural design. We investigate Polynomial Chaos Expansion (PCE) surrogates which require extensive training sets. We then face two issues: high computational costs of an individual Finite Element simulation and its limited precision. From numerical point of view and in order to limit the computational expense of the PCE construction we particularly focus on sparse PCE schemes. We also develop a custom Latin Hypercube Sampling scheme taking into account the finite precision of the simulation. From the modeling point of view, we propose a multifidelity approach involving a hierarchy of models ranging from full scale simulations through reduced order physics up to response surfaces. Finally, we investigate multiobjective optimization of structures under uncertainty. We extend the PCE model of design objectives by taking into account the design variables. We illustrate our work with examples in sheet metal forming and optimal design of truss structures. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished
178

Advances on Uncertainty Quantification Techniques for Dynamical Systems: Theory and Modelling

Burgos Simón, Clara 17 May 2021 (has links)
[ES] La cuantificación de la incertidumbre está compuesta por una serie de métodos y técnicas computacionales cuyo objetivo principal es describir la aleatoriedad presente en problemas de diversa índole. Estos métodos son de utilidad en la modelización de procesos biológicos, físicos, naturales o sociales, ya que en ellos aparecen ciertos aspectos que no pueden ser determinados de manera exacta. Por ejemplo, la tasa de contagio de una enfermedad epidemiológica o el factor de crecimiento de un volumen tumoral dependen de factores genéticos, ambientales o conductuales. Estos no siempre pueden definirse en su totalidad y por tanto conllevan una aleatoriedad intrínseca que afecta en el desarrollo final. El objetivo principal de esta tesis es extender técnicas para cuantificar la incertidumbre en dos áreas de las matemáticas: el cálculo de ecuaciones diferenciales fraccionarias y la modelización matemática. Las derivadas de orden fraccionario permiten modelizar comportamientos que las derivadas clásicas no pueden, como por ejemplo los efectos de memoria o la viscoelasticidad en algunos materiales. En esta tesis, desde un punto de vista teórico, se extenderá el cálculo fraccionario a un ambiente de incertidumbre, concretamente en el sentido de la media cuadrática. Se presentarán problemas de valores iniciales fraccionarios aleatorios. El cálculo de la solución, la obtención de las aproximaciones de la media y varianza de la solución y la aproximación de la primera función de densidad de probabilidad de la solución son conceptos que se abordarán en los próximos capítulos. Sin embargo, no siempre es sencillo obtener la solución exacta de un problema de valores iniciales fraccionario aleatorio. Por ello en esta tesis también se dedicará un capítulo para describir un procedimiento numérico que aproxime su solución. Por otro lado, desde un punto de vista más aplicado, se desarrollan técnicas computacionales para cuantificar la incertidumbre en modelos matemáticos. Combinando estas técnicas junto con modelos matemáticos apropiados, se estudiarán problemas de dinámica biológica. En primer lugar, se determinará la cantidad de portadores de meningococo en España con un modelo de competencia de Lotka-Volterra fraccionario aleatorio. A continuación, el volumen de un tumor mamario se modelizará mediante un modelo logístico con incertidumbre. Finalmente ayudándonos de un modelo matemático que describe el nivel de glucosa en sangre de un paciente diabético, se pretende dar una recomendación de carbohidratos e insulina que se debe de ingerir para que el nivel de glucosa del paciente esté dentro de una banda de confianza saludable. Es importante subrayar que para poder realizar estos estudios se requieren datos reales, los cuales pueden estar alterados debido a los errores de medición o proceso que se han cometido para obtenerlos. Por este motivo, modelizar correctamente el problema junto con la incertidumbre en los datos es de vital importancia. / [CA] La quantificació de la incertesa està composada per una sèrie de mètodes i tècniques computacionals, l'objectiu principal de les quals és descriure l'aleatorietat present en problemes de diversa índole. Aquests mètodes són d'utilitat en la modelització de processos biològics, físics, naturals o socials, ja que en ells apareixen certs aspectes que no poden ser determinats de manera exacta. Per exemple, la taxa de contagi d'una malaltia epidemiològica o el factor de creixement d'un volum tumoral depenen de factors genètics, ambientals o conductuals. Aquests no