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This article presents a bridge between topology optimization (TO) and additive manufacturing. On the one hand, it presents an algorithm that considers the design variables as binary and then solves the problem by binary linear programming to optimize a ferromagnetic core. On the other hand, a 3-D printing process is developed to manufacture the shapes obtained by TO. Finally, these magnetic parts are characterized through electrical measurements.

Optimization using finite element analysis and the adjoint variable method to solve engineering problems appears in various application areas. However, to the best of the authors’ knowledge, there is a lack of detailed explanation on the implementation of the adjoint variable method in the context of electromagnetic modeling. This paper aimed to provide a detailed explanation of the method in the simplest possible general framework. Then, an extended explanation is offered in the context of electromagnetism. A discrete design methodology based on adjoint variables for magnetostatics was formulated, implemented, and verified. This comprehensive methodology supports both linear and nonlinear problems. The framework provides a general approach for performing a very efficient and discretely consistent sensitivity analysis for problems involving geometric and physical variables or any combination of the two. The accuracy of the implementation is demonstrated by independent verification based on an analytical test case and using the finite-difference method. The methodology was used to optimize the parameters of a superconducting energy storage device and a magnet press and the optimization of the topology of an electromagnet. The objective function of each problem was successfully decreased, and all constraints stipulated were met.

Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to a huge computational cost in the case of expensive models. Three different RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective function and constraints. These methods use different infill sampling criteria (ISC) to add samples in the process of optimization or/and in the reliability analysis. Several enrichment criteria and strategies are compared in terms of number of evaluations and accuracy of the solution.

The motivation of this communication is to test a method for computing the gradient of a quantity of interest for an electromagnetic device modeled by finite elements method (FEM). The gradient is a key ingredient in many important tasks: sensitivity analysis, robust design, design optimization and reliability analysis. It can be computed efficiently using the adjoint method, its advantage is not only reducing the computational cost of computing the gradient compared to different methods (e.g. finite difference) but also handling the numerical noise that could appear when re-meshing in the case of finite elements analysis.

Meta-models proved to be a very efficient strategy for optimization of expensive black-box models, e.g. Finite Element simulation for electromagnetic devices. It enables to reduce the computational burden for optimization purposes. Kriging is a popular method to build meta-model. Its statistical properties were firstly used in efficient global optimization for unconstrained problems. Afterwards many extensions were introduced in the literature to deal with constrained optimization. This paper presents a comparative study of some infill criteria for constraints handling and a new strategy for parallelization of the expensive computations of models.

Reliability-Based Design Optimization (RBDO) in electromagnetic field problems requires the calculation of probability of failure leading to huge computational cost in the case of expensive models. Three different types of RBDO approaches using kriging surrogate model are proposed to overcome this difficulty by introducing an approximation of the objective and of the constraints. These methods use different infill searching criteria to add new samples in the process of optimization or/and in the reliability analysis. The enrichment criteria and the best suited enrichment strategies are discussed in this communication. These approaches are compared in terms of number of evaluations and accuracy of the solution.

This dissertation deals with the approaches for optimization and reliability analysis of electrical machines modelled by the finite element method. The finite element method is the most sophisticated tool to model the electromagnetic phenomenon. However, it is computationally expensive. Thus, its usage for optimization and reliability analysis (iterative processes) should be made with caution since only a limited number of evaluations of the model can be tolerated. Furthermore, the impact of the manufacturing process on the electrical machines is scarcely studied in the literature. The integration of this aspect in the design phase is one of the contributions of this thesis alongside the main contribution, which is the development and comparison of optimization approaches for electrical machines. We present the approaches adapted to the subject and develop new ones. On the one hand, the finite element model can be seen as a "black-box" for which we develop a non-intrusive approach based on Kriging meta-models. On the other hand, we consider an intrusive approach as we look inside the "black-box," we upgrade the model to provide the derivatives of the quantities of interest. The derivatives are essential to some optimization and reliability analysis tools. They are computed efficiently using the adjoint variable method. Finally, the methods are compared to give insight into the advantages and the shortcomings of each of them. Lastly, a real case study is considered; it consists of studying the impact of the manufacturing process on a claw-pole machine manufactured by Valeo. From the production line, machines are withdrawn to measure their dimensions and characterize their deviation from the nominal one. Then a statistical analysis is conducted to assess the reliability and impact on the performances.