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The purpose of this paper is to use a new rational approach for the design of some magnetic couplings. Our method is based on the association of analytical models and an exact global optimization algorithm named IBBA and developed by the third author. The analytical model presented in this paper is more sophisticated than those previously dealt using IBBA. Therefore, some under and over estimating functions have been constructed for those particular problems of design in order to improve the convergence of IBBA. Some optimal results highlight the efficiency of this approach. Index Terms--Analytical model, Branch&Bound, exact global optimization, interval arithmetic, inverse problem, magnetic coupling.

This paper presents a new methodology of design of electrical rotating machines. The methodology is an extension of previous works of the second author. Indeed, associating combinatorial analytical models with exact global optimization algorithms leads to rational solutions of predesign. These solutions need to be validated by a numerical tool (using a finite-element method) before the expansive phase of hand-making a prototype. Such an automatic numerical tool for computing some characteristic values, such as the torque, was previously developed. The idea of this paper is to extend the exact global optimization algorithm by inserting the direct use of this automatic numerical tool. This new methodology makes it possible to solve design problems more rationally. Some numerical examples validate the usefulness of this new approach. Index Terms--Analytical model, deterministic global optimization, finite-element methods, interval branch and bound algorithm, inverse problem of design, numerical model.

Study presented a deterministic and rational way of designing piezoelectric transformers in radical mode. This approach is based on the study of inverse problem of design and on its reformulation as a mixed constrained global optimization problem.

This paper solves, in a rational way, more sophisticated electrical machine design problems by extending the work done by Fitan et al., noted in references [1] and [2]. It addresses the special case of multi-airgap cylindrical concentric machines. The solution requires a reformulation of the inverse problem associated with the design of electrical machines. Thus, a new mixed-constrained global optimization problem has to be solved. From a mathematical point of view, a major difficulty is that the number of variables and constraints varies during the resolution, depending on the number of considered airgaps. Moreover, this involves extensions of analytical models used for permanent-magnet machines. The paper uses numerical tests for concentric rotor machines with one, two, and three (in one case) mechanical airgaps permit to validate this methodology of design. Index Terms--Analytical model, global optimization, interval analysis, inverse problem, mixed problem, multi-airgap concentric machine.

The article discusses about the use of finite elements method (FEM) software in order to help lecturer to teach design of electrical machines. Nowadays, lecturers have less and less time to teach the design of electrical machines. Special tools based on FEM can help them in this task. For the past years, such tools needing sophisticated environments have been realized for designers in industry. Assuming minimum equipment, requirements and guidelines for the realization of a specific tool are presented. Index Terms--Design, electrical machines, finite elements method (FEM).

This paper clearly delineates the problem of the design of electromagnetic actuators and presents it as an inverse problem. It discusses optimal formulations and explains the most general and rational way to solve this inverse problem. The methodology is based on the association of an exact interval global optimization algorithm and a new, more general analytical model that represents the structure and the composition of the actuators as well as their dimensions. The methodology can be considered both general and rational. The paper concludes with some practical examples of design that validate the approach. Index Terms--Analytical models, direct and inverse design problems, exact branch and bound global optimization algorithm, interval analysis, mixed-constrained optimization problems, permanent-magnet machines.

The aim of this paper is to show the advantage of a deterministic global-optimization method in the optimal design of electromechanical actuators. The numerical methods classically used are founded either on nonlinear programming techniques (i.e., augmented Lagrangian, sequential quadratic programming) or on stochastic approaches which are more satisfactorily adapted to global optimum research (i.e., genetic algorithm, simulated annealing). However, the latter methods only guarantee reaching this global optimum with some probability. The present paper proposes a deterministic Branch and Bound algorithm associated with interval arithmetic which is then applied to the dimensioning of a slotless permanent magnet machine. The problem is formulated as a multiobjective-optimization problem with mixed variables. Original and unexpected results in this optimal design are obtained, and comparisons with previous works are presented. Index Terms - Branch and Bound method, electromechanical actuators, global optimization, interval arithmetic, optimal design.

Simplicial based Global Optimization branch and bound methods require tight bounds on the objective function value. Recently, a renewed interest appears on bound calculation based on Interval Arithmetic by Karhbet and Kearfott [Reliable Comput.25 (2017) 53–73] and on exploiting second derivative bounds by Mohand [RAIRO Oper. Res.55 (2021) S2373–S238]. The investigated question here is how partial derivative ranges can be used to provide bounds of the objective function value over the simplex. Moreover, we provide theoretical properties of how this information can be used from a monotonicity perspective to reduce the search space in simplicial branch and bound. [ABSTRACT FROM AUTHOR]

This work deals with the optimal regulation of a large thermal process when the final state is fixed and the control is subject to some constraints, for which we propose a relaxation method coupled with the shooting one. We study the behavior of this method. The studied example concerns the optimal control law for two ovens with three and twelve heating zones. [ABSTRACT FROM AUTHOR]

We propose a simple, but efficient method for design problems. Instead of using directly, a heavy numerical code in an optimization process, we successively define some approximated subproblems because of an appropriate analytical model. These subproblems can then be solved exactly by a deterministic global optimization solver and the procedure is updated until the approximation matches a 3-D FEM computation. The method is applied to an axial magnetic coupling. Comparative results show the effectiveness of this approach, and real design cases are studied because of this method. [ABSTRACT FROM PUBLISHER]

In this paper, we present a method to solve inverse problems of electromagnetic circuit design, which are formulated as a topology optimization problem. Indeed, by imposing the magnetic field inside a region, we search the best material distribution into variable domains. To perform this, we minimize the quadratic error between the prescribed magnetic field and the one computed by a finite element method (FEM). A dedicated software was developed in MATLAB using fmincon routine and FEM Magnetics (FEMM) software; this code is named ATOP^TO for algorithm to optimization propulsion using topology optimization. To perform the first derivative of the objective function, we implemented an adjoint variable method. Indeed, this approach makes it possible to provide the derivative by only two uses of the finite element tool. Nevertheless, the problem is discrete because we take only two possibilities: with or without material. Thus, the solid isotropic material with penalization method was used to penalize intermediate values to have discrete solutions. Some numerical experiments with 40 and 800 variables concerning circuit designs validated our approach. This represents a first study to design a Hall effect thruster. [ABSTRACT FROM AUTHOR]