发表机构
Tohoku University; Delft University of Technology; University of Massachusetts Amherst（东北大学; 代尔夫特理工大学; 马萨诸塞大学阿默斯特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对严重污染流场，提出库学习辅助鲁棒主成分分析（LLA-RPCA），通过限制空间基为候选库函数组合并规定模态容量，在高达90%污染下优于标准RPCA，改善去噪与模态恢复。
AI 中文摘要
大幅度的逐点污染会扭曲流场数据并污染提取的模态。鲁棒主成分分析（RPCA）将低秩流场内容与稀疏污染分量分离，但当污染占据测量值的很大比例时，恢复效果会恶化。我们引入了库学习辅助鲁棒主成分分析（LLA-RPCA），该方法将恢复的空间基限制为固定候选库中函数的组合，并规定可用的模态容量。这里，库包含标准三角函数和图拉普拉斯特征函数。分解通过增广拉格朗日交替最小化求解。该方法在失速后NACA0012尾流、振荡圆柱尾流视频数据以及经历横向阵风遭遇的平板的粒子图像测速（PIV）测量上进行了评估。对于前两种情况，在0%至90%的比例上施加了合成的大幅度逐点污染。LLA-RPCA在标准RPCA保留残余污染、衰减重建场或坍缩为一维重建的污染水平下，保持连贯的尾流结构并恢复主导线性模态。对于实验性阵风遭遇案例，标准RPCA随着其调节因子增加，在衰减连贯流场内容和保留自然发生的PIV伪影之间表现出权衡。相反，LLA-RPCA抑制伪影，同时一致地保留连贯的速度和导出涡量结构。这些结果表明，当规定表示充分捕获相关空间内容时，具有规定模态容量的库约束重建改善了去噪和模态恢复。
英文摘要
Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.
