Hyang-Beom Lee

Inverse problem application of topology optimization method with mutual energy concept and design sensitivity

In this paper, a new topology optimization technique that incorporates design sensitivity and mutual energy concept is presented and applied to the inverse problem. The sensitivity in each design cell is calculated directly from potential distribution obtained from FEM (finite element method) simulation, and the material property in each cell is changed simultaneously using sensitivity information. The steepest-descent method is used as an optimization technique. The proposed method is applied to a numerical model whose permittivity of the design region is under consideration.

Design sensitivity analysis for transient eddy current problems using finite element discretization and adjoint variable method

For shape design problems subjected to the transient eddy current equation, a shape design sensitivity expressed explicitly in terms of design variables is derived using a discrete system equation of finite elements and an adjoint equation method. The original state equation is an initial-value problem which is to be solved by time-stepping finite element method. On the other hand, the adjoint equation is obtained as a terminal-value problem which is also to be solved by time-stepping finite element method. With the state and adjoint variables solved, the sensitivity is evaluated, which is employed in a gradient-based optimization algorithm. As a numerical example, an eddy current distribution control on a metal surface is treated using the proposed method in an induction heating system.

Design sensitivity analysis for steady state eddy current problems by continuum approach

In two dimensional steady state eddy current problems, the exact sensitivity formula to the interface shape variation is derived using the material derivative concept of continuum mechanics and an adjoint variable method. The obtained sensitivity formula is expressed in a line integral along the interface and it is calculated using the existing finite element analysis codes. For the rotor slot shape design of the induction motor driven by balanced 3-phase voltage source, the sensitivity for voltage source problems is calculated with the sensitivity for current source problems and the circuit equation. As an optimization algorithm, the Gradient Projection method is used to control easily the torques for various speeds of rotor. >

Temperature analysis of induction motor with distributed heat sources by finite element method

This paper presents a more accurate method to estimate the temperature distribution of the induction motor. Distributed heat sources are calculated by solving the voltage source eddy current problem. The analyzed model has several equivalent layers replacing the very narrow region such as the contact of frame and stator core. The numerical results shows the heat sources and temperature distribution well in a full FE analysis model.

Stator slot shape design of induction motors for iron loss reduction

The shape design of stator slot of 3-phase cage induction motors for iron loss reduction is presented. For optimum shape design, the sensitivity analysis by discrete approach is employed and the gradient projection method for nonlinear constraint problems is chosen for an optimization algorithm. The 2D finite element method with voltage source is used to find the flux distribution in induction motors. >

A New Unified Design Environment for Optimization of Electric Machines Based on Continuum Sensitivity and B-Spline Parametrization

In this paper, a unified design environment is developed for the optimization of electric machines based on continuum sensitivity. For electromagnetic (EM) system analysis, COMSOL scripting environment is used. Optimization module is developed by MATLAB programming, which can be combined with COMSOL script commands. The modules are combined into one MATLAB project, and iteration process necessary for the optimization of EM system can be performed efficiently. During the design process, visual feedback of the current design status is given to the designer. In addition, the B-Spline parametrization of the nodal points is implemented to obtain smooth boundary of the device. The developed software is applied to the problem of finding uniform flux density distribution at the air gap of an electromagnet to verify its feasibility and effectiveness.

Optimal design of transient eddy current systems driven by voltage source

The structure and the characteristics of an optimal design procedure of electromagnetic devices are examined and the three different approaches to design sensitivity derivation are reviewed. For the shape design problems of the transient eddy current systems driven by voltage sources, the design sensitivity is derived in an explicit form to the design variables using the finite element algebraic system equation and the adjoint variable method. The original state variable equation is an initial value problem, but the adjoint variable equation is derived as a terminal value problem. Both equations are solved using a time-stepping finite element method. As a numerical example, the coil-positioning problem of an induction heating system is tested and the proposed algorithm is validated.

B-spline parametrization of finite element models for optimal design of electromagnetic devices

This paper presents B-spline parametrization method for the optimal shape design of electromagnetic devices. As an optimal design technique, the design sensitivity method based on the finite element method is used. Since the design variables of one-to-one correspondence with node points of finite element model can cause saw-tooth shape and serious accuracy problem, the design interface is parameterized into smooth curves using geometrical relation of design variables and node points of finite element model. B-spline technique used widely in computer graphics is capable of representing smooth curves and surfaces and can generate a wide variety of shapes. In addition, its geometry data can be easily connected to many commercial CAD tools. To show validity of the presented technique, we test two numerical examples: a magnet shape design problem for uniform magnetic field and a electrode shape design problem for uniform electric field.

A New Material Sensitivity Analysis for Electromagnetic Inverse Problems

This paper presents a new self-adjoint material sensitivity formulation for optimal designs and inverse problems in the high frequency domain. The proposed method is based on the continuum approach using the augmented Lagrangian method. Using the self-adjoint formulation, there is no need to solve the adjoint system additionally when the goal function is a function of the S-parameter. In addition, the algorithm is more general than most previous approaches because it is independent of specific analysis methods or gridding techniques, thereby enabling the use of commercial EM simulators and various custom solvers. For verification, the method was applied to the several numerical examples of dielectric material reconstruction problems in the high frequency domain, and the results were compared with those calculated using the conventional method.

Shape design of stator slot for the reduction of stator core loss in the induction motor

This paper deals with the shape design for the reduction of stator core loss of the induction motor. The improved loss analysis is proposed which is based on core loss measurement under alternating flux with a certain harmonic component and elliptically rotating flux. The time step finite element analysis is used for the computation of state core loss of the induction motor.