翼型不确定性量化中正交匹配追踪的应用

不确定性在实际系统中广泛存在,为了研究不确定性因素影响下系统输出的随机响应特性,传统的不确定性量化方法如蒙特卡洛采样、混沌多项式展开等需要大量的样本,制约了在飞机机翼等复杂系统中的应用。近年来,在信号处理领域发展迅速的压缩感知技术,利用原始信号的稀疏性可以用少量的样本精确重构信号。这一特性促使研究人员探索将压缩感知技术应用于不确定性量化研究中。以RAE2822实际翼型为研究对象,使用类函数/形函数变换将原始翼型参数化,考虑加工、装配过程和实际飞行工况下的几何不确定性,将压缩感知技术与混沌多项式展开相结合,利用正交匹配追踪算法实现多项式系数的稀疏重构,获得翼型气动力系数和流场参数在考虑几何不确定性影响下的均值和标准差,并与蒙特卡洛采样和满秩概率配点法获得的结果进行对比。通过对收敛性能、样本数需求和重构精度等方面的对比分析表明,正交匹配追踪算法能够利用相对较少的样本获得与传统不确定性量化方法相近的精度。考虑到实际系统的随机响应在混沌多项式基底上大多具有稀疏的展开形式,因此将压缩感知技术应用到不确定性量化中可以显著降低样本数需求,从而降低时间成本,提高计算效率。

ROBUST OPTIMIZATION OF AERODYNAMIC DESIGN USING SURROGATE MODEL

To reduce the high computational cost of the uncertainty analysis, a procedure is proposed for the aerodynamic optimization under uncertainties, in which the surrogate model is used to simplify the computation of the uncertainty analysis. The surrogate model is constructed by using the Latin Hypercube design and the Kriging model. The random parameters are used to account for the small manufacturing errors and the variations of operating conditions. Based on the surrogate model, an uncertainty analysis approach, called the Monte Carlo simulation, is used to compute the mean value and the variance of the predicated performance. The robust optimization for aerodynamic design is formulated, and solved by the genetic algorithm. And then, an airfoil optimization problem is used to test the proposed procedure. Results show that the optimal solutions obtained from the uncertainty-based optimization formulation are less sensitive to uncertainties. And the design constraints are still satisfied under the uncertainties.