Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session ZC29: Modeling Methods IV: Data-driven and Machine-Learning Techniques
12:50 PM–3:00 PM,
Tuesday, November 21, 2023
Room: 152B
Chair: Mohammad Farazmand, North Carolina State University
Abstract: ZC29.00008 : A Shift Procedure for Identifying Low Rank Behavior from Non-Stationary Dynamical System Data*
2:21 PM–2:34 PM
Presenter:
Jack Sullivan
(Ohio State University)
Authors:
Jack Sullivan
(Ohio State University)
Datta V Gaitonde
(Ohio State University)
riodicity or statistical stationarity properties in collected data to identify the
underlying physics and to build reduced order models. However, many sys-
tems of interest, such as scramjet unstart, do not exhibit these properties and
traditional approaches to applying data-driven decomposition techniques, such
as Proper Orthogonal Decomposition (POD), yield results that are difficult to
interpret, or use for reduced order models. However, shifting the data into a
suitably defined reference frame that travels with an identified feature of interest
can recover many of the attractive properties of typical decomposition methods,
at least to first-order. We propose a robust, data-driven way to execute this shift
by computing an instantaneously varying translational velocity vector from the
Empirical Mode Decomposition (EMD) of time series data which tracks the lo-
cation of targeted space-time features. Application of decomposition techniques
in the shifting reference frame recovers many of the low rank dynamics that
are not easily apparent in the original data. The approach is demonstrated by
application to four example problems ranging in complexity from a convecting
Gaussian pulse to unstarting shocks in a scramjet isolator.
*The authors are grateful for support from the AFRL Collaborative Center for Aeronautical Sciences, and for computing resources provided by the DOD High Performance Computing Modernization Program.
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