Multiobjective Shape Design in Electricity and Magnetism
(Sprache: Englisch)
This book examines electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. It features a problem-solving approach which offers examples solved by various methods.
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Produktinformationen zu „Multiobjective Shape Design in Electricity and Magnetism “
This book examines electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. It features a problem-solving approach which offers examples solved by various methods.
Klappentext zu „Multiobjective Shape Design in Electricity and Magnetism “
Multiobjective Shape Design in Electricity and Magnetism is entirely focused on electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. Direct problems are solved by means of finite-element analysis, while evolutionary computing is used to solve multiobjective inverse problems. This approach, which is original, is coherently developed throughout the whole manuscript. The use of game theory, dynamic optimisation, and Bayesian imaging strengthens the originality of the book. Covering the development of multiobjective optimisation in the past ten years, Multiobjective Shape Design in Electricity and Magnetism is a concise, comprehensive and up-to-date introduction to this research field, which is growing in the community of electricity and magnetism. Theoretical issues are illustrated by practical examples. In particular, a test problem is solved by different methods so that, by comparison of results, advantages and limitations of the various methods are made clear.
Inhaltsverzeichnis zu „Multiobjective Shape Design in Electricity and Magnetism “
Preface. 1 INTRODUCTION. 2 INVERSE PROBLEMS AND ERROR MINIMISATION. 2.1 A Copernican revolution: direct and inverse problems. 2.2 Insidiousness of inverse problems. 2.3 Classification of inverse problems. 2.4 Green formula and Fredholm equation. 2.5 Solving inverse problems by minimising a functional. 2.6 Constrained minimisation. 2.7 Local vs global search. 2.8 Evolutionary computing. 2.9 Solving inverse problems by means of rectangular systems of algebraic equations. 3 A PARETIAN APPROACH TO MOSD THEORY. 3.1 Need of a multiobjective formulation. 3.2 Multiobjective formulation of a design problem. 3.3 Paretian optimality. 4 FIELD MODELS AND SHAPE DESIGN. 4.1 Maxwell equations in differential form. 4.2 Wave, diffusion and steady-state equations in terms of vectors. 4.3 Wave, diffusion and steady-state equations in terms of potentials. 4.4 Boundary and transmission conditions. 4.5 Insidiousness of direct problems. 4.6 Field-based inverse problems. 4.7 More insidious difficulties. 4.8 A unifying view of analysis and synthesis. 5 SOLVING MULTIOBJECTIVE OPTIMISATION PROBLEMS. 5.1 Classical methods of multiobjective optimisation. 5.2 Classical vs Paretian formulation. 5.3 Evolutionary methods of multiobjective optimisation. 5.4 Multi-objective evolution strategy (MOESTRA). 5.5 The gradient-balance method for 2D problems. 6 A FIELD-BASED BENCHMARK. 6.1 A twofold meaning of benchmarking. 6.2 Test problem: shape design of a magnetic pole. 6.3 The test problem simplified. 6.4 Criticism to Pareto optimality in the static case. 7 STATIC MOSD. 7.1 A bibliographic insight. 7.2 FEM-assisted optimal design. 7.3 Test problem: a priori analysis of the objective space. 7.4 Optimisation strategies and results. 7.5 Processing clusters. 7.6 The test problem solved by means of the GB method. 7.7 An industrial case study: permanent-magnet alternator. 8 MOVING ALONG THE PARETO FRONT. 8.1 John optimality. 8.2 Reconsidering the industrial case study. 8.3 Exploring the Pareto front. 8.4
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Optimising along the front. 9 SENSITIVITY ANALYSIS AND MOSD. 9.1 Discrete sets and perturbation domains. 9.2 Case study: superconducting magnetic-bearing design. 9.3 Design optimisation of the PM-HTSC interaction. 9.4 An inexpensive evaluation of sensitivity. 9.5 Results. 10 NON-CONFLICTING MULTIPLE OBJECTIVES. 10.1 Case study: a system for magnetic induction tomography. 10.2 Design problem. 10.3 Analysis problem. 10.4 Optimal shape design of the MIT antenna. 11 HIGHER-ORDER DIMENSIONALITY. 11.1 Case study: an electrostatic micromotor. 11.2 Field analysis: doubly-connected domain. 11.3 Field synthesis and rotor shape design. 11.4 Results. 11.5 A criterion for decision making. 12 MULTI-SCALE EVOLUTION STRATEGY. 12.1 Industrial electromagnetic design. 12.2 A multi-scale evolutionary search. 12.3 Permanent-magnet alternator design. 12.4 Results. 13 GAME THEORY AND MOSD. 13.1 From Pareto front to Nash equilibrium. 13.2 Theoretical background. 13.3 Analytical validation. 13.4 Numerical implementation. 13.5 Case study: permanent-magnet motor design. 14 DYNAMIC MOSD. 14.1 From static to dynamic conditions. 14.2 Theoretical background. 14.3 An analytical benchmark. 14.4 Criticism to dynamic Pareto optimality. 14.5 Numerical benchmark. 14.6 Direct problem. 14.7 Design problem. 14.8 Auxiliary inverse problems. 14.9 Main inverse problem: synthesising the device geometry. 14.10 Computational aspects. 14.11 Results I. 14.12 The design problem revisited: recovering steady state from time evolution. 14.13 Results II. 15 AN INTRODUCTION TO BAYESIAN PROBABILITY THEORY. 15.1 Bayesian conception of probability. 15.2 Prior distributions. 15.3 Bayesian inference vs maximum likelihood. 15.4 Bayesian non-parametric problems. 15.5 Model choice. 16 A BAYESIAN APPROACH TO MULTIOBJECTIVE OPTIMISATION. 16.1 Reasons for a new approach. 16.2 Weak regularity. 16.3 Local Bayesian formulation. 16.4 Integral Bayesian formulation. 16.5 Computation of the Bayesian terms. 16.6 Bayesian imaging. 17 BAYESI
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Autoren-Porträt von Paolo Di Barba
tional journals; relevant applications concern electrical power engineering as well as biomedical engineering.
Bibliographische Angaben
- Autor: Paolo Di Barba
- 2010, 313 Seiten, Maße: 16,4 x 24,3 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 9048130794
- ISBN-13: 9789048130795
Sprache:
Englisch
Rezension zu „Multiobjective Shape Design in Electricity and Magnetism “
"The intention of this book is to try to dispel some of the myths surrounding computer-based optimisation. Professor Di Barba provides an up-to-date and comprehensive overview of optimisation techniques related to electromagnetic devices and systems in a logical and consistent way. An understanding of the contents of this book can help a designer to use the computational resources that are now available in a much more effective manner."David A. Lowther Ph.D., AKC, FCAE, FIETJames McGill ProfessorDepartment of Electrical and Computer EngineeringMcGill University, Montreal
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