Influence of reduced-order modelling of geometrical uncertainties on statistics

The quanti�cation of aerodynamic uncertainties due to random variations of aircraft geometry often involves large number of variables which necessitate model reduction techniques, e.g. by truncated Karhunen-Lo�eve expansion (KLE). This, however, comes along with some additional uncertainty in a twofold sense, i.e. a loss in variance caused by the model reduction and whether it is worthwhile to apply model reduction when surrogate methods make high dimensional integration viable. In this work we model the uncertainties in airfoil geometry with both truncated and full KLE and integrate for some statistics of aerodynamic performance with the help of surrogate methods. By this we are trying to quantify the in uence of the truncation on the statistics and to compare the accuracy of the statistics obtained on the basis of the truncated and full KLE using surrogate-based integration. The comparison is also extended to a 3D wing with a large but rank-de�cient covariance matrix for its random �eld of geometric uncertainty, which we approximate with a low-rank Cross Approxmation tech- nique.