Robust Optimization Approaches for the Design of an Electric Machine

TL;DR

This paper compares two robust optimization methods for designing electric machines, demonstrating that the uncertainty quantification approach yields less conservative magnet sizes and is more efficient when combined with model order reduction.

Contribution

It introduces and compares worst-case and UQ-based robust optimization formulations for electric machine design, utilizing affine geometry parametrization and model order reduction for efficiency.

Findings

UQ-based approach results in smaller magnets.

Both methods are equivalent under linearization.

UQ approach is less pessimistic regarding deviations.

Abstract

In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic behavior of the machine. The need for a robust optimization procedure originates from the fact that optimization parameters have deviations. The first approach, i.e., \textcolor{red}{worst-case} optimization, makes use of local sensitivities. The second approach takes into account expectation values and standard deviations. The latter are associated with global sensitivities. The geometry parametrization is elegantly handled thanks to the introduction of an affine decomposition. Since the stochastic quantities are determined by tools from uncertainty quantification (UQ) and thus require a lot of finite element evaluations, model order reduction is used in order to increase the efficiency of the procedure. It is shown that both approaches are equivalent if a linearization is carried out. \textcolor{blue}{This finding is supported by the application on an electric machine. The optimization algorithms used are sequential quadratic programming, particle swarm optimization and genetic algorithm}. While both formulations reduce the size of the magnets, the UQ based optimization approach is less pessimistic with respect to deviations and yields smaller magnets.