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This paper gives an overview of some stochastic optimization strategies, namely, evolution strategies, genetic algorithms, and simulated annealing, and how these methods can be applied to problems in electrical engineering. Since these methods usually require a careful tuning of the parameters which control the behavior of the strategies (strategy parameters), significant features of the algorithms implemented by the authors are presented. An analytical comparison among them is performed. Finally, results are discussed on three optimization problems.

A proposal for benchmark problems to test electromagnetic optimization methods, relevant to multiobjective optimization of a solenoidal superconducting magnetic energy storage with active and passive shielding is presented. The system has been optimized by means of different optimization procedures based on the global search algorithm, evolution strategies, simulated annealing and the conjugate gradient method, all coupled to integral or finite element codes. A comparison of results is performed and the features of the problem as a test of optimization procedures are discussed.

The authors present a vector environment, built around a reconfigurable data structure and a library of solver routines, devised for an efficient exploitation of vector features of computers to speed up magnetic analysis codes. The tests performed for the definition of the environment are reported and commented on, and the final results showing significant speedups in real magnetic analysis cases on a selected vector machine are presented and discussed. It is concluded that the use of the vector environment defined by the ITPLUS storage and the APPEAL library of solver routines has proven practical and successful as a way to allow users to efficiently exploit vector architectures, while protecting them from the need of large recoding efforts and of deep knowledge in computer architecture features and performances. >

A comparative evaluation of the quality of three different error estimation procedures used as refinement indicators and final error estimators is presented. The performance of each method, based on an element-by-element h-refinement technique, is assessed in a test case provided with an analytical solution, in a uniform environment. >

The present and possible future trends in development of computer hardware and system software for computer-intensive applications of computer-aided analysis and design are analyzed. An overview of the emerging products in each class of computers is presented, the authors' view of prospects of development of hardware and software products of interest to the CAD market is given, and hints for performance evaluation are provided. Finally, the present status of massively parallel computers is described, with emphasis on the architectures of interest for CAD applications. >

A comparative evaluation of the performance of adaptive meshing algorithms with different error estimators is presented. The algorithms are oriented toward electric and magnetic analysis applications. The performance of a selected set of algorithms that are based on an element-by-element h-refinement technique is assessed in some test cases in comparison with analytical results, in a uniform environment. Finally, the features of the various possible error estimation parameters are presented and discussed. >

For the LHC dipoles , mandatory electrical integrity tests are performed to qualify the cold mass (CM) at four production stages: individual pole, collared coil, CM before end cover welding and final CM. A description of the measurement equipment and its recent development are presented. After passing the demands set out in the specification, the results of the tests are transmitted to CERN where they are further analyzed. The paper presents the most important results of these measurements. We also report a review of the electrical nonconformities encountered e.g. inter-turn shorts and quench heater failure, their diagnostic and the cures

A full-Maxwell numerical algorithm based on the cell method, which is similar to finite-difference time-domain or FIT but allows complete freedom on the mesh, is presented in this paper. The algorithm can be used with tetrahedral or hexahedral primal meshes. The numerical scheme is explicit, does not need the introduction of new variables or local matrix inversions (as, e.g., in the microcell method), and allows the use of phase-matched layer type boundary conditions

C. Santoni, coll. Atlas, To be published in the proceeding of the conference.; During the construction of the LHC main dipoles, 12 cases of short circuits between the cables of the superconducting coils have been detected. Some of them appeared only under the press, making impossible their localization after disassembly. In this paper we describe a method to locate electrical shorts through the use of room temperature magnetic measurements. An example case is discussed in detail to illustrate the features of the approach, and a statistic of the cases met during the production of more that 70% of the dipole total quantity is presented.

The problem of global optimization of magnetic structures composed of solenoids is examined, using a modified simulated annealing algorithm able to deal with the functions of continuous and/or discrete variables. The algorithm is tested using a discrete problem which allows determination of the cost function for every possible configuration of the system, providing information about the pattern of the cost function with respect to design variables. Despite the difficulty of minimizing the function, the proposed algorithm was able to locate the global minimum, or a point where the cost function has a value very close to it, seven times out of a total of ten runs. The algorithm is described, and results are discussed. >

The LHC ring will contain 1232 main dipole and 382 main quadrupole twin aperture magnets. All main magnets are superconducting and employ NbTi/Cu Rutherford type cables operated at 1.9 K. The dipole production has reached the equivalent of almost three octants of cold masses and nearly four octants of collared coils. The quadrupole production has reached 75 cold masses and over 150 bare magnets. The ramping up of large scale magnet production has posed several challenges which will be discussed, like: the coil size uniformity, coil pre-stress control, cold mass welding technique and the geometrical shape issues. The magnetic measurement results at warm will be presented together with their usage for the quality control in the production. The common features and differences of the three dipole producers will be discussed. Finally the latest version of the production schedule will be presented.

