Download or read book Multi Level Monte Carlo Methods for Uncertainty Quantification and Robust Design Optimization in Aerodynamics written by Michele Pisaroni and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Mots-clés de l'auteur: Uncertainty Quantification ; Multi Level Monte Carlo ; Continuation Multi Level Monte Carlo ; Robust Design Optimization ; Reliability-based Design Optimization ; Optimization Under Uncertainties ; Aeronautics ; Aerodynamics.
Download or read book Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications written by Massimiliano Vasile and published by Springer Nature. This book was released on 2022-01-27 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2020 International Conference on Uncertainty Quantification & Optimization gathered together internationally renowned researchers in the fields of optimization and uncertainty quantification. The resulting proceedings cover all related aspects of computational uncertainty management and optimization, with particular emphasis on aerospace engineering problems. The book contributions are organized under four major themes: Applications of Uncertainty in Aerospace & Engineering Imprecise Probability, Theory and Applications Robust and Reliability-Based Design Optimisation in Aerospace Engineering Uncertainty Quantification, Identification and Calibration in Aerospace Models This proceedings volume is useful across disciplines, as it brings the expertise of theoretical and application researchers together in a unified framework.
Download or read book Efficient Uncertainty Quantification in Aerospace Analysis and Design written by Yi Zhang and published by . This book was released on 2013 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The main purpose of this study is to apply a computationally efficient uncertainty quantification approach, Non-Intrusive Polynomial Chaos (NIPC) based stochastic expansions, to robust aerospace analysis and design under mixed (aleatory and epistemic) uncertainties and demonstrate this technique on model problems and robust aerodynamic optimization. The proposed optimization approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes the stochastic measures which are minimized simultaneously to ensure the robustness of the final design to both aleatory and epistemic uncertainties. For model problems with mixed uncertainties, Quadrature-Based and Point-Collocation NIPC methods were used to create the response surfaces used in the optimization process. For the robust airfoil optimization under aleatory (Mach number) and epistemic (turbulence model) uncertainties, a combined Point-Collocation NIPC approach was utilized to create the response surfaces used as the surrogates in the optimization process. Two stochastic optimization formulations were studied: optimization under pure aleatory uncertainty and optimization under mixed uncertainty. As shown in this work for various problems, the NIPC method is computationally more efficient than Monte Carlo methods for moderate number of uncertain variables and can give highly accurate estimation of various metrics used in robust design optimization under mixed uncertainties. This study also introduces a new adaptive sampling approach to refine the Point-Collocation NIPC method for further improvement of the computational efficiency. Two numerical problems demonstrated that the adaptive approach can produce the same accuracy level of the response surface obtained with oversampling ratio of 2 using less function evaluations."--Abstract, page iii.
Download or read book Uncertainty Quantification of Engineering Systems Using the Multilevel Monte Carlo Method written by Helena Juliette Thomasin Unwin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Under Uncertainty with Applications to Aerospace Engineering written by Massimiliano Vasile and published by Springer Nature. This book was released on 2021-02-15 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Multilevel Monte Carlo Methods and Uncertainty Quantification written by Aretha Leonore Teckentrup and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such equations arise, for example, in stochastic groundwater ow modelling. Models for random coefficients frequently used in these applications, such as log-normal random fields with exponential covariance, lack uniform coercivity and boundedness with respect to the random parameter and have only limited spatial regularity. To give a rigorous bound on the cost of the multilevel Monte Carlo estimator to reach a desired accuracy, one needs to quantify the bias of the estimator. The bias, in this case, is the spatial discretisation error in the numerical solution of the partial differential equation. This thesis is concerned with establishing bounds on this discretisation error in the practically relevant and technically demanding case of coefficients which are not uniformly coercive or bounded with respect to the random parameter. Under mild assumptions on the regularity of the coefficient, we establish new results on the regularity of the solution for a variety of model problems. The most general case is that of a coefficient which is piecewise Hölder continuous with respect to a random partitioning of the domain. The established regularity of the solution is then combined with tools from classical discretisation error analysis to provide a full convergence analysis of the bias of the multilevel estimator for finite element and finite volume spatial discretisations. Our analysis covers as quantities of interest several spatial norms of the solution, as well as point evaluations of the solution and its gradient and any continuously Fréchet differentiable functional. Lastly, we extend the idea of multilevel Monte Carlo estimators to the framework of Markov chain Monte Carlo simulations. We develop a new multilevel version of a Metropolis Hastings algorithm, and provide a full convergence analysis.
Download or read book Multilevel Monte Carlo Methods for Uncertainty Quantification in Brain Simulations written by Matteo Croci and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multidisciplinary Design Optimization in Computational Mechanics written by Piotr Breitkopf and published by John Wiley & Sons. This book was released on 2013-02-04 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical and algorithmic methods for the Multidisciplinary Design Optimization (MDO) of complex mechanical systems such as aircraft or car engines. We have focused on the presentation of strategies efficiently and economically managing the different levels of complexity in coupled disciplines (e.g. structure, fluid, thermal, acoustics, etc.), ranging from Reduced Order Models (ROM) to full-scale Finite Element (FE) or Finite Volume (FV) simulations. Particular focus is given to the uncertainty quantification and its impact on the robustness of the optimal designs. A large collection of examples from academia, software editing and industry should also help the reader to develop a practical insight on MDO methods.
Download or read book Uncertainty Management for Robust Industrial Design in Aeronautics written by Charles Hirsch and published by Springer. This book was released on 2018-07-21 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations.
Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2016-10-20 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.
Download or read book Multi level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws written by Siddhartha Mishra (Mathematiker.) and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multi Level Monte Carlo Finite Volume Methods for Uncertainty Quantification of Acoustic Wave Propagation in Random Heterogeneous Layered Medium written by Siddharta Sankar Mishra and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Needs and Opportunities for Uncertainty Based Multidisciplinary Design Methods for Aerospace Vehicles written by and published by . This book was released on 2002 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization of Weighted Monte Carlo Methods written by Gennadii A. Mikhailov and published by Springer. This book was released on 1992-02-13 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent statistical experiments to be simulated simultaneously. The weighted Monte Carlo estimates are constructed in order to diminish errors and to obtain dependent estimates for the calculated functionals for different values of parameters of the problem, i.e., to improve the functional dependence. In addition, the weighted estimates make it possible to evaluate special functionals, for example, the derivatives with respect to the parameters. There are many works concerned with the development of the weighted estimates. In Chap. 1 we give the necessary information about these works and present a set of illustrations. The rest of the book is devoted to the solution of a series of mathematical problems related to the optimization of the weighted Monte Carlo estimates.
Download or read book Optimization Under Uncertainty written by Giovanni Petrone and published by . This book was released on 2012 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Trends in Structural and Solid Mechanics 3 written by Noel Challamel and published by John Wiley & Sons. This book was released on 2021-06-29 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book – comprised of three separate volumes – presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This third volume is devoted to non-deterministic mechanics. Modern Trends in Structural and Solid Mechanics 3 has broad scope, covering topics such: design optimization under uncertainty, interval field approaches, convex analysis, quantum inspired topology optimization and stochastic dynamics. The book is illustrated by many applications in the field of aerospace engineering, mechanical engineering, civil engineering, biomedical engineering and automotive engineering. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.
Download or read book Active Subspaces written by Paul G. Constantine and published by SIAM. This book was released on 2015-03-17 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
