This paper presents an effective approach for uncertain aerodynamic analysis of airfoils via the polynomial chaos expansion (PCE). To achieve this, the multivariate polynomial is first setup to represent random factors within the aerodynamic model, whereas the expansion coefficient is expressed as the multivariate stochastic integral of the input random vector. In this regard, the statistical regression in conjunction with a small number of representative samples is employed to determine the expansion coefficient. Then, a combination of the PCE surrogate model with brutal-force Monte Carlo simulation allows to determine numerical results for the uncertain aerodynamic analysis. Potential applications of this approach are first illustrated by the uncertainty analysis of the Helmholtz equation with spatially varied wave-number random field, and its effectiveness is further examined by the uncertain aerodynamic analysis of the NACA 63-215 airfoil. Results for the small regression error and a close agreement between simulated and benchmark results have confirmed numerical accuracy and efficiency of this approach. It, therefore, has a potential to deal with computationally demanding aerodynamical models for the uncertainty analysis.
Probabilistic surrogate models for uncertainty analysis: Dimension reduction‐based polynomial chaos expansion
