基于灵敏度的电磁结构形状优化方法研究

RESEARCH ON SENSITIVITY BASED SHAPE OPTIMIZATION METHOD FOR ELECTROMAGNETIC STRUCTURES

研究基于灵敏度的电磁结构形状优化设计方法。针对以往用磁位作为状态变量不方便的情况 ,文中直接采用磁通密度为状态变量。在用直接法求解矢量磁位灵敏度方程的基础上 ,给出适合形状优化的磁通密度灵敏度分析的两种方法———半解析法和局部差分法。前者在磁通密度灵敏度计算中对形函数导数采用了差分近似 ,后者用一阶近似方法得到设计变量扰动后的矢量磁位和磁通密度 ,然后用差分法计算磁通密度灵敏度。两种方法简单且计算效率高 ,精度能够满足要求。优化问题求解采用序列线性规划算法。应用本文方法对电磁铁和同步电机磁极进行形状优化 ,取得了满意的结果。

The methods of shape design optimization of electromagnetic structures based on the design sensitivities are studied in the paper. Considering the inconvenience of using the magnetic vector potential as state variable, magnetic flux density is used as the state variable in the design optimization. Two kinds of methods particularly suitable to shape optimization, semi-analytic method and local difference method, are proposed to calculate the first-order derivatives of magnetic flux density with respect to the design variables on the basis of solving sensitivity equations of the magnetic vector potential. The semi-analytic method uses the difference approximation for the derivatives of shape function in calculating the design sensitivities of the magnetic flux density. The local difference method firstly uses the first-order approximation to obtain the magnetic vector potential and the magnetic flux density with respect to the perturbation of design variable, and then, calculates the design sensitivities of the magnetic flux density with difference method. Both of these methods are simple, efficient, and satisfied in accuracy. The optimization problem is solved with the sequential linear programming algorithm. The methods proposed in the paper are applied in example problems of shape design optimization for electromagnet and pole of salient synchronous machines and satisfied results have been obtained.