Uncertain Input Data Problems And The Worst Scenario Method

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Uncertain Input Data Problems and the Worst Scenario Method

Ivan Hlavacek,Jan Chleboun,Ivo Babuska
Uncertain Input Data Problems and the Worst Scenario Method Book PDF

Author : Ivan Hlavacek,Jan Chleboun,Ivo Babuska
Publisher : Elsevier
Page : 485 pages
File Size : 46,9 Mb
Release : 2004-12-09
Category : Science
ISBN : 9780080543376

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Uncertain Input Data Problems and the Worst Scenario Method by Ivan Hlavacek,Jan Chleboun,Ivo Babuska Pdf

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience. · Rigorous theory is established for the treatment of uncertainty in modeling· Uncertainty is considered in complex models based on partial differential equations or variational inequalities · Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more · Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present· Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form· Fairly self-contained book

Numerical Mathematics and Advanced Applications

Karl Kunisch,Günther Of,Olaf Steinbach
Numerical Mathematics and Advanced Applications Book PDF

Author : Karl Kunisch,Günther Of,Olaf Steinbach
Publisher : Springer Science & Business Media
Page : 825 pages
File Size : 55,6 Mb
Release : 2008-09-19
Category : Mathematics
ISBN : 9783540697770

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Numerical Mathematics and Advanced Applications by Karl Kunisch,Günther Of,Olaf Steinbach Pdf

The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.

Optimization and Anti-optimization of Structures Under Uncertainty

Isaac Elishakoff,Makoto Ohsaki
Optimization and Anti optimization of Structures Under Uncertainty Book PDF

Author : Isaac Elishakoff,Makoto Ohsaki
Publisher : World Scientific
Page : 425 pages
File Size : 45,9 Mb
Release : 2010
Category : Technology & Engineering
ISBN : 9781848164772

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Optimization and Anti-optimization of Structures Under Uncertainty by Isaac Elishakoff,Makoto Ohsaki Pdf

The volume presents a collaboration between internationally recognized experts on anti-optimization and structural optimization, and summarizes various novel ideas, methodologies and results studied over 20 years. The book vividly demonstrates how the concept of uncertainty should be incorporated in a rigorous manner during the process of designing real-world structures. The necessity of anti-optimization approach is first demonstrated, then the anti-optimization techniques are applied to static, dynamic and buckling problems, thus covering the broadest possible set of applications. Finally, anti-optimization is fully utilized by a combination of structural optimization to produce the optimal design considering the worst-case scenario. This is currently the only book that covers the combination of optimization and anti-optimization. It shows how various optimization techniques are used in the novel anti-optimization technique, and how the structural optimization can be exponentially enhanced by incorporating the concept of worst-case scenario, thereby increasing the safety of the structures designed in various fields of engineering.

Mathematical and Computational Methods in Biomechanics of Human Skeletal Systems

Jiri Nedoma,Jiri Stehlik,Ivan Hlavacek,Josef Danek,Tatjana Dostalova,Petra Preckova
Mathematical and Computational Methods in Biomechanics of Human Skeletal Systems Book PDF

Author : Jiri Nedoma,Jiri Stehlik,Ivan Hlavacek,Josef Danek,Tatjana Dostalova,Petra Preckova
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 49,8 Mb
Release : 2011-06-09
Category : Science
ISBN : 9781118006467

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Mathematical and Computational Methods in Biomechanics of Human Skeletal Systems by Jiri Nedoma,Jiri Stehlik,Ivan Hlavacek,Josef Danek,Tatjana Dostalova,Petra Preckova Pdf

Cutting-edge solutions to current problems in orthopedics, supported by modeling and numerical analysis Despite the current successful methods and achievements of good joint implantations, it is essential to further optimize the shape of implants so they may better resist extreme long-term mechanical demands. This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplasty The definition of selected simulated orthopedic problems Constructions of mathematical model problems of the biomechanics of the human skeleton and its parts Replacement parts of the human skeleton and corresponding mathematical model problems Detailed mathematical analyses of mathematical models based on functional analysis and finite element methods Biomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacements A discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomography This timely book offers a wealth of information on the current research in this field. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models. This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.

Numerical Approximation of the Magnetoquasistatic Model with Uncertainties

Ulrich Römer
Numerical Approximation of the Magnetoquasistatic Model with Uncertainties Book PDF

Author : Ulrich Römer
Publisher : Springer
Page : 114 pages
File Size : 52,7 Mb
Release : 2016-07-27
Category : Technology & Engineering
ISBN : 9783319412948

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Numerical Approximation of the Magnetoquasistatic Model with Uncertainties by Ulrich Römer Pdf

This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.

