TEAM Workshop Problem Research Articles

Kriging: A Useful Tool for Electromagnetic Device Optimization

This paper deals with the use of the Kriging models for objective function approximations and their use on electromagnetic device optimization. The models are compared with some radial basis function neural networks and with the diffuse element method. Comparative tests are done on an analytical function and on the TEAM workshop problem 25.

Fast Multipole Acceleration of the Hybrid Finite-Element/Boundary-Element Analysis of 3-D Eddy-Current Problems

This paper deals with the acceleration of the hybrid finite-element/boundary-element analysis of three-dimensional (3-D) eddy-current problems by means of the fast multipole method. An adaptive truncation scheme for the multipole expansion of the 3-D Laplace Green function is proposed. As an application example, the TEAM workshop problem 28 is considered. The computational cost without and with fast multipole acceleration is discussed.

Transient Eddy Current Analysis of Pulsed Eddy Current Testing by Finite Element Method

Transient eddy current analysis of pulsed eddy current testing was performed by time-stepping method and Fourier transform method. The characteristics of two methods were evaluated by using a simple model. The accuracy was examined by the comparison of calculated and measured data. The calculated results of the two methods provided good agreement with measured data. However, it was clear that the Fourier transform method provided higher accuracy of amplitude than the time-stepping method. As a three-dimensional problem of pulsed eddy current testing, the TEAM Workshop Problem 27 was analyzed by an edge-element finite element method.

TEAM Workshop Problem 25: A Multiobjective Analysis

In this paper, we propose a multiobjective analysis for TEAM workshop problem 25. In order to obtain the Pareto frontier, the objective functions are replaced by approximations. A straightforward method, based on the use of approximations, is used to obtain a Pareto set.

Comparison of radial basis function approximation techniques

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.

An object-oriented library based on computational intelligence techniques for optimization in electromagnetics

This paper proposes a structure of classes that uses the concepts of object-oriented programming to develop a library based on computational intelligence techniques for optimization in electromagnetics. In this library, artificial neural networks and neurofuzzy networks are considered. Based on this division, the required classes for the library implementation are presented. Finally, the TEAM workshop problem 22 is investigated. The results obtained are in accordance with the best known in the literature.

Nonlinear update scheme for partially filled cells

This paper presents a method for the consideration of mesh cells which are partially filled with nonlinear materials within the framework of the finite integration technique. The necessary modifications of the nonlinear update method are described and verified by the simulation of the TEAM Workshop Problem 20.

Nonlinear analysis of eddy current and hysteresis losses of 3-D stray field loss model (Problem 21)

The evaluation method of stray field loss of engineering oriented loss model (TEAM Workshop Problem 21) is investigated. It is shown that the nonlinear eddy current analysis is obligatory in order to investigate the eddy current loss in the steel plate, because the flux and eddy current in steel are affected by the permeability of the plate. The hysteresis loss in such a steel plate having a substantial skin effect is not negligible, even if the flux density in air is small.

Computation results of the TEAM workshop Problem 7 by finite element methods using tetrahedral and hexahedral elements

In this paper, two types of finite element codes are applied to Problem 7 of TEAM workshop benchmark problems and the computation results are compared with the experimental results which were presented at the workshop. The computation model consists of an asymmetrical conductor with hole and an exciting coil. The model is solved as a three-dimensional problem by finite element methods using edge elements. A tetrahedral edge element and a hexahedral edge element are introduced to the two types of codes. The characteristics of the two codes are discussed by using the computation results of the benchmark problem.

Embedded stochastic-deterministic optimization method with accuracy control

A distributed evolutionary strategy is used to solve the optimization problem in a subspace of the searching space. At each cost function evaluation, a deterministic method is used to find the optimal solution in the complementary subspace, with an imposed accuracy. The proposed method is applied to solve TEAM Workshop problem 22 with the control of the numerical error. In this case the stochastic method acts in the geometrical parameter subspace and an embedded deterministic technique is used in the 2D current densities subspace. The application of the technique to superconducting magnetic energy storage is discussed.

Transient eddy-current calculation with the FI-method

This paper introduces time-domain formulations based on the Maxwell grid equations of the consistent finite integration (FI) method which allows calculation of slowly-varying electromagnetic fields with various implicit time-stepping techniques. The resultant large sparse linear systems of equations have to be solved by iterative methods for each time step. The preconditioned conjugate gradient methods allow the calculation of nongauged (quasi-)static problems efficiently. Numerical results are shown for the TEAM workshop problem 7 and an SRC high density magnetic head problem, which could be calculated with more than one million degrees of freedom.

