Multivariate Sensitivity Analysis of Electric Machine Efficiency Maps and Profiles Under Design Uncertainty

TL;DR

This work tackles uncertainty in electric machine design by introducing multivariate global sensitivity analysis (MV-GSA) to assess how uncertain design parameters affect multidimensional outputs such as efficiency maps and profiles. By forming generalized sensitivity indices $G_n$ and $G_{Tn}$ from the covariance of multivariate outputs, MV-GSA provides a single, holistic measure of parameter importance and avoids the interpretability issues of elementwise Sobol' indices. The authors compare Monte Carlo and polynomial chaos expansion approaches, demonstrating substantial computational advantages for PCE on maps and profiles, and use MV-GSA to fix non-influential parameters while preserving accuracy, validated on two PMSM models (an ECM and an isogeometric model). The results advocate MV-GSA as a practical tool for uncertainty quantification and design simplification in multidimensional performance spaces, with potential extensions to other multidimensional outputs such as torque signals or field distributions.

Abstract

This work proposes the use of multivariate global sensitivity analysis for assessing the impact of uncertain electric machine design parameters on efficiency maps and profiles. Contrary to the common approach of applying variance-based (Sobol') sensitivity analysis elementwise, multivariate sensitivity analysis provides a single sensitivity index per parameter, thus allowing for a holistic estimation of parameter importance over the full efficiency map or profile. Its benefits are demonstrated on permanent magnet synchronous machine models of different fidelity. Computations based on Monte Carlo sampling and polynomial chaos expansions are compared in terms of computational cost. The sensitivity analysis results are subsequently used to simplify the models, by fixing non-influential parameters to their nominal values and allowing random variations only for influential parameters. Uncertainty estimates obtained with the full and reduced models confirm the validity of model simplification guided by multivariate sensitivity analysis.

Figures (11)

• Figure 1: .
• Figure 2: Mean and standard deviation of the 's efficiency map, along with pointwise absolute errors between - and -based estimates.
• Figure 3: Elementwise Sobol' of the 's efficiency map. Only first-order indices are shown, due to negligible higher order interactions.
• Figure 4: Multivariate of the 's efficiency map.
• Figure 5: Mean and standard deviation of the 's efficiency profile, along with pointwise absolute errors between - and -based estimates.