Abstract Particle image velocimetry (PIV) has been extensively used in wind-tunnel test for flow-field measurement. However, the sampling frequency of traditional PIV is low and physics of flow field in high-frequency range is hard to capture. A data processing approach is proposed to obtain time-resolved flow field around a circular cylinder with PIV measurement data (high spatial precision) and wind speed measurement data using probes (high time resolution at discrete downstream locations). Proper orthogonal decomposition (POD) is used to extract the compact spatial representations of the flow field based on PIV measurement data, and bidirectional recurrent neural networks (RNNs) with gated recurrent units are designed to learn the time sequences of coefficients of the first few POD modes based on both PIV and probe measurement data. We analyze qualitatively the relationship between the velocity time sequence and the spatial distribution of velocity. Based on this qualitative relationship, an RNN with a unique “many-to-one” architecture is designed to learn the coefficients and make use of the intrinsic property that the velocity time sequence contains information on the spatial distribution of velocity. The inputs to the RNN are the sequential velocity-probe measurements with high sampling frequency, and the outputs are the coefficients of the first few POD modes. The proposed approach is validated by using both simulated datasets for two low Reynolds numbers (200 and 500) and experimental dataset for Reynolds number of 2.4 × 10 4 . We also investigate the influence of velocity time length used in the inputs as well as the number and distribution of velocity probes on prediction accuracy. This study provides a feasible approach to get time-resolved flow field with high accuracy while low cost for all Reynolds numbers. Graphic abstract

中文翻译：

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基于非时间分辨粒子图像测速测量的循环神经网络对圆柱体周围流场的时间分辨重建

摘要 粒子图像测速（PIV）已广泛应用于风洞试验中的流场测量。然而，传统PIV的采样频率较低，高频范围内的流场物理特性难以捕捉。提出了一种数据处理方法，利用 PIV 测量数据（高空间精度）和使用探针的风速测量数据（离散下游位置的高时间分辨率）获得围绕圆柱体的时间分辨流场。使用适当的正交分解 (POD) 提取基于 PIV 测量数据的流场的紧凑空间表示，并设计具有门控循环单元的双向循环神经网络 (RNN) 来学习前几个 POD 系数的时间序列基于 PIV 和探头测量数据的模式。我们定性地分析了速度时间序列与速度空间分布之间的关系。基于这种定性关系，设计具有独特“多对一”架构的 RNN 来学习系数并利用速度时间序列包含有关速度空间分布的信息的内在属性。RNN 的输入是具有高采样频率的连续速度探针测量，输出是前几个 POD 模式的系数。所提出的方法通过使用两个低雷诺数（200 和 500）的模拟数据集和雷诺数 2.4 × 10 4 的实验数据集得到验证。我们还研究了输入中使用的速度时间长度以及速度探针的数量和分布对预测精度的影响。该研究提供了一种可行的方法来获得高精度、低成本的所有雷诺数的时间分辨流场。图形摘要