Fengyi Jin

Topology optimization is an effective method for obtaining high-performance material distributions with novel configurations. However, its application to complex electromagnetic devices remains challenging because of the difficulty of deriving sensitivities and the low computational efficiency associated with repeated finite element method (FEM) evaluations for nonlinear materials. This paper proposes an efficient gradient-free topology optimization method that integrates superellipse curves with a multilayer perceptron (MLP) surrogate model while accounting for nonlinearity. First, based on the general superellipse curve, an improved expression is introduced, in which the size, shape, and position can be flexibly controlled by only seven parameters. Then, a parameterized superellipse-curve-based gradient-free topology optimization framework is established, which can be applied to complex electromagnetic devices with nonlinear materials and complex objective functions. Moreover, a lightweight MLP-based surrogate model is constructed using limited training samples generated by Latin hypercube sampling and FEM, and it can replace FEM for evaluating nonlinear material behavior with negligible computational cost. Finally, the proposed topology optimization framework is applied to the design of a magnetic actuator, both with and without considering nonlinear B–H characteristics, demonstrating its effectiveness.

Structural optimization plays a crucial role in enhancing the performance of magnetic actuators. Traditional design approaches, such as parametric scanning, are limited by their reliance on empirical geometries. Meanwhile, widely used topology optimization techniques—including the Solid Isotropic Material with Penalization (SIMP) method and level-set methods—often encounter difficulties such as a large number of design variables, high computational cost, and unclear structural boundaries. To overcome these limitations, this paper proposes a novel gradient-free topology optimization method based on superellipses for designing magnetic actuator yokes. The proposed approach offers three key benefits: (1) It requires very few design variables, with each superellipse described by only seven parameters, thereby reducing the dimensionality of the design space and simplifying the optimization problem. (2) It yields clear and smooth structural boundaries without the need for post-processing. (3) It operates without gradient information, employing stochastic algorithms such as genetic algorithms that rely solely on objective function evaluations. A case study on yoke optimization demonstrates that our method achieves magnetic force output comparable to or better than the SIMP method, but with significantly fewer variables and a simpler implementation. This work provides an efficient and new tool for the conceptual design of magnetic actuators and related electromagnetic devices.