sempre poden definir-se íntegrament i per tant, comporten una aleatorietat intrínseca que afecta en el desenvolupament final. L'objectiu principal d'aquesta tesi doctoral és estendre tècniques per a quantificar la incertesa en dues àrees de les matemàtiques: el càlcul d'equacions diferencials fraccionàries i la modelització matemàtica. Les derivades d'ordre fraccionari permeten modelitzar comportaments que les derivades clàssiques no poden, com per exemple, els efectes de memòria o la viscoelasticitat en alguns materials. En aquesta tesi, des d'un punt de vista teòric, s'estendrà el càlcul fraccionari a un ambient d'incertesa, concretament en el sentit de la mitjana quadràtica. Es presentaran problemes de valors inicials fraccionaris aleatoris. El càlcul de la solució, l'obtenció de les aproximacions de la mitjana i, la variància de la solució i l'aproximació de la primera funció de densitat de probabilitat de la solució són conceptes que s'abordaran en els pròxims capítols. No obstant això, no sempre és senzill obtindre la solució exacta d'un problema de valors inicials fraccionari aleatori. Per això en aquesta tesi també es dedicarà un capítol per a descriure un procediment numèric que aproxime la seua solució. D'altra banda, des d'un punt de vista més aplicat, es desenvolupen tècniques computacionals per a quantificar la incertesa en models matemàtics. Combinant aquestes tècniques juntament amb models matemàtics apropiats, s'estudiaran problemes de dinàmica biològica. En primer lloc, es determinarà la quantitat de portadors de meningococ a Espanya amb un model de competència de Lotka-Volterra fraccionari aleatori. A continuació, el volum d'un tumor mamari es modelitzará mitjançant un model logístic amb incertesa. Finalment ajudant-nos d'un model matemàtic que descriu el nivell de glucosa en sang d'un pacient diabètic, es pretén donar una recomanació de carbohidrats i insulina que s'ha d'ingerir perquè el nivell de glucosa del pacient estiga dins d'una banda de confiança saludable. És important subratllar que per a poder realitzar aquests estudis es requereixen dades reals, els quals poden estar alterats a causa dels errors de mesurament o per la forma en que s'han obtés. Per aquest motiu, modelitzar correctament el problema juntament amb la incertesa en les dades és de vital importància. / [EN] Uncertainty quantification collects different methods and computational techniques aimed at describing the randomness in real phenomena. These methods are useful in the modelling of different processes as biological, physical, natural or social, since they present some aspects that can not be determined exactly. For example, the contagious rate of a epidemiological disease or the growth factor of a tumour volume depend on genetic, environmental or behavioural factors. They may not always be fully described and therefore involve uncertainties that affects on the final result. The main objective of this PhD thesis is to extend techniques to quantify the uncertainty in two mathematical areas: fractional calculus and mathematical modelling. Fractional derivatives allow us to model some behaviours that classical derivatives cannot, such as memory effects or the viscoelasticity of some materials. In this PhD thesis, from a theoretical point of view, fractional calculus is extended into the random framework, concretely in the mean square sense. Initial value problems will be studied. The calculus of the analytic solution, approximations for the mean and for the variance and the computation of the first probability density function are concepts we deal with them thought the following chapters. Nevertheless, it is not always possible to obtain the analytic solution of an initial value problem. Therefore, in this dissertation a chapter is addressed to describe a numerical procedure to approximate the solution for an initial value problem. On the other hand, from a modelling point of view, computational techniques to quantify the uncertainty in mathematical models are developed. Merging these techniques with appropriate mathematical models, problems of biological dynamics are studied. Firstly, the carriers of meningococcus in Spain are determined using a competition Lotka-Volterra random fractional model. Then, the volume of breast tumours is modelled by a random logistic model. Finally, taking advantage of a mathematical model which describes the glucose level of a diabetic patient, a recommendation of insulin shots and carbohydrate intakes is proposed to a patient in order to maintain her/his glucose level in a healthy confidence range. An important observation is that to carry out these studies real data is required and they may include uncertainties contained in the measurements on the process to perform the corresponding study. This it is the reason why it is crucial to properly model the problem taking also into account the randomness of the data. / Burgos Simón, C. (2021). Advances on Uncertainty Quantification Techniques for Dynamical Systems: Theory and Modelling [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/166442 / TESIS
