气动光学效应波前模态的泽尼克-本征正交分解  

Zernike and Proper Orthogonal Decomposition of Wavefront Modes of Aero-Optical Effects

作　　者：陈勇[1] 李玉栋 袁强[1] 姚向红[1] 申俊琦 常伟 李宏勋 Chen Yong;Li Yudong;Yuan Qiang;Yao Xianghong;Shen Junqi;Chang Wei;Li Hongxun(Facility Design and Instrumentation Institute,China Aerodynamics Research and Development Center,Mianyang 621000,Sichuan,China;Institute of Computational Aerodynamics,China Aerodynamics Research and Development Center,Mianyang 621000,Sichuan,China)

机构地区：[1]中国空气动力研究与发展中心设备设计与测试技术研究所,四川绵阳621000 [2]中国空气动力研究与发展中心计算空气动力学研究所,四川绵阳621000

出　　处：《光学学报》2023年第24期220-228,共9页Acta Optica Sinica

摘　　要：本征正交分解(POD)方法已经广泛应用于时间变化随机场的分析,但其直接法或快照法存在自身固有缺陷,前者使关联矩阵求解特征值和特征向量较为困难,后者的有限抽样帧数会影响对随机场的统计特性分析。鉴于此,本文建立了基于泽尼克(Zernike)多项式加权系数的Zernike-POD方法,用于气动光学效应的波前模态统计分析。对于圆域问题,Zernike多项式阶数给定后,各阶加权系数与波前分布是一一对应的,并且通常用几百阶多项式就足以复原各种复杂波面形状。Zernike-POD方法由对波前本身改为对Zernike多项式加权系数的分解和模态计算,由于多项式阶数远少于波前的空间离散点数,因此,关联矩阵的维数降低,计算量减少,计算效率显著提高。Zernike-POD方法不损失空间分辨率,同时不需要限制最高采样帧数,因此,时间统计特性不受影响,预估的波前模态具有较高的时空分辨率。为验证该方法的有效性,用大涡模拟方法开展圆柱绕流数值仿真,并计算圆柱尾迹卡门涡街结构产生的时间系列气动光学效应数据,将该数据用于波前模态分析,波前空间分辨率为100×100,采样帧数为2万帧,Zernike多项式阶数取为217阶。一阶模态与稳态波前分布相似,二阶与三阶、四阶与五阶模态近似互为配对关系;前10阶模态能够基本复原波面形状,前49阶模态含能在97%以上,用完整模态重构的波前与原始波前没有本质差异;模态加权系数及其功率谱随阶数增加而呈下降趋势,前五阶模态加权系数的功率谱尖峰频率与光学窗口中心点脉动速度情况较为一致,对应卡门涡街的主频,斯特劳哈尔数St约为0.22。Zernike-POD方法适用于圆域波前模态分析,也适用于环形域和正方形域,并能够推广到流场结构、图像与信号等处理领域。Objective Proper orthogonal decomposition(POD)method has been widely applied to time-dependent field analysis,but its direct method and snapshot method both have their inherent problems.The former makes it difficult to solve eigenvalues and eigenvectors of correlation matrices,and the limited sampling number of the latter will affect statistical random field analysis.The direct method needs to solve eigenvalues and eigenvectors of spatial correlation matrices,and the correlation matrix dimensions are the spatial discrete points of the field.When there are more discrete points in the space,the matrix dimensions are high,which results in a large amount of computation,consumed time,occupied memory,and even difficult solutions.The snapshot method is to solve temporal correlation matrices.Generally,by sampling about 200 frames,the correlation matrix dimensions and computation amount are significantly reduced,which makes the POD method practical and operable.However,the few sampling frames will affect the statistical analysis of random field modes,and the calculated modes will vary with the frame number and interval time between frames.Thus,the Zernike and proper orthogonal decomposition(Z-POD)method based on the Zernike polynomial weighted coefficient is established for statistical wavefront mode analysis of aero-optical effects.Methods The Z-POD method which introduces the wavefront reconstruction method based on Zernike polynomials is changed from the decomposition of the wavefront itself to that of the weighted coefficients of Zernike polynomials.For the circle domain,given the Zernike polynomial order,weighted coefficients correspond to wavefront distribution one by one,and polynomials of several hundred orders are usually enough to recover various complex wavefront shapes.Since the polynomial order is far less than the discrete point number in the wavefront space,the correlation matrix dimensions are reduced,with reduced computation amount and significantly improved computation calculation efficiency.The Z-POD me

关 键 词：气动光学 波前模态 本征正交分解 泽尼克多项式 

分 类 号：O436[机械工程—光学工程] O355[理学—光学]