Computational Science — ICCS 2002

Peter M.A. Sloot,C.J. Kenneth Tan,Jack J. Dongarra,Alfons G. Hoekstra
Computational Science ICCS 2002 Book PDF

Author : Peter M.A. Sloot,C.J. Kenneth Tan,Jack J. Dongarra,Alfons G. Hoekstra
Publisher : Springer
Page : 1230 pages
File Size : 46,6 Mb
Release : 2003-08-01
Category : Computers
ISBN : 9783540477891

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Computational Science — ICCS 2002 by Peter M.A. Sloot,C.J. Kenneth Tan,Jack J. Dongarra,Alfons G. Hoekstra Pdf

Computational Science is the scientific discipline that aims at the development and understanding of new computational methods and techniques to model and simulate complex systems. The area of application includes natural systems - such as biology environ mental and geo-sciences, physics, and chemistry - and synthetic systems such as electronics and financial and economic systems. The discipline is a bridge bet ween 'classical' computer science - logic, complexity, architecture, algorithm- mathematics, and the use of computers in the aforementioned areas. The relevance for society stems from the numerous challenges that exist in the various science and engineering disciplines, which can be tackled by advances made in this field. For instance new models and methods to study environmental issues like the quality of air, water, and soil, and weather and climate predictions through simulations, as well as the simulation-supported development of cars, airplanes, and medical and transport systems etc. Paraphrasing R. Kenway (R.D. Kenway, Contemporary Physics. 1994): 'There is an important message to scientists, politicians, and industrialists: in the future science, the best industrial design and manufacture, the greatest medical progress, and the most accurate environmental monitoring and forecasting will be done by countries that most rapidly exploit the full potential of computational science'. Nowadays we have access to high-end computer architectures and a large range of computing environments, mainly as a consequence of the enormous sti mulus from the various international programs on advanced computing, e.g.

Combinatorial Optimization Under Uncertainty

Ritu Arora,Shalini Arora,Anand J Kulkarni,Patrick Siarry
Combinatorial Optimization Under Uncertainty Book PDF

Author : Ritu Arora,Shalini Arora,Anand J Kulkarni,Patrick Siarry
Publisher : CRC Press
Page : 184 pages
File Size : 46,8 Mb
Release : 2023-05-12
Category : Business & Economics
ISBN : 9781000859850

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Combinatorial Optimization Under Uncertainty by Ritu Arora,Shalini Arora,Anand J Kulkarni,Patrick Siarry Pdf

This book discusses the basic ideas, underlying principles, mathematical formulations, analysis and applications of the different combinatorial problems under uncertainty and attempts to provide solutions for the same. Uncertainty influences the behaviour of the market to a great extent. Global pandemics and calamities are other factors which affect and augment unpredictability in the market. The intent of this book is to develop mathematical structures for different aspects of allocation problems depicting real life scenarios. The novel methods which are incorporated in practical scenarios under uncertain circumstances include the STAR heuristic approach, Matrix geometric method, Ranking function and Pythagorean fuzzy numbers, to name a few. Distinct problems which are considered in this book under uncertainty include scheduling, cyclic bottleneck assignment problem, bilevel transportation problem, multi-index transportation problem, retrial queuing, uncertain matrix games, optimal production evaluation of cotton in different soil and water conditions, the healthcare sector, intuitionistic fuzzy quadratic programming problem, and multi-objective optimization problem. This book may serve as a valuable reference for researchers working in the domain of optimization for solving combinatorial problems under uncertainty. The contributions of this book may further help to explore new avenues leading toward multidisciplinary research discussions.

Design Methods for Reducing Failure Probabilities with Examples from Electrical Engineering

Mona Fuhrländer
Design Methods for Reducing Failure Probabilities with Examples from Electrical Engineering Book PDF

Author : Mona Fuhrländer
Publisher : Springer Nature
Page : 168 pages
File Size : 44,9 Mb
Release : 2023-08-28
Category : Technology & Engineering
ISBN : 9783031370199

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Design Methods for Reducing Failure Probabilities with Examples from Electrical Engineering by Mona Fuhrländer Pdf

