Robust feasibility verification and region inner-point detection algorithms for geometric shape objects applied to electric machine optimization workflow

Abstract

In most cases, the search for the optimal design of an electrical machine is closely related to its 2D radial cross section. When optimizing a 2D cross section, special attention must be paid to the geometry and to the definition of the parameters along with their boundaries. Even if properly bounded, complex geometries generated by optimization algorithms can lead to geometrically infeasible candidates. These cannot be manufactured because they contain generally undesirable geometric relationships between air, magnets, and steel. Different commercial and open-source finite element analysis (FEA) design tools treat the infeasible designs differently. The results vary from simulation stop to successful FEA calculation of the infeasible candidate, which wastes time by producing useless data. To prevent the infeasible designs from entering the optimization competition and possibly appearing incorrectly as optimal solutions, and to reduce optimization time, it is important to capture the infeasible designs during optimization. Moreover, the FEA tool requires a precisely determined interior point to assign the material to each closed region (air, steel, epoxy, magnet...). This can be very challenging for complex geometries. To avoid creating geometry or material regions that are not valid, this paper proposes a novel robust methods for checking feasibility and determining interior points on geometric shape objects. In this paper, the proposed method is applied to the optimization of electrical machines.