In recent years, probabilistic methods have become
increasingly important in engineering applications. They allow
a quantification of the impact of the variability of components
on result values. In this thesis, existing probabilistic methods
are analyzed and new ones are introduced to improve their
performance, especially in the context of the probabilistic
analyses of jet engine components.
A major focus of the thesis is on the analysis of sampling
methods, especially with regard to the resulting surrogate
model quality. For this purpose, Latinized Particle Sampling is
introduced as a new method in which the realizations of the
sample are considered as charged particles. This new method
is then compared with existing sampling methods.
Another focus is on sensitivity analysis with correlated input
variables. Established methods such as the Sobol indices or
Shapley values cannot reliably identify input variables without
functional influence in such cases. Therefore, the modified
coefficient of importance is introduced as a new sensitivity
measure. Finally, the discussed methods are applied to the
analysis of compressor blades subject to manufacturing
variability and their advantage is demonstrated.