In this paper, a World Wide Web-based tool for the remote definition and analysis of optimization problems in electromagnetic design is described. The tool can find effective applications both in advanced teaching and in industrial design activities, thanks to its user-friendliness. The architecture of the system and its current implementation, based on commonly available tools, are presented and discussed in detail. Examples of the use of the tool for the design of a magnet to be used in high energy physics experiments and a simple electromagnetic actuator are given.

In this paper a short description of the EPOCH design optimization environment will be given and results on the parallelization of the electromagnetic analysis codes based on the Bulk Synchronous Parallel approach, as well as testing of the environment using industrially relevant 2d and 3d test cases, such as the design of a microwave oven, eddy current brake, advanced accelerator magnet and thin film recording head, will be presented.

The present paper discusses a technique, based on the combined use of Radial Basis Functions (RBF), which provide an analytical approximation of the true cost function, and self adaptive fuzzy sets, which allow a flexible combination of conflicting objectives, for the stochastic optimisation of multiminima problems. The proposed technique is fully described, its features of interest for industrial level design optimisation are outlined and some initial positive results are presented.

Results from a European collaborative project to create an open system for engineering design, with particular emphasis toward electromagnetic devices, are presented. The system, code named MIDAS, is based on the new ISO STEP standard for data exchange and utilises state-of-the-art graphical user interfaces, 3D geometric modelling and three-dimensional automatic mesh generation with an advanced 2D subset.

A procedure to significantly reduce the computational cost of the simulated annealing optimization algorithm coupled with analysis methods is proposed for EM devices. The chosen approach relies on the application of the simulated annealing method to an analytical approximation of the true objective function, expressed in the form of a multiquadric expansion. The algorithm is fully described, its potential advantages are pointed out and some test cases showing the effectiveness of the implemented strategy are reported and discussed. As an example the superconducting magnet energy storage device is mentioned.

A new parallel global optimization algorithm is presented and evaluated. It is based on simulated annealing and on speculative computation. It is particularly suited for parallel architectures from some units to some tens of processors and for problems characterized by a cost function whose evaluation takes a long time, features that fit well with the design of magnetic structures. Comparative tests with respect to traditional sequential SA is presented on the design of a magnet for Magnetic Resonance Imaging. >

The theory of electro-dielectrophoretic force and torque acting on a spherical impurity particle embedded in a dielectric fluid and subjected to an unrestricted time-varying electric field is developed under linear conditions. It takes into account the combined effects of conduction and polarization of both the liquid and the particle, and is valid under general transient conditions. On the basis of the above theory, a computer model of impurity particle motion in the bulk of a dielectric fluid is developed, which takes into account all the forces acting on the particle once suitable initial values of particle position, velocity and superficial charge density are provided. Examples of trajectories showing the influence of some of the involved parameters are given, and the features of the model are briefly discussed.

On the basis of a more accurate experimental study of the charge exchange mechanism between particles and electrodes, some improvements are introduced in the charge exchange models previously developed by the authors. This allows the application range of a model of particle motion to be extended to sizes of greater practical interest, down to some microns. New identification procedures of the model parameters are proposed, whose extension to smaller sizes seems to be more practical. To show the potentiality of the model, experimental data obtained by high speed movie are compared with model simulations and results are discussed.

The new version of the package COMPELL (rev. 2.0) is designed to extend to the finite element method the generalized data input already present in the finite difference version (rev. 1.0). The algorithm used is based on the Galerkin method, generalized to allow the discretization of any system of partial differential equations. In the package the procedure is designed only for plane or axisymmetrical second order partial differential equations under nonlinear time-varying conditions; the extension to higher order equations is straightforward in principle.

In this paper the first results of an investigation aimed to obtain additional data on breakdown strength of liquid helium are presented; the work is performed under as controlled as possible conditions not too far removed from those relevant to practical engineering applications, by means of a purpose-built helium cryostat whose main features are briefly described. To get results suitable for direct engineering use, a first group of tests was performed with IEC normalized spherical cap electrodes, investigating the statistical behaviour of breakdown strength as a function of gap setting and test conditions. A second group of tests was performed with cylindrical electrodes to get data on the amount of the area effect on the statistical features of breakdown, also as function of test conditions. Finally, a statistical analysis of the obtained data is performed and results are discussed.

The study of impurity particles motion in a dielectric fluid under the action of an electric field can be of interest in the analysis of conduction and breakdown processes, especially in order to assess the changes in impurity concentrations. To this aim, rather sophisticated models of particle motion are required. In this paper, on the basis of a theory of electro-dielectrophoretic forces previously developed by the authors for spherical particles, a simulation algorithm of impurity particles motion is implemented by proposing models of the charge exchange mechanism at the particle-electrode contact. Experimental identification procedures of some model parameters are outlined and performed, and simulations of particle trajectories under a.c. and d.c. voltages for a sphere plane geometry, in the case of both conducting and dielectric particles in n-hexane, are compared with experimental results obtained by high-speed movie.

