基 于 多 项 式 混 沌 法 的 翼 型 不 确 定 性 分 析 及 梯 度优 化 设 计

An efficient and reliable uncertainty gradient optimization design method is developed by coupling the adjoint method and the non-intrusive polynomial chaos method. Using the adjoint equation method to solve the derivative of the objective function with respect to the uncertain variable，we develop a gradient-enhanced polynomial chaos expansion method. Various examples at subsonic and transonic speeds prove that this method can improve the efficiency and ac⁃ curacy of uncertainty analysis. Meanwhile，the sensitivity of uncertain variables is quantified using a global sensitivity analysis method based on variance decomposition. A statistical moment gradient solution method for the coupled ad⁃ joint equation of polynomial chaos is established，and an uncertain gradient optimization design system built by combin⁃ ing the gradient-enhanced polynomial chaos expansion method. Based on the optimization design system，the deter⁃ ministic and uncertain optimization design research of two-dimensional low subsonic and transonic airfoils is conducted. The optimization results show that，compared with the deterministic optimal design，the uncertain optimal design can improve the ability to resist the uncertainty perturbation of Mach number and angle of attack by reasonably balancing the deterministic performance and the uncertain performance，and optimize the average performance and performance ro⁃ bustness. The mean value and the standard deviation of the drag coefficient can be reduced by up to 17% and 80%，respectively. The deterministic optimization design may lead to a decrease in performance robustness.