A Parametrical Determination of the Influence Region of Holes in Electromagnetic Devices by the Compensation Theorem

In the optimal design of electromagnetic devices, the robustness is a critical aspect. In the modern robust optimization procedures, the evaluation of suitable partial derivatives is required at each step of the search process; the estimate of the sensitivity is required also in non robust optimizations if the robustness of the final design with respect to a number of independent parameters must be assessed. On the other hand, the tolerance analysis is a widely adopted tool in the analysis of electromagnetic devices, whose main aim is to assess the impact of some independent uncertain parameters (e.g. geometrical dimensions or materials properties) on a device performance as, for example, the electromagnetic field in a volume of interest. Similar considerations apply when a general property in nominal design, such as symmetry, is lost due to non symmetrical deformations. In both cases - robust design and tolerance analysis - if assuming a linear behavior of the system, the classical compensation theorem can reveal to be a quite powerful tool.