In this paper a modular package, named COMPELL, for the solution of two-variable time-varying problems of the elliptic type is presented. The package allows the solution of standard magnetic problems, also under quasi-stationary or rapidly time-varying conditions, in the cases with nonlinear, anisotropic and nonhomogeneous materials with eddy currents, but can also face different problems, taking into account for instance the presence of moving bodies or the reciprocal interaction between magnetic fields, thermal fields and so on. The procedures used for field solution are generalized finite differences, least square finite differences, first presented in this paper, or finite elements. In the paper examples of magnetic field solutions are given, in particular by showing the field in a Tokamak structure accounting for the Hall effect. The data deck and the obtained results are displayed and the main features of the package are discussed.

In this paper an analysis of the breakdown strength of liquid nitrogen with IEC spherical electrodes and adjustable gap setting under as controlled as possible conditions is presented. The analysis is performed on commercial quality liquid nitrogen in the millimetre gap range, to collect data on the reduction of performances with respect to the technically pure liquids in a range of gaps not too far from those of practical applications, and with normalized electrodes to simplify technical comparison with other dielectric liquids. With a specially developed apparatus several series of tests are performed, to get additional informations on the gap effect in the millimetre gap range, and a thorough investigation on the influence of stirring between tests is carried out. Finally, a statistical analysis of the obtained results is performed to get further hints also on the conditioning effect as well as on the influence of sample size, and all the obtained results are compared and discussed.

On the basis of models, previously developed by the authors, of the motion of impurity particles in a dielectric liquid and of the mechanism of charge exchange at the electrodes, a model of conduction current due to charge convection by impurity particles in a dielectric liquid is described. The model can be applied to three-dimensional axisymmetrical geometries with conducting or dielectric impurity particles. Experimental tests performed, under d.c. conditions, with different impurity particles, down to a radius of a few microns, and with different electrode geometries, are reported. A comparison between experimental data and simulation results indicates satisfactory agreement.

In this paper an investigation is performed of the influence of pressure on breakdown strength of liquid nitrogen in the millimetre gap range. The experimental setup has been designed in order to get a very effective thermal stabilisation at 77 K, without any temperature drift during tests. Three sets of uniform field electrodes of different uniform field area are used, and tests are performed up to 1.75 atm overpressure, with sample sizes of 100 data. Finally, a statistical analysis of test data is performed, and results are discussed.

This paper describes a program for the solution of boundary-value problems of the elliptic type by means of the finite-element method and a generalized finite-difference method developed by the authors. The program is oriented toward the reduction of input operations to those strictly needed to define a given problem physically, and it has been designed to allow automatic grid optimization. The generalized finite-difference method can handle completely irregular grids, and allows the discretization of any form of second-order elliptic equation under general boundary and interface conditions. To show the potentiality of the method, an example of magnetic field problem with sharp boundary, non-homogeneous anisotropic material and non-uniform current density distribution is presented, and the results are compared with the theoretical solution. Finally, the results obtained and the potentiality of the program are discussed.

In this paper the usefulness of a multiformulational approach to the numerical computation of electromagnetic fields of technical interest, including coupled problems, is discussed. Several field computation problems arising from various application areas are presented to sample some of the many formulations required to face the existing computational needs. The problems are solved by means of a code designed for a multiformulational management of field computation, and the versatility of the approach and the obtained results are discussed.

A procedure designed to solve as a single system the set of differential equations describing a coupled problem, including transient nonlinear cases, is presented. The procedure is based on the discretization of the equations to produce a single algebraic system. The implementation of the method is explained, and applications to a nonlinear thermomagnetic problem and a sinusoidal steady-state eddy current problem are described. The potential advantages and drawbacks, as compared to those of other procedures, are discussed. >

A package developed for both research and industrial application for computer aided design of electromagnetic devices is presented and the main features are discussed. From the research point of view the main feature of the package is to allow the definition of the differential equations of the problem to be solved in their analytical form by means of input data for both finite differences and finite elements. From the point of view of practical application, the main features are based on an input processor allowing the input of data in a parametric form. Besides, procedures for optimization of integral and differential quantities and for profile optimization are implemented in the package. For both purposes, automatic grid generation procedures controlled by the user are at disposal and grid optimization is at an advanced stage of development.

The paper discusses the use of different, "design of experiment" and statistical theory based methods to improve and speed up the "generalised response surface method", using multiquadrics to describe the objective function in parameter space, for the optimization of multiminima design problems in magnetics. The effectiveness of the proposed approach to enhance the convergence of stochastic optimisation algorithms is tested on a couple of test problems and the results are discussed.

A grid optimization iterative procedure is presented in the paper. It represents the first step of a two step algorithm and is named grid iteration method. Together with the second step, named metric iteration method, it has been developed previously by the authors for simple examples and has been proven to be potentially very efficient. In this paper the grid iteration method is further developed. It is extended to problems with various unknowns; more efficient techniques are developed in order to apply the method to more complex geometries, to improve the convergence tests and to better solve magnetic problems.