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An efficient streaming algorithm for spectral proper orthogonal decomposition

Schmidt, Oliver T. (2017) An efficient streaming algorithm for spectral proper orthogonal decomposition. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20180618-105113900

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Abstract

A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated cross-spectral density (CSD) matrix is performed. The algorithm converges orthogonal sets of SPOD modes at discrete frequencies that are optimally ranked in terms of energy. We define measures of error and convergence, and demonstrate the algorithm's performance on two datasets. The first example is that of a high-fidelity numerical simulation of a turbulent jet, and the second optical flow data obtained from high-speed camera recordings of a stepped spillway experiment. For both cases, the most energetic SPOD modes are reliably converged. The algorithm's low memory requirement enable real-time deployment and allow for the convergence of second-order statistics from arbitrarily long streams of data.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1711.04199arXivDiscussion Paper
ORCID:
AuthorORCID
Schmidt, Oliver T.0000-0002-7097-0235
Additional Information:Support of the Office of Naval Research grant No. N00014- 16-1-2445 with Dr. Knox Millsaps as program manager is gratefully acknowledged. Special thanks are due to Aaron Towne and Patrick Vogler for reviewing the manuscript and sharing their insights, and to Tim Colonius, Andres Goza and Matthias Kramer for making valuable comments. The author gratefully acknowledges Matthias Kramer and Hubert Chanson for providing the experimental optical flow data. The experiments were undertaken in the hydraulics laboratory at the University of Queensland. The LES study was supported by NAVAIR SBIR project, under the supervision of Dr. John T. Spyropoulos. The main LES calculations were carried out on CRAY XE6 machines at DoD HPC facilities in ERDC DSRC.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-16-1-2445
Naval Air Systems Command (NAVAIR)UNSPECIFIED
Record Number:CaltechAUTHORS:20180618-105113900
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180618-105113900
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87188
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Jun 2018 20:38
Last Modified:18 Jun 2018 20:38

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