Uncertainty Quantification and Propagation Framework in Electrical Machine Design

This thesis delves into the critical domain of uncertainty quantification and prop- agation within the context of electrical machine design, aiming to enhance the reliability and robustness of these integral components in various applications. As electrical machines continue to play a pivotal role in diverse industries, such as transportation, renewable energy, and manufacturing, the need for a comprehen- sive modelling of uncertainties becomes essential. The work begins by directing its attention to the intricate interplay between un- certainties and the performance of electrical machines. This involves an in-depth investigation into the sources of uncertainties, ranging from manufacturing toler- ances and material properties to environmental conditions and operating param- eters. The thesis then adapts a framework for quantifying and propagating uncertain- ties through computational models, integrating stochastic simulation for electrical machine problems. For a stochastic quantification of input parameters, methods are introduced by which the deviations in actual occurring geometries, sources and material properties can be efficiently described in terms of joint probability den- sity function. Uncertainty propagation techniques involve the selection of suitable models to map the inputs and outputs; thereby, methods for forward propagation, sensitivity, and reliability analysis can be applied. The curse of dimensionality poses a significant drawback when dealing with multi- ple dependent stochastic parameters, and non-intrusive surrogate modelling meth- ods such as Kriging and Polynomial Chaos Expansion are applied together to re- duce the computational effort involved in performing the usual collocation-type Monte-Carlo simulations. The presented methods and models are then used in two case studies. The first deals with the effect of system tolerances on the estimated position of a low-cost, direct-driven, tubular permanent magnet linear motor. Effective use of surrogate modelling techniques enables a robust design and assembling process, thereby increasing the performance of the motors for the same cost. The second case study deals with the circulating current losses in the stator wind- ings of high-speed machines with many parallel-stranded round wires per winding turn. The inherent stochasticity in the trickling process of winding assembly is mathematically quantified, and the uncertainties are propagated.