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

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

Year:    2023

Author:    Wai Ming Chau, Shingyu Leung

Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 824–848

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/ 10.4208/cicp.OA-2022-0177

Communications in Computational Physics, Vol. 33 (2023), Iss. 3 : pp. 824–848

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Dynamical system visualization finite time Lyapunov exponent numerical methods for differential equations k-means clustering.

Author Details

Wai Ming Chau

Shingyu Leung