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Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

Wai Ming ChauShingyu Leung
Dec 2022
摘要
We propose a clustering-based approach for identifying coherent flowstructures in continuous dynamical systems. We first treat a particletrajectory over a finite time interval as a high-dimensional data point andthen cluster these data from different initial locations into groups. Themethod then uses the normalized standard deviation or mean absolute deviationto quantify the deformation. Unlike the usual finite-time Lyapunov exponent(FTLE), the proposed algorithm considers the complete traveling history of theparticles. We also suggest two extensions of the method. To improve thecomputational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite timeinterval. To start the computation in parallel to the flow trajectory datacollection, we also develop an on-the-fly approach to improve the solution aswe continue to provide more measurements for the algorithm. The method canefficiently compute the WCVE over a different time interval by modifying theavailable data points.
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