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Numerical methodologies for topology optimization of electromagnetic devices

Abstract : Topology optimization is the conceptual design of a product. Comparing with conventional design approaches, it can create a novel topology, which could not be imagined beforehand, especially for the design of a product without prior-experiences or knowledge. Indeed, the topology optimization technique with the ability of finding efficient topologies starting from scratch has become a serious asset for the designers. Although originated from structure optimization, topology optimization in electromagnetic field has flourished in the past two decades. Nowadays, topology optimization has become the paradigm of the predominant engineering techniques to provide a quantitative design method for modern engineering design. However, due to its inherent complex nature, the development of applicable methods and strategies for topology optimization is still in progress. To address the typical problems and challenges encountered in an engineering optimization process, considering the existing methods in the literature, this thesis focuses on topology optimization methods based on deterministic and stochastic algorithms. The main work and achievement can be summarized as: Firstly, to solve the premature convergence to a local optimal point of existing ON/OFF method, a Tabu-ON/OFF, an improved Quantum-inspired Evolutionary Algorithm (QEA) and an improved Genetic Algorithm (GA) are proposed successively. The characteristics of each algorithm are elaborated, and its performance is compared comprehensively. Secondly, to solve the intermediate density problem encountered in density-based methods and the engineering infeasibility of the finally optimized topology, two topology optimization methods, namely Solid Isotropic Material with Penalization-Radial Basis Function (SIMP-RBF) and Level Set Method-Radial Basis Function (LSM-RBF) are proposed. Both methods calculate the sensitivity information of the objective function, and use deterministic optimizers to guide the optimizing process. For the problem with a large number of design variables, the computational cost of the proposed methods is greatly reduced compared with those of the methods accounting on stochastic algorithms. At the same time, due to the introduction of RBF data interpolation smoothing technique, the optimized topology is more conducive in actual productions. Thirdly, to reduce the excessive computing costs when a stochastic searching algorithm is used in topology optimization, a design variable redistribution strategy is proposed. In the proposed strategy, the whole searching process of a topology optimization is divided into layered structures. The solution of the previous layer is set as the initial topology for the next optimization layer, and only elements adjacent to the boundary are chosen as design variables. Consequently, the number of design variables is reduced to some extent; and the computation time is thereby shortened. Finally, a multi-objective topology optimization methodology based on the hybrid multi-objective optimization algorithm combining Non-dominated Sorting Genetic Algorithm II (NSGAII) and Differential Evolution (DE) algorithm is proposed. The comparison results on test functions indicate that the performance of the proposed hybrid algorithm is better than those of the traditional NSGAII and Strength Pareto Evolutionary Algorithm 2 (SPEA2), which guarantee the good global optimal ability of the proposed methodology, and enables a designer to handle constraint conditions in a direct way. To validate the proposed topology optimization methodologies, two study cases are optimized and analyzed.
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Submitted on : Sunday, November 29, 2020 - 7:26:54 PM
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Yilun Li. Numerical methodologies for topology optimization of electromagnetic devices. Electronics. Sorbonne Université; Zhejiang University (Hangzhou, Chine), 2019. English. ⟨NNT : 2019SORUS228⟩. ⟨tel-03030125⟩

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