Design Sensitivity Analysis and Optimization of Electromagnetic Systems

ISBN-13: 9789811302299 / Angielski / Twarda / 2018 / 368 str.

Il Han Park

Opis

This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems.

Spis treści

1. Introduction. 1.1 Optimal Design Process. 1.2 Design Steps of Electromagnetic System. 1.3 Design Variables. 1.4 Equations and Characteristics of Electromagnetic Systems. 1.4.1 Maxwell’s Equations and Governing Equations. 1.4.2 Characteristics of Electromagnetic Systems. 1.5 Design Sensitivity Analysis. 1.5.1 Finite Difference Method. 1.5.2 Discrete Method. 1.5.3 Continuum Method.

2. Variational Formulation of Electromagnetic Systems. 2.1 Variational Formulation of Electrostatic System. 2.1.1 Differential State Equation. 2.1.2 Variational State Equation. 2.2 Variational Formulation of Magnetostatic System. 2.2.1 Differential State Equation. 2.2.2 Variational State Equation. 2.3 Variational Formulation of Eddy Current System. 2.3.1 Differential State Equation. 2.3.2 Variational State Equation. 2.4 Variational Formulation of DC Conductor System. 2.4.1 Differential State Equation. 2.4.2 Variational State Equation.

3. Continuum Shape Design Sensitivity of Electrostatic System. 3.1 Material Derivative and Formula. 3.1.1 Material Derivative. 3.1.2 Material Derivative Formula. 3.2 Shape Sensitivity of Outer Boundary. 3.2.1 Problem Definition and Objective Function. 3.2.2 Lagrange Multiplier Method for Sensitivity Derivation. 3.2.3 Adjoint Variable Method for Sensitivity Analysis. 3.2.4 Boundary Expression of Shape Sensitivity. 3.2.5 Analytical Example. 3.2.6 Numerical Examples. 3.3 Shape Sensitivity of Outer Boundary for System Energy. 3.3.1 Problem Definition. 3.3.2 Lagrange Multiplier Method for Energy Sensitivity. 3.3.3 Adjoint Variable Method for Sensitivity Analysis. 3.3.4 Boundary Expression of Shape Sensitivity. 3.3.5 Source Condition and Capacitance Sensitivity. 3.3.6 Analytical Example. 3.3.7 Numerical Examples. 3.4 Shape Sensitivity of Interface. 3.4.1 Problem Definition and Objective Function. 3.4.2 Lagrange Multiplier Method for Sensitivity Derivation. 3.4.3 Adjoint Variable Method for Sensitivity Analysis. 3.4.4 Boundary Expression of Shape Sensitivity. 3.4.5 Analytical Example. 3.4.6 Numerical Example. 3.5 Shape Sensitivity of Interface for System Energy. 3.5.1 Problem Definition. 3.5.2 Lagrange Multiplier Method for Energy Sensitivity. 3.5.3 Adjoint Variable Method for Sensitivity Analysis. 3.5.4 Boundary Expression of Shape Sensitivity. 3.5.5 Source Condition and Capacitance Sensitivity. 3.5.6 Analytical Example. 3.5.7 Numerical Examples.

 

4. Continuum Shape Design Sensitivity of Magnetostatic System. 4.1 Interface Shape Sensitivity. 4.1.1 Problem Definition and Objective Function. 4.1.2 Lagrange Multiplier Method for Sensitivity Derivation. 4.1.3 Adjoint Variable Method for Sensitivity Analysis. 4.1.4 Boundary Expression of Shape Sensitivity. 4.1.5 Interface Problems. 4.1.6 Analytical Example. 4.1.7 Numerical Examples. 4.2 Interface Shape Sensitivity for System Energy. 4.2.1 Problem Definition. 4.2.2 Lagrange Multiplier Method for Energy Sensitivity. 4.2.3 Adjoint Variable Method for Sensitivity Analysis. 4.2.4 Boundary Expression of Shape Sensitivity. 4.2.5 Interface Problems. 4.2.6 Source Condition and Inductance Sensitivity. 4.2.7 Analytical Examples. 4.2.8 Numerical Examples.

