传感器数量、位置和系统精度对流体流场能量稀疏重构的影响
Interplay of Sensor Quantity, Placement and System Dimensionality on Energy Sparse Reconstruction of Fluid Flows
摘要：
从稀疏数据重建精细尺度信息与许多实际的流体动力学应用相关，其中感测通常是稀疏的。理想意义下的流体流动是非线性多尺度PDE动力系统的表现形式，其固有的尺度分离影响系统的维数。有一个共同的需要，分析数据从流量测量或高保真计算的稳定性特征，识别相干结构和开发实时数据驱动控制的进化模型。鉴于稀疏重建本质上是一个不适定问题，最成功的方法需要的知识的基础上的基础空间跨越流形系统驻留。在这项研究中，我们采用了一种方法，从训练数据的奇异值分解（SVD）学习基础，以重建稀疏感知的信息在随机采样的位置。这使我们能够利用l2最小化的能量稀疏性，而不是更昂贵的稀疏性促进l1最小化。此外，对于只有全局操作参数（如雷诺数（Re）和原始数据）可用的未知流动系统，通常不清楚需要什么样的传感器的最佳数量和它们的位置来进行近似精确的重建。在这项工作中，我们探索了数据稀疏性，底层流系统的稀疏性和传感器放置对由数据驱动的SVD基础实现的能量稀疏重建性能的相互作用。为此，我们调查稀疏卷积为基础的重建性能的特征操作边界规范层流圆柱体尾流在极限环和瞬态制度。
英文摘要：
Reconstruction of fine-scale information from sparse data is relevant to many practical fluid dynamic applications where the sensing is typically sparse. Fluid flows in an ideal sense are manifestations of nonlinear multiscale PDE dynamical systems with inherent scale separation that impact the system dimensionality. There is a common need to analyze the data from flow measurements or high-fidelity computations for stability characteristics, identification of coherent structures and develop evolutionary models for real-time data-driven control. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches require the knowledge of the underlying basis space spanning the manifold in which the system resides. In this study, we employ an approach that learns basis from singular value decomposition (SVD) of training data to reconstruct sparsely sensed information at randomly sampled locations. This allows us to leverage energy sparsity with l2 minimization instead of the more expensive, sparsity promoting l1 minimization. Further, for unknown flow systems where only global operating parameters such as Reynolds (Re) number and raw data are available, it is often not clear what the optimal number of sensors and their placement for near-exact reconstruction needs to be. In this effort, we explore the interplay of data sparsity, sparsity of the underlying flow system and sensor placement on energy sparse reconstruction performance enabled by data- driven SVD basis. To this end, we investigate sparse convolution-based reconstruction performance by characterizing operational bounds for canonical laminar cylinder wake flows in both limit-cycle and transient regimes.
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