  In the last few decades, uncertainty quantification (UQ) methods have been
used widely to ensure the robustness of engineering designs. This chapter aims
to detail recent advances in popular uncertainty quantification methods used in
engineering applications. This chapter describes the two most popular
meta-modeling methods for uncertainty quantification suitable for engineering
applications (Polynomial Chaos Method and Gaussian Process). Further, the UQ
methods are applied to an engineering test problem under multiple
uncertainties. The test problem considered here is a supersonic nozzle under
operational uncertainties. For the deterministic solution, an open-source
computational fluid dynamics (CFD) solver SU2 is used. The UQ methods are
developed in Matlab and are further combined with SU2 for the uncertainty and
sensitivity estimates. The results are presented in terms of the mean and
standard deviation of the output quantities.
