Robust Design Optimization of Electrical Machines Considering Hybrid Random and Interval Uncertainties

For robust design optimization (RDO) of electrical machines, cases with random uncertainty and interval uncertainty are generally investigated separately. Accordingly, the performance fluctuation analysis under uncertainty is based on random method and interval method respectively. However, the problem with hybrid uncertainties can also be met yet rarely researched. Under this circumstance, the uncertainty analysis methods for a single type of uncertainty may no longer be applicable, which challenges the robust optimization conduction. For effective RDO of electrical machines with hybrid uncertainties, this article presents a robust optimizer based on evolutionary algorithms and the polynomial chaos Chebyshev interval (PCCI) method. The PCCI method is utilized for effectively modeling the fluctuations caused by the hybrid uncertainty with a small number of samples. As additional enhancements, the filtering strategy for the algorithm with deterministic constraints is proposed to reduce the solutions that require robustness analysis in each iteration and accelerate the optimization further while not affecting the global convergence ability. A design example of a brushless DC motor considering hybrid uncertainties is analyzed and optimized. The results confirm the feasibility of the proposed method.