2020/12/16 by Tim Krake, Stefan Reinhardt, Krake, Tim +7
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Graphics (cs.GR) #Human-Computer Interaction (cs.HC) #Machine Fault Diagnosis Techniques #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2012.09633
openalex publication_date 2020/12/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Dynamic Mode Decomposition (DMD) is a data-driven and model-free\ndecomposition technique. It is suitable for revealing spatio-temporal features\nof both numerically and experimentally acquired data. Conceptually, DMD\nperforms a low-dimensional spectral decomposition of the data into the\nfollowing components: The modes, called DMD modes, encode the spatial\ncontribution of the decomposition, whereas the DMD amplitudes specify their\nimpact. Each associated eigenvalue, referred to as DMD eigenvalue,\ncharacterizes the frequency and growth rate of the DMD mode. In this paper, we\ndemonstrate how the components of DMD can be utilized to obtain temporal and\nspatial information from time-dependent flow fields. We begin with the\ntheoretical background of DMD and its application to unsteady flow. Next, we\nexamine the conventional process with DMD mathematically and put it in\nrelationship to the discrete Fourier transform. Our analysis shows that the\ncurrent use of DMD components has several drawbacks. To resolve these problems\nwe adjust the components and provide new and meaningful insights into the\ndecomposition: We show that our improved components describe the flow more\nadequately. Moreover, we remove redundancies in the decomposition and clarify\nthe interplay between components, allowing users to understand the impact of\ncomponents. These new representations ,which respect the spatio-temporal\ncharacter of DMD, enable two clustering methods that segment the flow into\nphysically relevant sections and can therefore be used for the selection of DMD\ncomponents. With a number of typical examples, we demonstrate that the\ncombination of these techniques allow new insights with DMD for unsteady flow.\n