179

Efficient Spectral-Chaos Methods for Uncertainty Quantification in Long-Time Response of Stochastic Dynamical Systems

Hugo Esquivel (10702248) 06 May 2021 (has links)
<div>Uncertainty quantification techniques based on the spectral approach have been studied extensively in the literature to characterize and quantify, at low computational cost, the impact that uncertainties may have on large-scale engineering problems. One such technique is the <i>generalized polynomial chaos</i> (gPC) which utilizes a time-independent orthogonal basis to expand a stochastic process in the space of random functions. The method uses a specific Askey-chaos system that is concordant with the measure defined in the probability space in order to ensure exponential convergence to the solution. For nearly two decades, this technique has been used widely by several researchers in the area of uncertainty quantification to solve stochastic problems using the spectral approach. However, a major drawback of the gPC method is that it cannot be used in the resolution of problems that feature strong nonlinear dependencies over the probability space as time progresses. Such downside arises due to the time-independent nature of the random basis, which has the undesirable property to lose unavoidably its optimality as soon as the probability distribution of the system's state starts to evolve dynamically in time.</div><div><br></div><div>Another technique is the <i>time-dependent generalized polynomial chaos</i> (TD-gPC) which utilizes a time-dependent orthogonal basis to better represent the stochastic part of the solution space (aka random function space or RFS) in time. The development of this technique was motivated by the fact that the probability distribution of the solution changes with time, which in turn requires that the random basis is frequently updated during the simulation to ensure that the mean-square error is kept orthogonal to the discretized RFS. Though this technique works well for problems that feature strong nonlinear dependencies over the probability space, the TD-gPC method possesses a serious issue: it suffers from the curse of dimensionality at the RFS level. This is because in all gPC-based methods the RFS is constructed using a tensor product of vector spaces with each of these representing a single RFS over one of the dimensions of the probability space. As a result, the higher the dimensionality of the probability space, the more vector spaces needed in the construction of a suitable RFS. To reduce the dimensionality of the RFS (and thus, its associated computational cost), gPC-based methods require the use of versatile sparse tensor products within their numerical schemes to alleviate to some extent the curse of dimensionality at the RFS level. Therefore, this curse of dimensionality in the TD-gPC method alludes to the need of developing a more compelling spectral method that can quantify uncertainties in long-time response of dynamical systems at much lower computational cost.</div><div><br></div><div>In this work, a novel numerical method based on the spectral approach is proposed to resolve the curse-of-dimensionality issue mentioned above. The method has been called the <i>flow-driven spectral chaos</i> (FSC) because it uses a novel concept called <i>enriched stochastic flow maps</i> to track the evolution of a finite-dimensional RFS efficiently in time. The enriched stochastic flow map does not only push the system's state forward in time (as would a traditional stochastic flow map) but also its first few time derivatives. The push is performed this way to allow the random basis to be constructed using the system's enriched state as a germ during the simulation and so as to guarantee exponential convergence to the solution. It is worth noting that this exponential convergence is achieved in the FSC method by using only a few number of random basis vectors, even when the dimensionality of the probability space is considerably high. This is for two reasons: (1) the cardinality of the random basis does not depend upon the dimensionality of the probability space, and (2) the cardinality is bounded from above by <i>M+n+1</i>, where <i>M</i> is the order of the stochastic flow map and <i>n</i> is the order of the governing stochastic ODE. The boundedness of the random basis from above is what makes the FSC method be curse-of-dimensionality free at the RFS level. For instance, for a dynamical system that is governed by a second-order stochastic ODE (<i>n=2</i>) and driven by a stochastic flow map of fourth-order (<i>M=4</i>), the maximum number of random basis vectors to consider within the FSC scheme is just 7, independent whether the dimensionality of the probability space is as low as 1 or as high as 10,000.