*3.1. Sensitivity Analysis*

The influence of changes in geometry and material parameters on physical quantities as well as temporal and spatial characteristics is investigated and quantified by means of sensitivity analyses. In the case of coupling one of the presented electromagnetic machine models with another, for example structural dynamic or thermal model, they also provide information about the required accuracy of the coupled model, since the latter does not have to have an influence on machine parameters to which the electromagnetic model is not sensitive.

The starting point of the sensitivity analysis for the IM is a reference geometry. Based on this, a second, slightly modified machine geometry is generated, depending on the geometry or material parameter to be investigated. For this, the parameter is changed by a user defined factor *r*sens. In this case, too small a change leads to numerical instabilities, and too large changes possibly lead to inconsistent machine geometries. If the sensitivity to a geometry parameter is to be investigated, it is also necessary to consider the influence of this parameter on other geometry variables. For example, if the air gap width is changed, the stator or rotor diameter must also be adjusted. These influences are described via a correlation matrix, which describes for each possible variable geometry parameter which other geometry parameters must also be changed. Subsequently, the machine models are simulated for both geometries and the output quantities are compared. In this work, a T-FEM simulation is not performed in the context of the sensitivity analysis due to the high computational effort associated with it. Instead, the same results are assigned to the T-FEM as to the TH-FEM, since the value ranges and levels of detail are very similar

due to analogous procedures in meshing. The following findings can be derived from the comparison of the output quantities of both geometries:


$$
\epsilon\_{\text{phys}} = \frac{r\_{\text{phys}}}{r\_{\text{sens}}} ,\tag{25}
$$

where *r*phys describes the relative change of the physical quantity between the two simulated machine models. This allows us to capture, for each model, how much a certain quantity changes when the parameter under investigation is modified.

4. Level of Detail: The description of the level of detail of the detection of a geometry or material change, related to a physical quantity can be done by means of a reference model. For this purpose, the TH-FEM is selected in this work, since it has the highest average precision after the T-FEM. The degree of detail of a physical quantity, therefore, follows from the relative deviation of the elasticity of the model under consideration from the elasticity of the TH-FEM.
