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The definition of a simple model of low frequency magnetic field created by power industrial installations can be approached by using an equivalent source system (ESS). Given a set of measured magnetic field points, the ESS, made by a limited set of current carrying wires or turns, must be placed and supplied in order to fit the measured magnetic field values. An optimisation procedure can be used to define the current values and the location of the ESS which minimize the error between the measured and computed magnetic field values.

A two‐step optimal procedure is defined: in the outer step a stochastic optimisation routine is used to drive the geometric control parameters of the ESS while, in the inner step, the current values flowing through the sources are computed to find the minimization of the error with respect to a set of measured magnetic field values. The optimisation procedure is based on an artificial immune system algorithm which focuses on a deep exploration of the search space and gave interesting results both in terms of accuracy and computational efficiency.

The results show that the proposed approach is able to reconstruct the magnetic field created by complex source system and give some accuracy measure on the reconstruction error. The optimisation process carried out also on conductor positions has allowed to find out the location of the real sources in an accurate way, also in presence of measurement errors.

The approach proposed uses optimisation procedures to solve the inverse problem of source reconstruction starting by a set of measured magnetic field values. The definition of a simple equivalent source structure, together with an optimisation procedure to set its control parameters, allows to simulate complex magnetic field sources, like power substations or cable systems, in a very efficient and compact way.

The paper presents an hybrid optimization technique which couples the artificial immune system (AIS) algorithm with a zeroth order deterministic method.

AIS has been developed to tackle multi‐modal optimization problems and it has shown a great ability to explore the objective function space. The algorithm is subdivided into two phases: an outer and an inner cycle. The outer cycle is devoted to the exploration of the space while the inner is a local exploration of the objective function. The new hybrid method proposes to replace the local search by a zeroth order deterministic search to speed up the overall convergence.

Results on two multi‐modal analytical objective functions show an increase of speed of the new procedure with respect to the standard AIS. The method is also tested on the TEAM 22 numerical problem and some a posteriori techniques for the analysis of multimodal blind objective functions are discussed.

The new Multimodal optimization algorithm has allowed to explore thoroughly feasibility space giving rise to a partition of the whole space, the use of hybrid technique increases the performances of standard AIS increasing the convergence to the optimal points.

The purpose of this study is to investigate and compare the ability of a new optimization technique based on the emulation of the immune system to detect the global maximum with multimodal functions and to test the capability of exploring the parameter space with respect to clustering enhanced Genetic Algorithms (GA).

Both algorithms have been tested on analytical test functions and on numerical functions of applicative interest. A set of performance criteria has been defined in order to numerically compare the performances of both optimization strategies.

Results show the great ability of Artificial Immune Systems (AIS) in thoroughly exploring the space of variables. On the other side, GA are faster to converge to the global optimum, but selection pressure can reduce the number of detected local optima.

This work is an attempt to assess the performances of a relatively new optimization algorithm based on AIS and to find its behavior on multimodal test functions, using GAs as reference optimization technique.

The purpose of this paper is to obtain a fully analytical model of an eddy current coupler and to use it in a multi‐objective optimisation algorithm.

Analytical expressions of device performances are adopted in the objective function and are obtained from a closed solution of the field problem. The optimisation has been carried out by considering both the torque and the momentum of inertia of the object. Two different structures have been considered.

A fully analytical expression of the torque has been obtained for two different geometrical configurations. The optimisation procedure has been used to compare these structures and it is possible to observe that the DSPM performances are better than the SSPM ones.

To obtain a closed form of the torque function, the non‐linearities of the iron have been neglected. Nevertheless, in the optimisation procedure has been limited the magnetic flux density in the iron core to a feasible value in the linear part of the ferromagnetic characteristic. The thermal effects have been neglected.

In the industry, eddy current couplers can be used as transmission, dampers and brakes. The use of objective functions (OFs) in a closed formulation allows to perform a light optimisation from the point of view of the time computation and to drastically increase the development efficiency.

In this paper, a model for computing the electromagnetic behaviour of eddy current couplers is presented. The optimisation of both the torque and the inertia momentum allows to obtain good static and dynamic performances.

To apply two different integral formulations of full‐Maxwell's equations to the numerical study of interconnects in a low‐frequency range and compare the results.

The first approach consists of a surface formulation of the full‐Maxwell's equations in terms of potentials, giving rise to a surface electric field integral equation. The equation, given in a weak form, is solved by using a finite element technique. The solenoidal and non‐solenoidal components of the electric current density are separated using the null‐pinv decomposition to avoid the low‐frequency breakdown. The second model is an extension of partial element equivalent circuit technique to unstructured meshes allowing the use of triangular meshes. Two systems of meshes tied by duality relations are defined on multiconductor systems. The key point in the definition of the equivalent network is to associate the pair primal edge/dual face to a circuit branch. Solution of the resulting electrical network is performed by a modified nodal analysis method and regularization of the outcoming matrix is accomplished by standard techniques based on the addition of suitable resistors.