</div><div><br></div><div>With the aim of reducing the complexity of the presentation, this dissertation includes three levels of abstraction for the FSC method, namely: a <i>specialized version</i> of the FSC method for dealing with structural dynamical systems subjected to uncertainties (Chapter 2), a <i>generalized version</i> of the FSC method for dealing with dynamical systems governed by (nonlinear) stochastic ODEs of arbitrary order (Chapter 3), and a <i>multi-element version</i> of the FSC method for dealing with dynamical systems that exhibit discontinuities over the probability space (Chapter 4). This dissertation also includes an implementation of the FSC method to address the dynamics of large-scale stochastic structural systems more effectively (Chapter 5). The implementation is done via a modal decomposition of the spatial function space as a means to reduce the number of degrees of freedom in the system substantially, and thus, save computational runtime.</div>
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Inversion cinématique progressive linéaire de la source sismique et ses perspectives dans la quantification des incertitudes associées / Progressive linear kinematic source inversion method and its perspectives towards the uncertainty quantification.

Sanchez Reyes, Hugo Samuel 28 October 2019 (has links)
La caractérisation des tremblements de terre est un domaine de recherche primordial en sismologie, où l'objectif final est de fournir des estimations précises d'attributs de la source sismique. Dans ce domaine, certaines questions émergent, par exemple : quand un tremblement de terre s’est-il produit? quelle était sa taille? ou quelle était son évolution dans le temps et l'espace? On pourrait se poser d'autres questions plus complexes comme: pourquoi le tremblement s'est produit? quand sera le prochain dans une certaine région? Afin de répondre aux premières questions, une représentation physique du phénomène est nécessaire. La construction de ce modèle est l'objectif scientifique de ce travail doctoral qui est réalisé dans le cadre de la modélisation cinématique. Pour effectuer cette caractérisation, les modèles cinématiques de la source sismique sont un des outils utilisés par les sismologues. Il s’agit de comprendre la source sismique comme une dislocation en propagation sur la géométrie d’une faille active. Les modèles de sources cinématiques sont une représentation physique de l’histoire temporelle et spatiale d’une telle rupture en propagation. Cette modélisation est dite approche cinématique car les histoires de la rupture inférées par ce type de technique sont obtenues sans tenir compte des forces qui causent l'origine du séisme.Dans cette thèse, je présente une nouvelle méthode d'inversion cinématique capable d'assimiler, hiérarchiquement en temps, les traces de données à travers des fenêtres de temps évolutives. Cette formulation relie la fonction de taux de glissement et les sismogrammes observés, en préservant la positivité de cette fonction et la causalité quand on parcourt l'espace de modèles. Cette approche, profite de la structure creuse de l’histoire spatio-temporelle de la rupture sismique ainsi que de la causalité entre la rupture et chaque enregistrement différé par l'opérateur. Cet opérateur de propagation des ondes connu, est différent pour chaque station. Cette formulation progressive, à la fois sur l’espace de données et sur l’espace de modèle, requiert des hypothèses modérées sur les fonctions de taux de glissement attendues, ainsi que des stratégies de préconditionnement sur le gradient local estimé pour chaque paramètre du taux de glissement. Ces hypothèses sont basées sur de simples modèles physiques de rupture attendus. Les applications réussies de cette méthode aux cas synthétiques (Source Inversion Validation Exercise project) et aux données réelles du séisme de Kumamoto 2016 (Mw=7.0), ont permis d’illustrer les avantages de cette approche alternative d’une inversion cinématique linéaire de la source sismique.L’objectif sous-jacent de cette nouvelle formulation sera la quantification des incertitudes d’un tel modèle. Afin de mettre en évidence les propriétés clés prises en compte dans cette approche