Variance-Based Robust Optimization of a Permanent Magnet Synchronous Machine

This paper focuses on the application of the variance-based global sensitivity analysis for a topological derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasi-static interface problem. To illustrate the approach a permanent magnet (PM) 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 2-D simulations and analysis, which confirm the usefulness of the proposed method and yield a novel topology of a PM synchronous machine.