A fast volume rendering method for time-varying 3-D scalar field visualization using orthonormal wavelets

Animation of a time-varying 3-D scalar field distribution requires generation of a set of images at a sampled time intervals i.e. frames. Although, volume rendering method can be very advantageous for such 3-D scalar field visualizations, in case of animation, the computation time needed for generation of the entire set of images can be considerably long. To address this problem, this paper proposes a fast volume rendering method which utilizes orthonormal wavelets. The coherency between frames, in the proposed method, is eliminated by expanding the scalar field into a series of wavelets. Application of the proposed method for time-varying eddy-current density distribution inside an aluminum plate (TEAM Workshop Problem 7) is given.

A boundary element formulation using higher order curvilinear edge elements

A boundary element method in terms of the field variable is applied to three-dimensional magnetostatic problems. We propose higher order edge elements of quadrilateral shape for the field approximation on curved surfaces. The tangential component of the unknown field variable is interpolated by the edge element. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by TEAM Workshop problem 13 assuming linear material properties.

Shape design with great geometrical deformations using continuously moving finite element nodes

In this paper design sensitivity analysis is applied to solve the TEAM workshop problem 25. In order to justify the use of a gradient method, it is necessary to assume a continuously differentiable dependence of the stiffness matrix on the design parameters. Since design sensitivity analysis is mainly applicable to optimization problems, where the geometrical parameters undergo small changes only - which is not the case for the problem investigated in this paper-a procedure is proposed, which allows this method to be applied also when the changes in geometry are significant.

Utilizing feedforward neural networks for acceleration of global optimization procedures [SMES problems

Global optimization in electrical engineering usually requires an enormous amount of CPU time to evaluate the objective function when stochastic methods are used. Approximating the objective function can drastically reduce the computational demands. The use of feedforward neural networks is proposed in this paper and its application is investigated using an unconstrained and a constrained version of the TEAM Workshop problem 22.

Comparison of analytical and numerical integration techniques for the boundary integrals in the BEM-FEM coupling considering TEAM workshop problem no. 13

When the BEM-FEM coupling is used for the solution of a boundary value problem the domain is decomposed into a multiple connected BEM subdomain and generally several FEM subdomains. Magnetic materials are treated in the FEM subdomains only. To keep the discretization process simple, the parts containing magnetic materials coincide with the FEM subdomains. The surrounding air space is described with the help of boundary elements. The coupling of both methods is carried out on the surface of the magnetic materials. The solution of problems discretized this way shows that the accuracy of the results strongly depends on the accuracy of the boundary element integral calculation. Therefore either a large number of Gauss points or an analytical integration scheme has to be used for the calculation of the BEM integrals.

H-version adaptive finite element method using edge element for 3D non-linear magnetostatic problems

The h-version adaptive finite element method employing edge elements for 3D non-linear magnetostatic problems is presented. Two different techniques for the mesh refinement procedure are performed. One is to reconstruct a new mesh using the Delaunay method and the other is to subdivide elements into 2, 4 or 8 tetrahedral elements. The error estimation method proposed by Zienkiewich and Zhu (1987) is applied to the edge element code. The TEAM Workshop Problem 20 is calculated using two techniques, and the results confirm the efficiency of the presented approaches.

A new vector element in the volume integral equation method for nonlinear magnetostatics

To calculate nonlinear magnetostatics a new vector element in the volume integral equation has been developed. The magnetization vector in an element is expressed by using co- and contra-variant vectors corresponding to the each surface of the hexahedron element. To accelerate the conversion process, the iteration procedure has been divided into initialization and convergence parts. The method has been applied to TEAM workshop problem 13 of IEEE. Its calculated results agree with the measured data within 2%, indicating the method provides good accuracy. >

SOLUTION OF TEAM WORKSHOP PROBLEM 7 BY RELUCTANCE NETWORK METHOD (ASYMMETRICAL CONDUCTOR WITH A HOLE)

This paper presents the numerical solution of the TEAM Workshop Problem 7 obtained by Reluctance Network Method (RNM). The problem represents a three‐dimensional multiply connected eddy current problem with a time — harmonic excitation. The numerical results obtained by RNM in reasonable computing time, agree extremely well with experimental data and other methods results.

Hierarchal scalar and vector tetrahedra

A novel set of scalar and vector tetrahedral finite elements are presented. The elements are hierarchical, allowing mixing of polynomial orders. Scalar orders up to three and vector orders up to two are defined. The vector elements impose tangential continuity on the field but not normal continuity, making them suitable for representing the vector electric or magnetic field. The scalar and vector elements can easily be used in the same mesh, a requirement of many quasi-static formulations. Results are presented for two 50-Hz problems: the Bath cube and the TEAM Workshop problem 7.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>