Performance analysis of a robust design optimization of a solenoid with different sensitivity metrics

Abstract

Optimization is an essential part of designing electrical machines and devices. Considering the uncertainties and tolerances from the beginning of the design process can lead to a more robust design and significantly reduce the number of waste products during the manufacturing process. However, the computational demand for these robust design optimization problems is amazingly high. This paper examines how the computational demand and the robustness of the results depend on the applied sensitivity metric. The multi-objective TEAM 35 benchmark problem has been used as the basis of the comparison. This optimization task aims to create a homogeneous magnetic field in a predefined coil region, which is insensitive to the positioning errors of the coil turns. The original definition of the problem uses a simple worst-case sensitivity metric calculated from the extreme values of the optimized turn parameters in the given tolerance range. This sensitivity metric has been replaced by Plackett–Burman, Box–Behnken, and Central Composite Design-based metrics. It was shown in this simple geometry that there is a significant difference between the resulting sensitivities. Nevertheless, Plackett–Burman and Central Composite Design provided the more accurate and consistent estimate of the sensitivity of the examined layouts, with a higher but still reasonable computation demand than the worst-case metric.