 

5. Continuum Shape Design Sensitivity of Eddy Current System. 5.1 Interface Shape Sensitivity. 5.1.1 Problem Definition and Objective Function. 5.1.2 Lagrange Multiplier Method for Sensitivity Derivation. 5.1.3 Adjoint Variable Method for Sensitivity Analysis. 5.1.4 Boundary Expression of Shape Sensitivity. 5.1.5 Interface Problems. 5.1.6 Numerical Examples. 5.2 Interface Shape Sensitivity for System Power. 5.2.1 Problem Definition. 5.2.2 Adjoint Variable Method for Power Sensitivity. 5.2.3 Boundary Expression of Shape Sensitivity. 5.2.4 Sensitivities of Resistance and Inductance. 5.2.5 Numerical Examples.

 

6. Continuum Shape Design Sensitivity of DC Conductor System. 6.1 Shape Sensitivity of Outer Boundary. 6.1.1 Problem Definition and Objective Function. 6.1.2 Lagrange Multiplier Method for Sensitivity Derivation. 6.1.3 Adjoint Variable Method for Sensitivity Analysis. 6.1.4 Boundary Expression of Shape Sensitivity. 6.2 Shape Sensitivity of Outer Boundary for Joule loss power. 6.2.1 Problem Definition. 6.2.2 Boundary Expression of Shape Sensitivity. 6.2.3 Resistance Sensitivity. 6.2.4 Analytical Examples. 6.2.5 Numerical Examples.

 

7. Level Set Method and Continuum Sensitivity. 7.1 Level Set Method. 7.2 Coupling of Continuum Sensitivity and Level Set Method. 7.3 Numerical Considerations.

 

8. Hole and Dot Sensitivity for Topology Optimization. 8.1 Hole Sensitivity. 8.1.1 Hole Sensitivity in Dielectric Material. 8.1.2 Hole Sensitivity in Magnetic Material. 8.1.3 Numerical Examples. 8.2 Dot Sensitivity. 8.2.1 Dot Sensitivity in Dielectric Material. 8.2.2 Dot Sensitivity in Magnetic Material. 8.2.3 Numerical Examples. 

 

Appendix A. More Examples of Electrostatic System. A.1 Outer Boundary Design. A.2 Outer Boundary Design for System Energy. A.3 Interface Design. A.4 Interface Design for System Energy. 

Appendix B. More Examples of Magnetostatic System. B.1 Interface Design. B.2 Interface Design for System Energy.

Appendix C. More Examples of Eddy Current System. C.1 Interface Design for System Power. 

Appendix D. More Examples of DC Conductor System. D.1 Outer Boundary Design for Joule Loss Power.

O autorze

Il-Han Park (PhD Seoul National University) is a Professor in the department of Electronic and Electrical Engineering at Sungkyunkwan University. His main interests are in optimization and numerical analysis of electromagnetic systems. His optimization method is based on the design sensitivity analysis for the shape and topology design, and the numerical analysis is focused on the multi-physics electromagnetic problems coupled with the mechanical systems; deformation, dynamics, fluidics, heat transfer.

Blurb

This book presents a comprehensive introduction to design sensitivity analysis theory as applied to electromagnetic systems. It treats the subject in a unified manner, providing numerical methods and design examples. The specific focus is on continuum design sensitivity analysis, which offers significant advantages over discrete design sensitivity methods. Continuum design sensitivity formulas are derived from the material derivative in continuum mechanics and the variational form of the governing equation. Continuum sensitivity analysis is applied to Maxwell equations of electrostatic, magnetostatic and eddy-current systems, and then the sensitivity formulas for each system are derived in a closed form; an integration along the design interface.

The book also introduces the recent breakthrough of the topology optimization method, which is accomplished by coupling the level set method and continuum design sensitivity. This topology optimization method enhances the possibility of the global minimum with minimised computational time, and in addition the evolving shapes during the iterative design process are easily captured in the level set equation. Moreover, since the optimization algorithm is transformed into a well-known transient analysis algorithm for differential equations, its numerical implementation becomes very simple and convenient.

Despite the complex derivation processes and mathematical expressions, the obtained sensitivity formulas are very straightforward for numerical implementation. This book provides detailed explanation of the background theory and the derivation process, which will help readers understand the design method and will set the foundation for advanced research in the future.