This book deals with efficient estimation and optimization methods to improve the design of electrotechnical devices under uncertainty. Uncertainties caused by manufacturing imperfections, natural material variations, or unpredictable environmental influences, may lead, in turn, to deviations in operation. This book describes two novel methods for yield (or failure probability) estimation. Both are hybrid methods that combine the accuracy of Monte Carlo with the efficiency of surrogate models. The SC-Hybrid approach uses stochastic collocation and adjoint error indicators. The non-intrusive GPR-Hybrid approach consists of a Gaussian process regression that allows surrogate model updates on the fly. Furthermore, the book proposes an adaptive Newton-Monte-Carlo (Newton-MC) method for efficient yield optimization. In turn, to solve optimization problems with mixed gradient information, two novel Hermite-type optimization methods are described. All the proposed methods have been numerically evaluated on two benchmark problems, such as a rectangular waveguide and a permanent magnet synchronous machine. Results showed that the new methods can significantly reduce the computational effort of yield estimation, and of single- and multi-objective yield optimization under uncertainty. All in all, this book presents novel strategies for quantification of uncertainty and optimization under uncertainty, with practical details to improve the design of electrotechnical devices, yet the methods can be used for any design process affected by uncertainties.

Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells

Isaac Elishakoff
Dramatic Effect of Cross Correlations in Random Vibrations of Discrete Systems Beams Plates and Shells Book PDF

Author : Isaac Elishakoff
Publisher : Springer Nature
Page : 356 pages
File Size : 48,9 Mb
Release : 2020-04-11
Category : Technology & Engineering
ISBN : 9783030403942

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Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells by Isaac Elishakoff Pdf

This volume explains the dramatic effect of cross-correlations in forming the structural response of aircraft in turbulent excitation, ships in rough seas, cars on irregular roads, and other dynamic regimes. It brings into sharp focus the dramatic effect of cross correlations often neglected due to the analytical difficulty of their evaluation. Veteran author Professor Isaac Elishakoff illustrates how neglect of cross correlations could result in underestimation of the response by tens or hundreds of percentages the effect of the random vibrations of structures’ main elements, including beams, plates, and shells.

Philosophies of Structural Safety and Reliability

Vladimir Raizer,Isaac Elishakoff
Philosophies of Structural Safety and Reliability Book PDF

Author : Vladimir Raizer,Isaac Elishakoff
Publisher : CRC Press
Page : 266 pages
File Size : 49,6 Mb
Release : 2022-07-28
Category : Technology & Engineering
ISBN : 9781000550740

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Philosophies of Structural Safety and Reliability by Vladimir Raizer,Isaac Elishakoff Pdf

Uncertainty is certain to be found in structural engineering, making it crucial to structure design. This book covers three competing philosophies behind structural safety and reliability: probabilistic analysis, fuzzy set-based treatments, and the convex approach. Explaining the theory behind probabilistic analysis, fuzzy set-based treatments, and the convex approach in detail, alongside their implementation, use, and benefits, the book compares and contrasts these methods, enabling the reader to solve problems associated with uncertainty. These uncertainty issues can be seen in civil engineering structures, risk of earthquakes, impact of rough seas on ships, and turbulence affecting aerospace vehicles. Building on the authors’ many years of experience in the field, Philosophies of Structural Safety and Reliability is an essential guide to structural uncertainty. Topics covered in the book include properties of materials and their structural deterioration, safety factor and reliability, risk evaluation and loads, and their combinations. This book will be of interest to students and professionals in the fields of aerospace, civil, mechanical, marine, and ocean engineering.

Interval Methods for Uncertain Power System Analysis

Alfredo Vaccaro
Interval Methods for Uncertain Power System Analysis Book PDF

Author : Alfredo Vaccaro
Publisher : John Wiley & Sons
Page : 148 pages
File Size : 40,5 Mb
Release : 2023-07-12
Category : Technology & Engineering
ISBN : 9781119855064

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Interval Methods for Uncertain Power System Analysis by Alfredo Vaccaro Pdf

Interval Methods for Uncertain Power System Analysis In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples. The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as: A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis In-depth examinations of uncertain optimal power flow analysis Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.

