Why engineers should care about semi-infinite programming: Nominal versus tolerance-aware geometry optimization of a proportional electromagnetic actuator

The geometry of a proportional electromagnetic actuator is optimized using a recent method for semi-infinite programming. To ensure cost-efficient manufacturing, both the nominal geometry and the manufacturing tolerances are optimized simultaneously to achieve the required force characteristics across all tolerance combinations. To minimize the number of FEM simulations, the applied method employs adaptive learning via a Gaussian process model to model the relationship between the nominal geometry, tolerances, and the resulting force characteristics. Moreover, the proposed algorithm avoids multiple optimization stages but allows for a direct solution of semi-infinite programs, which further increases the sample efficiency. Two formulations of the optimization problem are compared based on the number of FEM simulations required. It is demonstrated that a feasible nominal geometry and tolerances can be identified with reasonable overhead compared to optimizing the nominal geometry alone. Further, it is shown that in contrast to the simultaneous optimization the combination of nominal optimal geometries with separately defined tolerances leads to actuators which violate the specification.