Multi-Objective Robust Optimization of a Dual-Flux-Modulator Magnetic Geared Machine with Hybrid Uncertainties

In order to improve the robustness and torque performance of a dual-flux-modulator magnetic-geared machine (DFM-MGM) considering simultaneously both random and interval uncertainties of design parameters, a multi-objective robust optimization (MORO) method with multiple Monte Carlo simulations (MCSs) is proposed. In this method, the multiple MCSs are adopted to evaluate the effects of parametric hybrid uncertainties on the robustness of optimization results. To build a MORO model of the DFM-MGM, the three-dimensional finite element model is established firstly and then validated by the experiment. Through a parametric study, it is found that five dimensional parameters of the permanent magnets (PMs) and stator have more significant effects on the stall torque (ST) and ST per PM volume (STPPV). Finally, a multi-objective particle swarm optimization algorithm with surrogate models, sigma criteria design and multiple MCSs method is implemented to solve the MORO problem. Both the average standard deviations and standard deviation differences of the ST and STPPV are used to deal with hybrid uncertainties during MORO. The optimized DFM-MGM by MORO has a STPPV 6.3% higher than that of the initial design under the same ST constraint. Moreover, the average standard deviations and standard deviation differences obtained by MORO are much smaller than those achieved by the deterministic optimization, indicating that the robustness of optimal results can also be significantly improved by the MORO.