Nonsmooth Mechanics and Convex Optimization

Yoshihiro Kanno
Nonsmooth Mechanics and Convex Optimization Book PDF

Author : Yoshihiro Kanno
Publisher : CRC Press
Page : 447 pages
File Size : 41,8 Mb
Release : 2011-04-05
Category : Science
ISBN : 9781420094237

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Nonsmooth Mechanics and Convex Optimization by Yoshihiro Kanno Pdf

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity... I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimization." — Prof. Graham M.L. Gladwell, Distinguished Professor Emeritus, University of Waterloo, Fellow of the Royal Society of Canada "... reads very well—the structure is good, the language and style are clear and fluent, and the material is rendered accessible by a careful presentation that contains many concrete examples. The range of applications, particularly to problems in mechanics, is admirable and a valuable complement to theoretical and computational investigations that are at the forefront of the areas concerned." — Prof. B. Daya Reddy, Department of Mathematics and Applied Mathematics, Director of Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa "Many materials and structures (e.g., cable networks, membrane) involved in practical engineering applications have complex responses that cannot be described by smooth constitutive relations. ... The author shows how these difficult problems can be tackled in the framework of convex analysis by arranging the carefully chosen materials in an elegant way. Most of the contents of the book are from the original contributions of the author. They are both mathematically rigorous and readable. This book is a must-read for anyone who intends to get an authoritative and state-of-art description for the analysis of nonsmooth mechanics problems with theory and tools from convex analysis." — Prof. Xu Guo, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology

A Posteriori Estimates for Partial Differential Equations

Sergey I. Repin
A Posteriori Estimates for Partial Differential Equations Book PDF

Author : Sergey I. Repin
Publisher : Walter de Gruyter
Page : 329 pages
File Size : 47,5 Mb
Release : 2008-10-31
Category : Mathematics
ISBN : 9783110203042

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A Posteriori Estimates for Partial Differential Equations by Sergey I. Repin Pdf

This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.

Decision Making Applications in Modern Power Systems

Shady H.E. Abdel Aleem,Almoataz Youssef Abdelaziz,Ahmed F. Zobaa,Ramesh Bansal
Decision Making Applications in Modern Power Systems Book PDF

Author : Shady H.E. Abdel Aleem,Almoataz Youssef Abdelaziz,Ahmed F. Zobaa,Ramesh Bansal
Publisher : Academic Press
Page : 576 pages
File Size : 47,5 Mb
Release : 2019-09-21
Category : Science
ISBN : 9780128166260

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Decision Making Applications in Modern Power Systems by Shady H.E. Abdel Aleem,Almoataz Youssef Abdelaziz,Ahmed F. Zobaa,Ramesh Bansal Pdf

Decision Making Applications in Modern Power Systems presents an enhanced decision-making framework for power systems. Designed as an introduction to enhanced electricity system analysis using decision-making tools, it provides an overview of the different elements, levels and actors involved within an integrated framework for decision-making in the power sector. In addition, it presents a state-of-play on current energy systems, strategies, alternatives, viewpoints and priorities in support of decision-making in the electric power sector, including discussions of energy storage and smart grids. As a practical training guide on theoretical developments and the application of advanced methods for practical electrical energy engineering problems, this reference is ideal for use in establishing medium-term and long-term strategic plans for the electric power and energy sectors. Provides panoramic coverage of state-of-the-art energy systems, strategies and priorities in support of electrical power decision-making Introduces innovative research outcomes, programs, algorithms and approaches to address challenges in understanding, creating and managing complex techno-socio-economic engineering systems Includes practical training on theoretical developments and the application of advanced methods for realistic electrical energy engineering problems

Resolution Of The Twentieth Century Conundrum In Elastic Stability

Isaac E Elishakoff
Resolution Of The Twentieth Century Conundrum In Elastic Stability Book PDF

Author : Isaac E Elishakoff
Publisher : World Scientific
Page : 352 pages
File Size : 50,5 Mb
Release : 2014-05-29
Category : Technology & Engineering
ISBN : 9789814583558

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Resolution Of The Twentieth Century Conundrum In Elastic Stability by Isaac E Elishakoff Pdf

There have been stability theories developed for beams, plates and shells — the most significant elements in mechanical, aerospace, ocean and marine engineering. For beams and plates, the theoretical and experimental values of buckling loads are in close vicinity. However for thin shells, the experimental predictions do not conform with the theory, due to presence of small geometric imperfections that are deviations from the ideal shape.This fact has been referred to in the literature as ‘embarrassing’, ‘paradoxical’ and ‘perplexing’. Indeed, the popular adage, “In theory there is no difference between theory and practice. In practice there is”, very much applies to thin shells whose experimental buckling loads may constitute a small fraction of the theoretical prediction based on classical linear theory; because in practice, engineers use knockdown factors that are not theoretically substantiated.This book presents a uniform approach that tames this prima-donna-like and capricious behavior of structures that has been dubbed the ‘imperfection sensitivity’ — thus resolving the conundrum that has occupied the best minds of elastic stability throughout the twentieth century.