基于压缩感知的高频响流场重构方法及其应用  

High-frequency flow field reconstruction method based on compressed sensing and its applications

作　　者：陈子玉 周楷文 刘应征[1] 温新 CHEN Ziyu;ZHOU Kaiwen;LIU Yingzheng;WEN Xin(School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学机械与动力工程学院,上海200240

出　　处：《空气动力学学报》2022年第1期26-32,共7页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(12072196);上海市科学技术委员会“科技创新行动计划”(19JC1412900)。

摘　　要：粒子图像测速(PIV)方法具有高空间分辨率的优势,但是往往受到采样频率的限制(一般在15 Hz以下),难以完成高频响测量。压缩感知(CS)能够基于稀疏采样数据获得高频信息,但如果直接应用于所有的数据点则计算量过大。基于亚采样(sub-Nyquist)PIV数据,本文提出了基于压缩感知和本征正交分解(POD)的高频响流场重构方法。首先采用POD对数据降维,同时获取空间模态和相应的亚采样时间系数,将亚采样时间系数作为观测值,选取适当的稀疏基,通过求解基追踪问题来计算高频响的模态系数。结合空间模态和所得到的时间分辨模态系数,可以重构高频响的非定常流场。利用该方法分别对周期性的振荡器流场和非周期性的不同直径圆柱流场进行重构,检测该方法的适应性。结果表明,压缩感知方法无需侵入式的辅助测量,可以为周期性流场提供准确的重构,重构误差低于3%,而对于非周期性复杂流场,则出现较大的高频噪声。因此,本文所提出的方法可以应用到周期性流场中以提高测量数据的时间分辨率。Though particle image velocimetry(PIV)has a high spatial resolution,it is often limited by the temporal resolution,which is typically below 15 Hz and difficult to acquire high-frequency flow information.Compressive sensing(CS)is able to capture the high-frequency information based on sparse sampled data,but if directly employed to all spatial points,the massive data poses a great computational cost.In this study,a highfrequency response flow field reconstruction method via coupling POD and CS is proposed to solve the above difficulty.POD is used first to reduce the dimensionality of the sampled PIV data,and the spatial modes and corresponding time coefficients are calculated at the same time.By taking the time coefficients at the subNyquist sampling points in CS as the observable and selecting an appropriate sparse basis,the high-frequency mode coefficients can be computed via the basic pursuit method.The unsteady flow field with high-frequency temporal information can then be reconstructed via combining the spatial modes and the corresponding resolved time coefficients.Two cases,i.e.the periodic oscillator flow and the non-periodic double-cylinder wake flow,are used to test the adaptivity of the proposed method.The results show that without the aid from contact measurement,the proposed method can accurately reconstruct the original flow field for period flow and the reconstruction error is less than 3%,while for nonperiodic complex flow,the error is significantly increased due to high-frequency noise.Overall,the proposed method can be used for periodic flow to improve the temporal resolution of the measured experimental data.

关 键 词：粒子图像测速 本征正交分解 压缩感知 流场重构 亚采样 

分 类 号：O353.5[理学—流体力学] TP391.41[理学—力学]