论文标题
集群内变异性指数，用于识别动态系统中的相干结构
Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems
论文作者
论文摘要
我们提出了一种基于聚类的方法，用于识别连续动力学系统中的相干流量结构。我们首先将粒子轨迹在有限的时间间隔视为高维数据点，然后将这些数据从不同初始位置组成组。然后，该方法使用归一化的标准偏差或平均绝对偏差来量化变形。与通常的有限时间Lyapunov指数（FTLE）不同，所提出的算法考虑了颗粒的完整旅行历史。我们还建议该方法的两个扩展。为了提高计算效率，我们开发了一种自适应方法，该方法基于有限的时间间隔构建整个粒子轨迹的不同子样本。为了与流轨迹数据收集并行启动计算，我们还开发了一种在线方法来改进解决方案的方法，因为我们继续为算法提供更多的测量。该方法可以通过修改可用数据点来有效地在不同的时间间隔内计算WCVE。
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data from different initial locations into groups. The method then uses the normalized standard deviation or mean absolute deviation to quantify the deformation. Unlike the usual finite-time Lyapunov exponent (FTLE), the proposed algorithm considers the complete traveling history of the particles. We also suggest two extensions of the method. To improve the computational efficiency, we develop an adaptive approach that constructs different subsamples of the whole particle trajectory based on a finite time interval. To start the computation in parallel to the flow trajectory data collection, we also develop an on-the-fly approach to improve the solution as we continue to provide more measurements for the algorithm. The method can efficiently compute the WCVE over a different time interval by modifying the available data points.
