  This paper focuses on the application of the variance-based global
sensitivity analysis for a topology derivative method in order to solve a
stochastic nonlinear time-dependent magnetoquasistatic interface problem. To
illustrate the approach a permanent magnet synchronous machine has been
considered. Our key objective is to provide a robust design of the rotor poles
and of the tooth base in a stator for the reduction of the torque ripple and
electromagnetic losses, while taking material uncertainties into account. Input
variations of material parameters are modeled using the polynomial chaos
expansion technique, which is incorporated into the stochastic collocation
method in order to provide a response surface model. Additionally, we can
benefit from the variance-based sensitivity analysis. This allows us to reduce
the dimensionality of the stochastic optimization problems, described by the
random-dependent cost functional. Finally, to validate our approach, we provide
the two-dimensional simulations and analysis, which confirm the usefulness of
the proposed method and yield a novel topology of a permanent magnet
synchronous machine.
