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Author: Géraud Blatman
Publisher:
ISBN:
Category :
Languages : en
Pages : 238
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Book Description
Cette thèse s'insère dans le contexte générale de la propagation d'incertitudes et de l'analyse de sensibilité de modèles de simulation numérique, en vue d'applications industrielles. Son objectif est d'effectuer de telles études en minimisant le nombre d'évaluations du modèle, potentiellement coûteuses. Le présent travail repose sur une approximation de la réponse du modèle sur la base du chaos polynomial (CP), qui permet de réaliser des post-traitements à un coût de calcul négligeable. Toutefois, l'ajustement du CP peut nécessiter un nombre conséquent d'appels au modèle si ce dernier dépend d'un nombre élevé de paramètres (e.g. supérieur à 10). Pour contourner ce problème, on propose deux algorithmes pour ne sélectionner qu'un faible nombre de termes importants dans la représentation par CP, à savoir une procédure de régression pas-à-pas et une procédure basée sur la méthode de Least Angle Regression (LAR). Le faible nombre de coefficients associés aux CP creux obtenus peuvent ainsi être déterminés à partir d'un nombre réduit d'évaluations du modèle. Les méthodes sont validées sur des cas-tests académiques de mécanique, puis appliquées sur le cas industriel de l'analyse d'intégrité d'une cuve de réacteur à eau pressurisée. Les résultats obtenus confirment l'efficacité des méthodes proposées pour traiter les problèmes de propagation d'incertitudes et d'analyse de sensibilité en grande dimension.
Author: Géraud Blatman
Publisher:
ISBN:
Category :
Languages : en
Pages : 238
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Book Description
Cette thèse s'insère dans le contexte générale de la propagation d'incertitudes et de l'analyse de sensibilité de modèles de simulation numérique, en vue d'applications industrielles. Son objectif est d'effectuer de telles études en minimisant le nombre d'évaluations du modèle, potentiellement coûteuses. Le présent travail repose sur une approximation de la réponse du modèle sur la base du chaos polynomial (CP), qui permet de réaliser des post-traitements à un coût de calcul négligeable. Toutefois, l'ajustement du CP peut nécessiter un nombre conséquent d'appels au modèle si ce dernier dépend d'un nombre élevé de paramètres (e.g. supérieur à 10). Pour contourner ce problème, on propose deux algorithmes pour ne sélectionner qu'un faible nombre de termes importants dans la représentation par CP, à savoir une procédure de régression pas-à-pas et une procédure basée sur la méthode de Least Angle Regression (LAR). Le faible nombre de coefficients associés aux CP creux obtenus peuvent ainsi être déterminés à partir d'un nombre réduit d'évaluations du modèle. Les méthodes sont validées sur des cas-tests académiques de mécanique, puis appliquées sur le cas industriel de l'analyse d'intégrité d'une cuve de réacteur à eau pressurisée. Les résultats obtenus confirment l'efficacité des méthodes proposées pour traiter les problèmes de propagation d'incertitudes et d'analyse de sensibilité en grande dimension.
Author: Bruno Sudret
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Themistocles M. Rassias
Publisher: Springer Nature
ISBN: 3030606228
Category : Mathematics
Languages : en
Pages : 546
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Book Description
This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Author: Roger Ghanem
Publisher: Springer
ISBN: 9783319123844
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.
