Multiobjective Shape Design in Electricity and Magnetism

ISBN-13: 9789048130795 / Angielski / Twarda / 2010 / 313 str.

Paolo Di Barba

Opis

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.

Recenzje

"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, FIET
James McGill Professor
Department of Electrical and Computer Engineering
McGill University, Montreal

Spis treści

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 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

O autorze

Paolo DI BARBA graduated in Electronic Engineering (MSc) in the year 1987-1988 at the University of Pavia, Italy. He obtained the PhD degree in Electrical Engineering from the Technical University of Lodz, Poland, in the year 2001-2002. At the time being, he is a full professor of electrical engineering (tenure position) at the University of Pavia, Faculty of Engineering. He is a member of the steering committees of some international symposia in the area of computational electromagnetism, in particular: Intl Symposium on Electromagnetic Fields in Electrical Engineering (ISEF), Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE).

The scientific interests of the author include the computer-aided design of electric, magnetic and electromechanical devices with special emphasis on the methodologies for multi-objective optimisation in electromagnetism. He is author of more than 100 papers, either presented to international conferences or published in international journals; relevant applications concern electrical power engineering as well as biomedical engineering.

Blurb

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.

Topics covered include:

• Maxwell equations and boundary-value problems;
• Paretian optimality;
• static optimisation;
• game theory;
• dynamic optimisation;
• Bayesian imaging.

Multiobjective Shape Design in Electricity and Magnetism collects the long-lasting experience matured by the author during his research activity both at the university and in cooperation with industrial laboratories.