Propagation of input model uncertainties with different marginal distributions using a hybrid polynomial chaos expansion

We propose the use of a hybrid polynomial chaos expansion using both Legendre and Hermite polynomials to assess the combined effect of uniform and Gaussian distributed uncertainties. We show that the hybrid method converges exponentially with respect to the polynomial order of the hybrid basis. We also show that mapping the uniformly distributed uncertainties to a Gaussian probability then expanding with a purely Hermite basis results in a severely deteriorated convergence rate.