几何不确定性区间分析及鲁棒气动优化设计

不确定性因素会导致飞行器偏离预先设计的气动性能，造成气动性能下降甚至产生严重的后果。针对工程中无法给出准确的几何不确定性概率分布以及跨声速条件下非线性气动问题，对几何不确定性的非概率参数化建模进行了研究，并结合Kriging模型及最优化方法建立了快速非线性区间分析方法。采用该方法对对称翼型进行不确定性分析，获得了气动性能参数的定量变化区间。在区间不确定性分析基础上建立了鲁棒优化设计流程。基于区间序关系及区间可能度转换模型将单目标区间不确定性优化问题转化为多目标确定性优化问题，并采用基于Pareto熵的自适应多目标粒子群算法对优化问题进行寻优。考虑几何不确定性以及升力、力矩、面积约束，以阻力性能为目标对超临界翼型进行了鲁棒优化设计。与确定性优化设计结果对比表明，确定性优化设计在不确定性因素的影响下易失效，而鲁棒设计可得到更安全可靠的结果。 

Interval analysis for geometric uncertainty and robust aerodynamic optimization design

Uncertainties will make aircraft deviate from the designed aerodynamic performance, resulting in the decrease in aerodynamic performance and even destruction. Due to the problem that the probability distribution of geometric uncertainty cannot be given in engineering and nonlinear aerodynamic problem in transonic flows, the non-probabilistic parametric modeling of geometric uncertainty is studied, and the fast nonlinear interval analysis method is established in combination with Kriging model and optimization method. The effects of geometric uncertainties on a symmetric airfoil are analyzed using the above method, and the quantitative variation range of aerodynamic performance is obtained. Based on interval uncertainty analysis, a robust optimization design process is established. The single-objective interval uncertainty optimization problem was transformed into deterministic multi-objective optimization problem based on the order relation and possibility degree model of interval number, and the optimization problem was solved by adaptive multi-objective particle swarm optimization which is based on Pareto entropy. The robust optimization design is implemented for the supercritical airfoil with the drag objective as well as lift, moment and area constraints under geometric uncertainties. The results compared with deterministic optimization design show that deterministic design is prone to failure under the influence of uncertainties, while the robust design is more secure and reliable.