Study on machine learning for generation of finite element models of electrical machines

在本研究中，我们开发了一种新的方法来实现电机有限元网格的自动生成。在该方法中，准备初始过程网格，并且计算元素属性P，其中P是元素特征的线性组合，诸如在元素处的磁感应强度、到磁性材料的最近角的距离、到最近电流源的距离等。具有最大P的元素被细分为两个较细的元素。并且重复该过程，直到元素的数量等于规定数量。然后对得到的网格进行了有限元分析的误差计算。该误差强烈依赖于网格质量，而网格质量又依赖于元素特征线性组合中的权重。利用遗传算法对权值进行了优化。当权值优化时，该方法也可应用于其他类似的电机有限元模型。结果表明，该方法具有较高的精度和较高的精度使用上述方法的有限元网格较多，称为SIMPLE方法，通常含有平面单元，不适合进行有限元分析。为了解决这一困难，我们引入了网格控制技术，以便根据单元边的长度来确定单元边的细分数量，以及选择要细分的单元的标准。结果表明，用这种方法得到的有限元网格比用SIMPLE方法得到的有限元网格质量要好，虽然网格控制方法提高了网格质量，但当初始过程网格中含有平面单元时，网格质量变差。只要网格是从初始网格生成的，就很难克服这个问题。为此，我们介绍了另一种方法，其中使用上述机器学习来确定节点的密度，并在上述节点的基础上使用Delaunay三角剖分来生成单元。结果表明，该方法提高了网格的质量。较少

In this research, we have developed a new method to realize automatic generation of finite element meshes for electric machines. In this method, an initial course mesh is prepared, and element properties P are computed where P is a linear combination of element features such as magnitude of magnetic induction at the element, distance from the nearest corner of magnetic material, distance from the nearest current source and so on. The element with largest P is subdivided into two finer elements. And this process is repeated until the number of elements equals a prescribed number. The error in the finite element analysis on the obtained mesh is then computed. This error strongly depends on the mesh quality, which is dependent on the weights in the linear combination of the element features. We optimize the weights using the genetic algorithm. When the weights are optimized, this method can be applied for other similar finite element models of electrical machines.It is shown that the resu … More ltant finite element mesh using the above method, called the simple method, often have flat elements which are inadequate for finite element analysis. To resolve this difficulty, we introduce mesh control techniques so that the number of subdivision of element edges is determined from their length and a criterion to choose elements to be subdivided. The finite element meshes obtained using this method, called the mesh control method, are shown to be better than those obtained using the simple method.Although the mesh quality is improved by the mesh control method, it becomes worse when the initial course mesh includes flat elements. It is difficult to overcome this problem as long as the mesh is generated from the initial mesh. For this reason, we introduce another method where the density of nodes is determined using the above mentioned machine learning, and elements are generated using the Delaunay triangulation on the basis of the nodes obtained above. This method is shown to improve the mesh quality. Less