摘要
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。
Uncertainties exist widely in realistic systems.To evaluate the stochastic response of the system output with various uncertainties,traditional uncertainty quantification methods such as Monte Carlo Sampling(MCS)and Polynomial Chaos Expansion(PCE)require large quantities of samples,restricting their application to complex sys⁃tems such as aircraft airfoils.The rapidly developed compressive sensing in signal processing field enables precise re⁃construction of the signal based on the sparsity of original signals with only a small number of samples.This feature has attracted researchers to explore the application of compressive sensing to uncertainty quantification research.This study considers the geometrical uncertainty of the RAE2822 airfoil in manufacturing,assembly,and flight,and param⁃eterizes the original shape with the Class-Shape Transformation(CST)method.We combine compressive sensing with polynomial chaos expansion for uncertainty quantification,and adopt the Orthogonal Matching Pursuit(OMP)al⁃gorithm to reconstruct the polynomial coefficients.In this way,the mean values and standard deviations of the aerody⁃namic forces and flow field quantities with geometrical uncertainty are obtained and compared to those of the Monte Carlo sampling and Full-Rank Probabilistic Collocations(FRPC)method.Comparison of convergence,sample num⁃ber requirement and accuracy shows that the orthogonal matching pursuit can use fewer samples to obtain similar re⁃sults as traditional methods.Since most of the stochastic responses of actual systems have sparse representations on polynomial chaos bases,the application of compressive sensing to uncertainty quantification can significantly decrease the required samples,thereby reducing time costs and improving computational efficiency.
作者
胡汉铎
宋彦萍
俞建阳
刘瑶
陈浮
高文秀
HU Handuo;SONG Yanping;YU Jianyang;LIU Yao;CHEN Fu;GAO Wenxiu(School of Energy Science and Engineering,Harbin Institute of Technology,Harbin 150001,China)
出处
《航空学报》
EI
CAS
CSCD
北大核心
2023年第18期119-131,共13页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(52006045)。
关键词
压缩感知
正交匹配追踪
混沌多项式展开
不确定性量化
翼型不确定性
类函数/形函数变换
compressive sensing
orthogonal matching pursuit
polynomial chaos expansion
uncertainty quantification
airfoil uncertainty
class-shape transformation
