Robust optimisation formulations for the design of an electric machine

In this study, two formulations for the robust optimisation of the size of the permanent magnet in a synchronous machine are discussed. The optimisation is constrained by a partial differential equation to describe the electromagnetic behaviour of the machine. The need for a robust optimisation procedure originates from the fact that optimisation parameters have deviations. The first approach, i.e. worst‐case optimisation, 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 parametrisation 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 linearisation is carried out. This finding is supported by the application on an electric machine. The optimisation algorithms used are sequential quadratic programming, particle swarm optimisation and genetic algorithm. While both formulations reduce the size of the magnets, the UQ‐based optimisation approach is less pessimistic with respect to deviations and yields smaller magnets.