Robustness Estimation in TEAM 35 Problem with Interacting Geometric and Current-Density Uncertainties

This paper revisits Problem A of the TEAM 35 benchmark from the viewpoint of robustness estimation under manufacturing uncertainty. Rather than treating the original extremal-position-based sensitivity metric as the formulation to be improved, it is used only as a baseline for comparison with other metrics. In this work, robustness is evaluated as the largest degradation of the nominal magnetic-field homogeneity objective observed over prescribed sets of admissible manufacturing perturbations. In addition to turn-position uncertainties, the present study also includes uncertainty in the excitation current density. While turn-position errors affect each turn individually, current-density uncertainty affects the error contributions of all turns simultaneously through a common term. This common-mode excitation uncertainty represents an extension of the original benchmark formulation and is one of the paper’s main focal points. Several Design of Experiments (DoE) methodologies, as well as search-based robustness estimation strategies, are compared in terms of error in estimated robustness and computational demand. The results show that the original extremal-position-based approximation can substantially underestimate the sampled robustness of the nominal field-homogeneity objective. Including current-density uncertainty further increases the discrepancy between the original metric and the sampled robustness estimates.