基于有限元法（FEM）的物理约束电磁线圈设计代理建模与优化框架
A FEM-Based Surrogate Modelling and Optimization Framework for Physics-Constrained Electromagnetic Coil Design
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中文总结 AI 辅助
本研究构建基于FEM的电磁线圈设计代理建模与优化框架，对比EI-BO、COBYLA、BOBYQA等算法，发现优化器表现与FEM评估预算相关，不同方法在仿真驱动设计中各有优势。
中文摘要 AI 辅助
本研究针对受几何、制造及铁芯、铜质量约束的七参数电流激励线圈-铁芯基准问题，评估代理辅助优化方法。采用Python-MPh-COMSOL工作流，将二维轴对称有限元法（FEM）模型与Matern 5/2高斯过程（GP）概率代理模型耦合；此处“物理约束”指由控制方程FEM模型评估且受显式物理、几何、制造及材料分配约束的设计问题，并非指物理信息型GP架构。序列贝叶斯优化（BO）采用期望改进（EI）对候选方案排序，所有报告的当前最优解均经FEM验证。五组配对运行显示，优化器排序取决于可用FEM评估预算：EI-BO在小延续预算下提升迅速，COBYLA在最早检查点表现更强，BOBYQA获得最高平均终端响应。回顾性有限池研究进一步发现，在该平滑响应曲面上，EI相较于后验均值排序无稳健终点优势。更广泛的结论是，在仿真驱动设计中，早期进展、终端响应、信息利用及挂钟时间成本可能倾向于不同方法。在相同总电流下的选定设计检查保持了观测到的BOBYQA-COBYLA-EI-BO排序。但结论仍以该轴对称基准为条件，未确定固定电流最优解、固定功率性能或电效率优势。
英文摘要
This work evaluates surrogate-assisted optimization of a seven-parameter current-excited coil--core benchmark subject to geometric, manufacturing, and separate core and copper mass constraints. A Python--MPh--COMSOL workflow couples a two-dimensional axisymmetric finite-element method (FEM) model to a Matern 5/2 Gaussian-process (GP) probabilistic surrogate. Here, physics-constrained denotes a design problem evaluated by a governing-equation FEM model and restricted by explicit physical, geometric, manufacturing, and material-allocation constraints; it does not denote a physics-informed GP architecture. Sequential Bayesian optimization (BO) ranks candidates using expected improvement (EI), and every reported incumbent is verified by FEM. Five paired runs show that optimizer ranking depends on the available FEM-evaluation budget: EI--BO improves rapidly at small continuation budgets, COBYLA is stronger at the earliest checkpoint, and BOBYQA attains the highest mean terminal response. A retrospective finite-pool study further finds no robust endpoint advantage of EI over posterior-mean ranking on this smooth response surface. The broader result is that early progress, terminal response, information use, and wall-clock cost can favor different methods in simulation-driven design. A selected-design check at a common total current preserves the observed BOBYQA--COBYLA--EI-BO ordering. The conclusions nevertheless remain conditional on this axisymmetric benchmark and do not establish a fixed-current optimum, fixed-power performance, or electrical-efficiency superiority.
发表机构
- University of Oxford（牛津大学）
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