Sparse Polynomial Chaos Expansions for Uncertainty Propagation and Sensitivity Analysis PDF Download
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Author: Bruno Sudret
Publisher:
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Languages : en
Pages :
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Author: Bruno Sudret
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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: 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: Ivica Vilibić
Publisher: Springer
ISBN: 3319127128
Category : Nature
Languages : en
Pages : 302
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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: Jan Peter Hessling
Publisher: BoD – Books on Demand
ISBN: 9535132792
Category : Computers
Languages : en
Pages : 228
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Uncertainty quantification may appear daunting for practitioners due to its inherent complexity but can be intriguing and rewarding for anyone with mathematical ambitions and genuine concern for modeling quality. Uncertainty quantification is what remains to be done when too much credibility has been invested in deterministic analyses and unwarranted assumptions. Model calibration describes the inverse operation targeting optimal prediction and refers to inference of best uncertain model estimates from experimental calibration data. The limited applicability of most state-of-the-art approaches to many of the large and complex calculations made today makes uncertainty quantification and model calibration major topics open for debate, with rapidly growing interest from both science and technology, addressing subtle questions such as credible predictions of climate heating.
Author: Bruno Sudret
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Themistocles M. Rassias
Publisher: Springer Nature
ISBN: 3030606228
Category : Mathematics
Languages : en
Pages : 546
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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: Janya-anurak, Chettapong
Publisher: KIT Scientific Publishing
ISBN: 3731506424
Category : Electronic computers. Computer science
Languages : en
Pages : 248
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Book Description
In this work, the Uncertainty Quantification (UQ) approaches combined systematically to analyze and identify systems. The generalized Polynomial Chaos (gPC) expansion is applied to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing the system systematically and reducing the disagreement between the model predictions and the measurements of the real processes to fulfill user defined performance criteria.
Author: Loïc Brevault
Publisher: Springer Nature
ISBN: 3030391264
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design.
Author: Zhanlin Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 103
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Uncertainties exist in both physics-based and data-driven models of systems. Understanding how system inputs affect a system output's uncertainty is essential to improve system outputs such as quality and productivity. Variance-based sensitivity analysis, which is widely used for uncertainty quantification, characterizes how the output variance is propagated from inputs. To estimate the variance-based sensitivity indices of the output with respect to inputs, polynomial chaos expansions (PCEs) are widely used. However, a majority of existing PCEs impose parametric distributional assumptions on inputs. Furthermore, existing sensitivity indices for dependent inputs impose strong assumptions on the dependence structure of the inputs or lack interpretability. Although recent studies proposed fully data-driven PCEs without strong assumptions on inputs, these PCEs are generally inefficient because the minimally required number of observations increases exponentially in the number of the inputs. To address these challenges, three data-driven PCEs are proposed in this dissertation. We first propose the sparse network PCE (SN-PCE) model for a broad class of systems whose input-output relationships are expressed as directed acyclic graphs. The proposed SN-PCE model accurately estimates variance-based sensitivity indices with far fewer observations than state-of-the-art black-box methods. Next, we propose data-driven sensitivity indices by constructing ordered partitions of linearly independent polynomials of dependent inputs for PCEs. The proposed sensitivity indices provide intuitive interpretations of how the dependent inputs affect the variance of the output without a priori knowledge of the dependence structure of the inputs. Finally, we propose a data-driven algorithm to build sparse PCEs for models with dependent inputs. The proposed algorithm not only reduces the number of minimally required observations but also improves upon the numerical stability and estimation accuracy of a state-of-the-art sparse PCE.
