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The density method is one of the powerful topology optimization methods of magnetic devices. The density method has the advantage that it has a high degree of freedom of shape expression which results in a high-performance design. On the other hand, it has also the drawback that unsuitable shapes for actually manufacturing are likely to be generated, e.g. checkerboards or grayscale. The purpose of this paper is to develop a method that enables topology optimization suitable for fabrication while taking advantage of the density method.

This study proposes a novel topology optimization method that combines convolutional neural network (CNN) as an effective smoothing filter with the density method and apply the method to the shield design with magnetic nonlinearity.

This study demonstrated some numerical examples verifying that the proposed method enables to efficiently obtain a smooth and easy-to-manufacture shield shape with high shielding ability. A network architecture suitable as smoothing filter was also exemplified.

In the field of magnetic field analysis, very few studies have verified the usefulness of smoothing by using CNN in the topology optimization of magnetic devices. This paper develops a novel topology optimization method that skillfully combines CNN with the nonlinear magnetic field analysis and also clarifies a suitable network architecture that makes it possible to obtain a target device shape that is easy to manufacture while minimizing the objective function value.

This paper aims to further improve the efficiency of multi-objective optimization design of synchronous reluctance motors (SynRMs) using the level set (LS) method, which has the advantage of obtaining a practical shape. The solutions obtained by gradient methods tend to be local ones due to the multi-modality of the objective function, especially when multiple objective functions. A huge number of trial calculations are required to obtain a high-quality and broadly distributed Pareto front. Therefore, it is indispensable to effectively get out of the local solutions in the optimization process with the LS method.

The authors propose a novel method appropriately switching multiple objective functions with high independence of sensitivity information. The authors adopt highly independent mathematical expressions for the objective functions of the average torque and torque ripple. In addition, the authors repeatedly perform the optimization while appropriately selecting the sensitivity information of one objective function from multiple ones, which enables the authors to effectively break out of local solutions in the optimization process.

The proposed method was applied to the shape optimization of SynRM flux barriers and successfully searched a more extensive and advanced Pareto front in comparison with the conventional method.

The proposed method adopts search spaces with mathematical high independence for average torque and torque ripple. In the optimization process, when the solution search is judged to get stuck by several criteria, the search space is alternately switched to effectively get out of local solutions.

The purpose of this paper is to solve efficiently the topology optimization (TO) in time domain problem with magnetic nonlinearity requiring a large-scale finite element mesh. As an actual application model, the proposed method is applied to induction heating apparatus.

To achieve TO with efficient computation time, a multistage topology is proposed. This method can derive the optimum structure by repeatedly reducing the design domain and regenerating the finite element mesh.

It was clarified that the structure derived from proposed method can be similar to the structure derived from the conventional method, and that the computation time can be made more efficient by parameter tuning of the frequency and volume constraint value. In addition, as a time domain induction heating apparatus problem of an actual application model, an optimum topology considering magnetic nonlinearity was derived from the proposed method.

Whereas the entire design domain must be filled with small triangles in the conventional TO method, the proposed method requires finer mesh division of only the stepwise-reduced design domain. Therefore, the mesh scale is reduced, and there is a possibility that the computation time for TO can be shortened.

Shape optimization using the level-set method is one of the most effective automatic design tools for electromagnetic machines. While level-set method has the advantage of being able to suppress unfeasible shape, it has a weakness of being unable to handle complex topology changes such as perforate at material region. With this method, it is only possible to define simple connected topology, and it is difficult to determine the optimal shape which has holes. Therefore, it is important to efficiently expand the searching area in the optimization process with level-set method.

In this paper, the authors introduce the newly defined hole sensitivity which is based on concept of topological derivatives, and combine it with level-set method to effectively create holes in the search process. Furthermore, they consider a variable bandwidth of gray scale, which indicates the transition width between air and magnetic body and combine it with the hole creation method described above. With these methods, the authors aim to expand the searching area in comparison with the conventional level-set method.

As a result of applying the proposed methods to a magnetic shielding problem, the multi-layered shielding which effectively reduces the magnetic flux in the target area, is successfully produced.

The proposed methods enable us to effectively create a hole and to expand the searching area in the topology optimization process unlike in the case of conventional level-set method.

The purpose of this paper is the improvement of topology optimization. The scope of the paper is focused on the speedup of optimization.

To achieve the speedup, the method of moving asymptotes (MMA) with constrained condition of level set function is applied instead of solving the Hamilton–Jacobi equation.

The acceleration of convergence of objective function is drastically improved by the implementation of MMA.

Normally, the level set method is solved through the Hamilton–Jacobi equation. However, the possibility of introducing mathematical programming is clear by the constrained condition. Furthermore, the proposed method is suitable for efficiently solving the topology optimization problem in the magnetic field system.

The purpose of this paper is to improve the multistep algorithm using evolutionary algorithm (EA) for the topology optimization of magnetostatic shielding, and the paper reveals the effectiveness of methodology by comparison with conventional optimization method. Furthermore, the design target is to obtain the novel shape of magnetostatic shielding.

The EAs based on random search allow engineers to define general-purpose objects with various constraint conditions; however, many iterations are required in the FEA for the evaluation of the objective function, and it is difficult to realize a practical solution without island and void distribution. Then, the authors proposed the multistep algorithm with design space restriction, and improved the multistep algorithm in order to get better solution than the previous one.

The variant model of optimized topology derived from improved multistep algorithm is defined to clarify the effectiveness of the optimized topology. The upper curvature of the inner shielding contributed to the reduction of magnetic flux density in the target domain.

Because the converged topology has many pixel element unevenness, the special smoother to remove the unevenness will play an important role for the realization of practical magnetostatic shielding.

The optimized topology will give us useful detailed structure of magnetostatic shielding.

First, while the conventional algorithm could not find the reasonable shape, the improved multistep optimization can capture the reasonable shape. Second, An additional search is attached to the multistep optimization procedure. It is shown that the performance of improved multistep algorithm is better than that of conventional algorithm.