Uncertainty Quantification by the Nonintrusive Polynomial Chaos Expansion with an Adjustment Strategy

Abstract

This paper proposes the criteria to adjust the polynomial order and the number of sample points employed in the nonintrusive polynomial chaos expansion method for effective uncertainty quantification. These criteria are calculated based on the total variations in approximated responses between different polynomial orders and different numbers of sample points to avoid Runge’s phenomena. The polynomial chaos expansion method adjusted by the proposed criteria is tested in analytic functions and then applied to the sonic boom propagation analysis considering the uncertainty in atmospheric temperature, humidity, and wind velocity. It is confirmed that the polynomial chaos expansion method with the proposed adjustment strategy can estimate the statistics of the sonic boom signature with sufficient accuracy and only 0.35% of the computational cost compared with the Monte–Carlo method.