Both the formulation have a regular behaviour at very low frequency. This is automatically achieved in the first approach by using the null‐pinv decomposition.

Surface sources of fields.

Two different integral formulations of full‐Maxwell's equations for the numerical study of interconnects are compared in terms of low‐frequency behaviour.

The purpose of this paper is to derive a new stress tensor for calculating the Lorentz force acting on an arbitrarily shaped nonmagnetic conductive specimen moving in the field of a permanent magnet. The stress tensor allows for a transition from a volume to a surface integral for force calculation.

This paper derives a new stress tensor which consists of two parts: the first part corresponds to the scaled Poynting vector and the second part corresponds to the velocity term. This paper converts the triple integral over the volume of the conductor to a double integral over its surface, where the subintegral functions are continuous through the different compartments of the model. Numerical results and comparison to the standard volume discretization using the finite element method are given.

This paper evaluated the performance of the new stress tensor computation on a thick and thin cuboid, a thin disk, a sphere and a thin cuboid containing a surface defect. The integrals are valid for any geometry of the specimen and the position and orientation of the magnet. The normalized root mean square errors are below 0.26% with respect to a reference finite element solution applying volume integration.

Tensor elements are continuous throughout the model, allowing integration directly over the conductor surface.

This paper aims to apply the non-linear impedance boundary condition (IBC) for a linear piecewise B–H curve in frequency domain simulations to find the equivalent impedance of a simple induction heating system model.

An electromagnetic description of the inductor system is performed to substitute the effects of the induction load, for a mathematical condition, the so-called IBC. This is suitable to be used in electromagnetic systems involving high conductive materials at medium frequencies, as it occurs in an induction heating system.

A reduction of the computational cost of electromagnetic simulation through the application of the IBC. The model based on linear piecewise B–H curve simplifies the electromagnetic description, and it can facilitate the identification of the induction load characteristics from experimental measurements.

This work is performed to assess the feasibility of using the non-linear boundary impedance condition of materials with linear piecewise B–H curve to simulate in the frequency domain with a reduced computational cost compared to time domain simulations.

In this paper, the use of the non-linear boundary impedance condition to describe materials with B–H curve by segments, which can approximate any dependence without hysteresis, has been studied. The results are compared with computationally more expensive time domain simulations.

Supplying remote wireless sensors is not an easy task if the site where the device is located is not easily accessible. In order to obtain direct measurements of the road-vehicle interactions, sensors must be placed inside the tyre environment thus a power supply must be available for their working there without any wire connection with the car main power. The paper aims to discuss these issues.

An electro-mechanical energy harvester has thus been developed for supplying an automotive wireless sensor of pressure, temperature and acceleration to be placed on the inner line of a tyre. The primary energy source is the vibrations or variable accelerations imposed to the device and induced in the tyre by the wheeling.

The harvester has been designed by means of a multi-physics optimisation based on an integrated electromagnetic-mechanical circuit simulator. Thus an automated optimisation of the device with respect to volume constraints, magnets dimensions, induction coils placement and size have been performed to increase the average power extracted from the device at different wheeling speeds.

The use of the multi-physics environment together with automated optimisation technique has been tested for the first time on the electromagnetic harvester structure.

The purpose of this paper is to present an electro‐thermo‐structural analysis based on the cell method (CM).

CM is useful for solving coupled problems when the same geometrical discretization can be adopted for different phenomena. In this case, the same geometrical structures and operators can be used, leading to a simplification of the numerical model.

In order to asses the performance of the proposed coupling scheme, results have been compared with values measured on a carbon‐fiber specimen heated by an electric current and with an applied the mechanical load.

A new dynamic coupling scheme based on the CM has been proposed and assessed with respect to measurements. A good agreement between model results and measurements has been shown, at least until second order effects appears, like the breaking of some fibers of the specimen or high‐temperature effects on epoxy resin.

The purpose of this paper is to present an approach to design passive loop systems in order to reach good performances.

The optimization has been performed by means of the MATLAB optimization toolbox “Gatool” which solves the optimization problems with a genetic algorithm.

Several configurations have been analyzed by varying the number of loops from 2 to 15, whose geometry has been chosen by the genetic algorithm. Considering a five loops configuration, along the reference path it is possible to obtain a shielding factor almost constant and equal to 3.5.

The optimized configurations have been compared with a practical employed layout composed of 17 closed loops placed above and around the junction zone. The shielding factors obtained by the six loops configuration are comparable with the ones of the practical layout.