Comparison of Hyper-Reduction Methods Combined With POD: Model Order Reduction of a Squirrel Cage Induction Machine in Nonlinear Case

In an industrial context of electrical device design or expertise, it is common for engineer to use models based on the Finite Element (FE) method. In the case of nonlinear magneto-quasistatic problems, it can lead to prohibitive computational times. Then, Model Order Reduction (MOR) approaches based on the Proper Orthogonal Decomposition (POD) combined with a hyper-reduction method can be employed to reduce the computational time but often leads to numerical instabilities. In this article, we aim to compare two hyper-reduction methods that were developed to improve the stability of the nonlinear reduced model: the Gaussian Newton Augmented Tensors (GNAT) method and the Energy-Conserving mesh Sampling and Weighting (ECSW) method. The reduced models are evaluated in terms of accuracy on global and local quantities of interest and in terms of speedup, with application to a squirrel cage induction machine. Improvement of the ECSW method has been proposed such that it appears that this method is more competitive than the GNAT method and enables to obtain very good results both in terms of accuracy and time computation, which was reduced by a factor 40 compared to the FE model.