In the analysis of Lagrangian particle tracking data, ensemble averaging with spatial bins is used to generate flow statistics. Due to the scattered nature of the particles over independent snapshots, the possible spatial resolution is directly dependent on the measured particle position accuracy and the amount of available data. This requires a balance between convergence of the underlying statistic and the bin resolution. Current binning approaches use the velocity information of the particle positions at single time steps directly and do not exploit the additional information available from the tracking process. We present a novel functional approach to the binning procedure that extracts all available information from the particle tracks and improves convergence speed. For a given experiment this allows for higher resolution of flow statistics than classical approaches or alternatively to reduce the necessary amount of data required for a given resolution. Furthermore, uncertainty measures from the particles position can be propagated directly by weighting coefficients.

中文翻译：

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功能分箱：通过拉格朗日粒子跟踪提高欧拉统计的收敛性

在分析拉格朗日粒子跟踪数据时，使用空间箱的整体平均来生成流统计。由于粒子在独立快照上的散射特性，可能的空间分辨率直接取决于测量的粒子位置精度和可用数据量。这需要在基础统计数据的收敛性和 bin 分辨率之间取得平衡。当前的分箱方法直接在单个时间步使用粒子位置的速度信息，并且不利用跟踪过程中可用的附加信息。我们提出了一种新的分箱程序功能方法，该方法从粒子轨迹中提取所有可用信息并提高收敛速度。对于给定的实验，这允许比经典方法更高的流量统计分辨率，或者减少给定分辨率所需的必要数据量。此外，粒子位置的不确定性度量可以通过加权系数直接传播。