Author: Olivier Le Maitre
Publisher: Springer Science & Business Media
ISBN: 9048135206
Category : Science
Languages : en
Pages : 542
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Book Description
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Author: Ivica Vilibić
Publisher: Springer
ISBN: 3319127128
Category : Nature
Languages : en
Pages : 302
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Book Description
The book encompasses a set of papers on meteorological tsunamis covering various aspects on this rare but potentially destructive multiresonant phenomenon. Altogether an editorial and 15 contributions are part of this book; eight of the contributions deal with different aspects of meteotsunamis along the U.S. East Coast and in the region of the Great Lakes, including one paper introducing a new methodology in meteotsunami research. Seven more papers are documenting meteotsunamis in various coastal areas of the world oceans. All continents, except Antarctica, have been covered, with the authors representing 11 countries. Previously Published in Natural Hazards, Volume 74, No. 1, 2014
Author: Wenhua Yu
Publisher: Artech House
ISBN: 1608078973
Category : Technology & Engineering
Languages : en
Pages : 597
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Book Description
This new resource covers the latest developments in computational electromagnetic methods, with emphasis on cutting-edge applications. This book is designed to extend existing literature to the latest development in computational electromagnetic methods, which are of interest to readers in both academic and industrial areas. The topics include advanced techniques in MoM, FEM and FDTD, spectral domain method, GPU and Phi hardware acceleration, metamaterials, frequency and time domain integral equations, and statistics methods in bio-electromagnetics.
Author: Massimiliano Vasile
Publisher: Springer Nature
ISBN: 3030601668
Category : Science
Languages : en
Pages : 573
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Book Description
In an expanding world with limited resources, optimization and uncertainty quantification have become a necessity when handling complex systems and processes. This book provides the foundational material necessary for those who wish to embark on advanced research at the limits of computability, collecting together lecture material from leading experts across the topics of optimization, uncertainty quantification and aerospace engineering. The aerospace sector in particular has stringent performance requirements on highly complex systems, for which solutions are expected to be optimal and reliable at the same time. The text covers a wide range of techniques and methods, from polynomial chaos expansions for uncertainty quantification to Bayesian and Imprecise Probability theories, and from Markov chains to surrogate models based on Gaussian processes. The book will serve as a valuable tool for practitioners, researchers and PhD students.
Author: Kok-Kwang Phoon
Publisher: CRC Press
ISBN: 1482227223
Category : Technology & Engineering
Languages : en
Pages : 624
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Book Description
Establishes Geotechnical Reliability as Fundamentally Distinct from Structural Reliability Reliability-based design is relatively well established in structural design. Its use is less mature in geotechnical design, but there is a steady progression towards reliability-based design as seen in the inclusion of a new Annex D on "Reliability of Geotechnical Structures" in the third edition of ISO 2394. Reliability-based design can be viewed as a simplified form of risk-based design where different consequences of failure are implicitly covered by the adoption of different target reliability indices. Explicit risk management methodologies are required for large geotechnical systems where soil and loading conditions are too varied to be conveniently slotted into a few reliability classes (typically three) and an associated simple discrete tier of target reliability indices. Provides Realistic Practical Guidance Risk and Reliability in Geotechnical Engineering makes these reliability and risk methodologies more accessible to practitioners and researchers by presenting soil statistics which are necessary inputs, by explaining how calculations can be carried out using simple tools, and by presenting illustrative or actual examples showcasing the benefits and limitations of these methodologies. With contributions from a broad international group of authors, this text: Presents probabilistic models suited for soil parameters Provides easy-to-use Excel-based methods for reliability analysis Connects reliability analysis to design codes (including LRFD and Eurocode 7) Maximizes value of information using Bayesian updating Contains efficient reliability analysis methods Accessible To a Wide Audience Risk and Reliability in Geotechnical Engineering presents all the "need-to-know" information for a non-specialist to calculate and interpret the reliability index and risk of geotechnical structures in a realistic and robust way. It suits engineers, researchers, and students who are interested in the practical outcomes of reliability and risk analyses without going into the intricacies of the underlying mathematical theories.
Author: Julien Baroth
Publisher: John Wiley & Sons
ISBN: 1118601122
Category : Technology & Engineering
Languages : en
Pages : 271
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Book Description
This book provides answers to the following problems: how to identify the most probable critical failures; how to describe and use data-concerning materials that are either heterogeneous, time-variant, or space-variant; how to quantify the reliability and lifetime of a system; how to use feedback information to actualize reliability results; and how to optimize an inspection politic or a maintenance strategy. Numerous authors from public research centers and firms propose a synthesis of methods, both new and well-known, and offer numerous examples concerning dams, geotechnical study, and structures from nuclear and civil engineering.
