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Sparse reduced-order modelling: sensor-based dynamics to full-state estimation

Published online by Cambridge University Press:  06 April 2018

Jean-Christophe Loiseau Open the ORCID record for Jean-Christophe Loiseau [Opens in a new window] ,
Bernd R. Noack Open the ORCID record for Bernd R. Noack [Opens in a new window]  and
Steven L. Brunton
Jean-Christophe Loiseau*
Affiliation:
Laboratoire DynFluid, Arts et Métiers ParisTech, 75013 Paris, France
Bernd R. Noack
Affiliation:
Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur, LIMSI-CNRS, rue John von Neumann, Campus Universitaire d’Orsay, Bât 508, F-91403 Orsay, France Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology, Shenzhen Campus, Shenzhen 58800, People’s Republic of China Institut für Strömungsmechanik und Technische Akustik (ISTA), Technische Universität Berlin, Müller-Breslau-Straße 8, D-10623 Berlin, Germany
Steven L. Brunton
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
*
†Email address for correspondence: loiseau.jc@gmail.com
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Abstract

We propose a general dynamic reduced-order modelling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved particle image velocimetry (PIV) snapshots. This framework can be decomposed into four building blocks. First, the sensor signals are lifted to a dynamic feature space without false neighbours. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to the velocity field is performed to reconstruct the full state of the system. