Robust optimisation formulations for the design of an electric machine

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., 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. 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.

Robust shape optimization of electric devices based on deterministic optimization methods and finite-element analysis with affine parametrization and design elements

“…, M . Inserting this approximation into (5), one obtains the linear approximation of the robust optimization problem:…”

“…Cross-section of one pole of the machine with the magnet depicted in gray and the region of the affine decomposition indicated by the dashed box. On the right hand side, the triangulation into L subdomains is shown by the dashed-dotted lines.Figure adapted from[5].…”

Sensitivity analysis of inverse problems in EM non‐destructive testing

“…Furthermore, Sobol indices are applied in EMs under many different guises. Just to name a few, robust design of EM machines [13], understanding complex EM scattering mechanisms in remote sensing [14] or analysis of wave propagation in random urban environment [15] are mentioned.…”

Reduced basis methods for quasilinear elliptic PDEs with applications to permanent magnet synchronous motors

“…One of the engineering design goals consists in improving the performance of the motor through modifying the size and/or location of the permanent magnets. This problem can be viewed as a parameter optimization problem [1,2,3,4], where the parameters determine the geometry of the computational domain. The underlying optimization problem then requires repeated solutions of the nonlinear (in general) elliptic problem on the parametrized domain.…”