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This article introduces a topology optimization method for a surface permanent magnet (SPM) motor with high torque density suitable for air mobility. The proposed method can be used to determine the material distribution and magnetization direction in PMs to maximize the torque density at a constant current. The torque performance of the optimized motor is superior to that of a conventional motor with a Halbach array, whose magnetization varies linearly along the circumferential direction. The novel optimized motor has a triangular magnetic material on the rotor surface and an air region inside the rotor.

This article presents a strategy of optimizing inductors with non-linear properties, using Monte Carlo tree search (MCTS). Compared with the existing optimization tools, the proposed method can simultaneously optimize global configuration, such as material, number of turns and winding arrangement, and local geometry. It indicates that the strategy statistically provides a best solution from global and local aspects after iterations with different lengths of chromosomes, which is challenging in conventional optimization techniques. The covariance matrix adaptation evolution strategy (CMA-ES) is used to solve the parametric optimization. For validation, the optimizations on 2-D inductors are performed. The proposed method is very suitable for the optimization of devices with possibly different global configurations. The most notable originality of this work is in the proposal of an inherited search for design targets with different emphases, suggesting that using an inherited search from the previous search history can make it easier to find the optimal solution.

In this study, we present a topology-parameter hybrid optimization of a permanent magnet motor with a step-skewed rotor. This optimization simultaneously performed topology optimization (TO) of the core shape and parameter optimization (PO) of the skew angle. Simultaneous optimization provides optimized motors that are superior to those obtained by parameter, topology, and sequential optimizations. Moreover, the optimized shape was shown to be robust with respect to variations in the skew angle.

This study proposes a novel multi-objective design method based on Monte Carlo tree search (MCTS) for the design of permanent magnet (PM) motors. The global configurations that define the entire structure are represented by nodes in a tree structure. After MCTS is performed to select a route extending from the root to leaf node, multi-objective topology optimization (TO) is performed at the leaf node to determine the detailed shape, considering a trade-off relationship among objective functions. The novelty of this work lies in the integration of MCTS with multi-objective TO where the score of a node is provided by the number of Pareto solutions obtained by selecting that node. This enables the scoring of nodes and the determination of the node selection criterion. The proposed method is applied to the multi-objective optimization of a PM motor with respect to average torque, and either torque ripple or iron loss. The proposed method successfully obtained Pareto solutions, which comprise various global configurations and shapes.

This study proposes a novel topology optimization (TO) method for permanent magnet (PM) motors based on a variational autoencoder (VAE) and a neural network (NN). The VAE is trained to embed various shapes generated from the TO into the latent space. The NN is trained to predict the characteristics of the PM motor from its latent representation derived using the VAE. After training, TO is performed in the latent space based on the prediction using the NN. We adopt the Monte Carlo dropout to maintain prediction reliability using the NN during optimization, where prediction deviation is evaluated and used to eliminate unreliable solutions. The proposed method yields Pareto solutions within 80 s in a single-thread CPU machine, which is considerably faster than numerical analysis-based optimization, such as finite-element analysis.

This paper proposes a multi-objective optimization method for permanent magnet motors using a fast optimization algorithm, Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and deep learning. Multi-objective optimization with topology optimization is effective in the design of permanent magnet motors. Although CMA-ES needs fewer population size than genetic algorithm for single objective problems, this is not evident for multi-objective problems. For this reason, the proposed method generates training data by solving the single-objective optimization multiple times using CMA-ES, and constructs a deep neural network (NN) based on the data to predict performance from motor images at high speed. The deep NN is then used for fast solution of multi-objective optimization problems. Numerical examples demonstrate the effectiveness of the proposed method.