Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification

We consider the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC) and augment linear system with gradient of Quantity Interest (QoI) respect to stochastic variables. The is computed very efficiently all variables from adjoint equations. To minimise condition number augmented LSQ system, an effective sampling strategy space required. compare two strategies. In first, we apply pivoted QR decomposition standard matrix evaluate both QoI its at sample points identified. second strategy, directly matrix. find that first more efficient in terms accuracy vs evaluations. call new approach sensitivity-enhanced chaos, or se-gPC, it several test cases including aerodynamic case 40 parameters. can produce accurate estimations statistical moments a small points. computational cost scales as ∼mp−1, instead ∼mp formulation, where m p order. solution equations implemented many mechanics packages, thus infrastructure exists application wide variety engineering problems.