Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published June 2008 | Submitted
Conference Paper Open

Temporal-Harmonic Specific POD Mode Extraction

Abstract

While POD / PCA / KL approximations are statistically energetically optimal, statistical optimality is indeed the sole consideration these (equivalent) methods invoke. This type of approximation is neither geared for, nor is it optimized to extract modes based on their significance to an underlying system dynamics. Furthermore, as computational considerations limit the size of empirical ensembles used for mode extraction, the resulting mode set is significantly effected by the arbitrariness of the ensemble selection. System theoretic model reductions methods aim to home on dynamically significant modes by direct interrogation of the underlying equation, such as the linearized Navier-Stokes equations. An alternative / complimentary approach is to impose a priori knowledge of structural properties, such as symmetry and periodicity, on the mode-extraction procedure. The idea is that these conditions will force the selection of physically meaningful modes, and thus enables an effective appeal to first principles. Here we focus on systems known to be periodically dominant, and describe a simple method to extract modes associated with temporal harmonics. The method accommodates time variations in the dominant frequency(ies) and exploits a preliminary data compression, such as by the standard POD procedure.

Additional Information

© 2008 by Gilead Tadmor. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Published Online: 15 Jun 2012.

Attached Files

Submitted - TadmorBissexNoackEtAl2008.pdf

Files

TadmorBissexNoackEtAl2008.pdf
Files (447.2 kB)
Name Size Download all
md5:cf1f3364a29c768c573d65359164e6a7
447.2 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023