Shape Optimization Under Uncertainty

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Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View

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Author : Harald Held
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30

Shape Optimization Under Uncertainty From A Stochastic Programming Point Of View written by Harald Held and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Mathematics categories.

Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.

Optimization And Anti Optimization Of Structures Under Uncertainty

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Author : Isaac Elishakoff
language : en
Publisher: World Scientific
Release Date : 2010

Optimization And Anti Optimization Of Structures Under Uncertainty written by Isaac Elishakoff and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

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.

Free Form Airfoil Shape Optimization Under Uncertainty Using Maximum Expected Value And Second Order Second Moment Strategies

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Author :
language : en
Publisher:
Release Date : 2001

Free Form Airfoil Shape Optimization Under Uncertainty Using Maximum Expected Value And Second Order Second Moment Strategies written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

Free-form shape optimization of airfoils poses unexpected difficulties. Practical experience has indicated that a deterministic optimization for discrete operating conditions can result in dramatically inferior performance when the actual operating conditions are different from the - somewhat arbitrary - design values used for the optimization. Extensions to multi-point optimization have proven unable to adequately remedy this problem of "localized optimization" near the sampled operating conditions. This paper presents an intrinsically statistical approach and demonstrates how the shortcomings of multi-point optimization with respect to "localized optimization" can be overcome. The practical examples also reveal how the relative likelihood of each of the operating conditions is automatically taken into consideration during the optimization process. This is a key advantage over the use of multipoint methods.

Optimization Under Uncertainty With Applications To Aerospace Engineering

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Author : Massimiliano Vasile
language : en
Publisher: Springer Nature
Release Date : 2021-02-15

Optimization Under Uncertainty With Applications To Aerospace Engineering written by Massimiliano Vasile and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-15 with Science categories.

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.

Design Optimization Under Uncertainty

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Author : Weifei Hu
language : en
Publisher: Springer Nature
Release Date : 2023-12-22

Design Optimization Under Uncertainty written by Weifei Hu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-22 with Mathematics categories.

This book introduces the fundamentals of probability, statistical, and reliability concepts, the classical methods of uncertainty quantification and analytical reliability analysis, and the state-of-the-art approaches of design optimization under uncertainty (e.g., reliability-based design optimization and robust design optimization). The topics include basic concepts of probability and distributions, uncertainty quantification using probabilistic methods, classical reliability analysis methods, time-variant reliability analysis methods, fundamentals of deterministic design optimization, reliability-based design optimization, robust design optimization, other methods of design optimization under uncertainty, and engineering applications of design optimization under uncertainty.

Advances In Uncertainty Quantification And Optimization Under Uncertainty With Aerospace Applications

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Author : Massimiliano Vasile
language : en
Publisher: Springer Nature
Release Date : 2022-01-27

Advances In Uncertainty Quantification And Optimization Under Uncertainty With Aerospace Applications written by Massimiliano Vasile and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Technology & Engineering categories.

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.

Optimal Control Of Pdes Under Uncertainty

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Author : Jesús Martínez-Frutos
language : en
Publisher: Springer
Release Date : 2018-08-30

Optimal Control Of Pdes Under Uncertainty written by Jesús Martínez-Frutos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-30 with Mathematics categories.

This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.

Advances In Visualization And Optimization Techniques For Multidisciplinary Research

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Author : Dean Vucinic
language : en
Publisher: Springer Nature
Release Date : 2019-09-27

Advances In Visualization And Optimization Techniques For Multidisciplinary Research written by Dean Vucinic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-27 with Technology & Engineering categories.

This volume presents several multidisciplinary approaches to the visual representation of data acquired from experiments. As an expansion of these approaches, it is also possible to include data examination generated by mathematical-physical modeling. Imaging Systems encompass any subject related to digital images, from fundamental requirements for a correct image acquisition to computational algorithms that make it possible to obtain relevant information for image analysis. In this context, the book presents selected contributions of a special session at the Conference on Advanced Computational Engineering and Experimenting (ACE-X) 2016.

Evolutionary Computation In Dynamic And Uncertain Environments

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Author : Shengxiang Yang
language : en
Publisher: Springer
Release Date : 2007-04-03

Evolutionary Computation In Dynamic And Uncertain Environments written by Shengxiang Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-03 with Technology & Engineering categories.

This book compiles recent advances of evolutionary algorithms in dynamic and uncertain environments within a unified framework. The book is motivated by the fact that some degree of uncertainty is inevitable in characterizing any realistic engineering systems. Discussion includes representative methods for addressing major sources of uncertainties in evolutionary computation, including handle of noisy fitness functions, use of approximate fitness functions, search for robust solutions, and tracking moving optimums.

Nanoelectronic Coupled Problems Solutions

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Author : E. Jan W. ter Maten
language : en
Publisher: Springer Nature
Release Date : 2019-11-06

Nanoelectronic Coupled Problems Solutions written by E. Jan W. ter Maten and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-06 with Mathematics categories.

Designs in nanoelectronics often lead to challenging simulation problems and include strong feedback couplings. Industry demands provisions for variability in order to guarantee quality and yield. It also requires the incorporation of higher abstraction levels to allow for system simulation in order to shorten the design cycles, while at the same time preserving accuracy. The methods developed here promote a methodology for circuit-and-system-level modelling and simulation based on best practice rules, which are used to deal with coupled electromagnetic field-circuit-heat problems, as well as coupled electro-thermal-stress problems that emerge in nanoelectronic designs. This book covers: (1) advanced monolithic/multirate/co-simulation techniques, which are combined with envelope/wavelet approaches to create efficient and robust simulation techniques for strongly coupled systems that exploit the different dynamics of sub-systems within multiphysics problems, and which allow designers to predict reliability and ageing; (2) new generalized techniques in Uncertainty Quantification (UQ) for coupled problems to include a variability capability such that robust design and optimization, worst case analysis, and yield estimation with tiny failure probabilities are possible (including large deviations like 6-sigma); (3) enhanced sparse, parametric Model Order Reduction techniques with a posteriori error estimation for coupled problems and for UQ to reduce the complexity of the sub-systems while ensuring that the operational and coupling parameters can still be varied and that the reduced models offer higher abstraction levels that can be efficiently simulated. All the new algorithms produced were implemented, transferred and tested by the EDA vendor MAGWEL. Validation was conducted on industrial designs provided by end-users from the semiconductor industry, who shared their feedback, contributed to the measurements, and supplied both material data and process data. In closing, a thorough comparison to measurements on real devices was made in order to demonstrate the algorithms’ industrial applicability.