We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then...We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.展开更多
文摘We propose a clustering-based approach for identifying coherent flow structuresin continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from differentinitial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improvethe computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan on-the-fly approach to improve the solution as we continue to provide more measurementsfor the algorithm. The method can efficiently compute the WCVE over adifferent time interval by modifying the available data points.
