Use of Compensation Theorem for the Robustness Assessment of Electromagnetic Devices Optimal Design

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 to define sensitivity at each step of the search process; the estimate of the sensitivity is required also in non robust design if the robustness of the final configuration must be assessed with respect to a number of independent parameters. More generally, 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. In both cases - robust design and tolerance analysis - if assuming a linear behavior of the system, a number of simplified approaches can be adopted to compute the effect of “deformations” starting from knowledge of nominal solution. One of the best known is the compensation theorem, which will be discussed with some detail in the paper, but other techniques, suited for particular numerical models, can also be exploited to simplify computations. An example of such possibilities will be discussed