linéaire, dans ce travail, j'explore l'application de la stratégie bayésienne connue comme Hamiltonian Monte Carlo (HMC). Cette méthode semble être l’une des possibles stratégies qui peut être appliquée à ce problème linéaire sur-paramétré. Les résultats montrent qu’elle est compatible avec la stratégie linéaire dans le domaine temporel présentée ici. Grâce à une estimation efficace du gradient local de la fonction coût, on peut explorer rapidement l'espace de grande dimension des solutions possibles, tandis que la linéarité est préservée. Dans ce travail, j'explore la performance de la stratégie HMC traitant des cas synthétiques simples, afin de permettre une meilleure compréhension de tous les concepts et ajustements nécessaires pour une exploration correcte de l'espace de modèles probables. Les résultats de cette investigation préliminaire sont encourageants et ouvrent une nouvelle façon d'aborder le problème de la modélisation de la reconstruction cinématique de la source sismique, ainsi, que de l’évaluation des incertitudes associées. / The earthquake characterization is a fundamental research field in seismology, which final goal is to provide accurate estimations of earthquake attributes. In this study field, various questions may rise such as the following ones: when and where did an earthquake happen? How large was it? What is its evolution in space and time? In addition, more challenging questions can be addressed such as the following ones: why did it occur? What is the next one in a given area? In order to progress in the first list of questions, a physical description, or model, of the event is necessary. The investigation of such model (or image) is the scientific topic I investigate during my PhD in the framework of kinematic source models. Understanding the seismic source as a propagating dislocation that occurs across a given geometry of an active fault, the kinematic source models are the physical representations of the time and space history of such rupture propagation. Such physical representation is said to be a kinematic approach because the inferred rupture histories are obtained without taking into account the forces that might cause the origin of the dislocation.In this PhD dissertation, I present a new hierarchical time kinematic source inversion method able to assimilate data traces through evolutive time windows. A linear time-domain formulation relates the slip-rate function and seismograms, preserving the positivity of this function and the causality when spanning the model space: taking benefit of the time-space sparsity of the rupture model evolution is as essential as considering the causality between rupture and each record delayed by the known propagator operator different for each station. This progressive approach, both on the data space and on the model space, does require mild assumptions on prior slip-rate functions or preconditioning strategies on the slip-rate local gradient estimations. These assumptions are based on simple physical expected rupture models. Successful applications of this method to a well-known benchmark (Source Inversion Validation Exercise 1) and to the recorded data of the 2016 Kumamoto mainshock (Mw=7.0) illustrate the advantages of this alternative approach of a linear kinematic source inversion.The underlying target of this new formulation will be the future uncertainty quantification of such model reconstruction. In order to achieve this goal, as well as to highlight key properties considered in this linear time-domain approach, I explore the Hamiltonian Monte Carlo (HMC) stochastic Bayesian framework, which appears to be one of the possible and very promising strategies that can be applied to this stabilized over-parametrized optimization of a linear forward problem to assess the uncertainties on kinematic source inversions. The HMC technique shows to be compatible with the linear time-domain strategy here presented. This technique, thanks to an efficient estimation of the local gradient of the misfit function, appears to be able to rapidly explore the high-dimensional space of probable solutions, while the linearity between unknowns and observables is preserved. In this work, I investigate the performance of the HMC strategy dealing with simple synthetic cases with almost perfect illumination, in order to provide a better understanding of all the concepts and required tunning to achieve a correct exploration of the model space. The results from this preliminary investigation are promising and open a new way of tackling the kinematic source reconstruction problem and the assessment of the associated uncertainties.

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