Schlueter-Kuck Kristy L, Dabiri John O
Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA.
Chaos. 2017 Sep;27(9):091101. doi: 10.1063/1.4993862.
We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data are available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.
我们提出了一种方法，即使仅能获取稀疏的粒子轨迹数据，也能识别与单个拉格朗日流轨迹相关的相干结构。该方法基于谱图理论技术，使用相干结构着色向量和相关特征向量来分析在高维特征空间中选定参考轨迹与流中其他示踪轨迹之间的距离。通过在层次聚类中分析此距离度量，可以识别参考粒子所属的相干结构。该算法已被证明在识别典型非定常流中不同复杂程度的相干结构方面是成功的。此外，该方法能够评估相关结构相对于周围流的相对相干性。尽管此方法是在流体流动运动学的背景下展示的，但该方法的通用性使其有可能应用于动力系统中的其他无监督聚类问题，如神经元活动、基因表达或社交网络。
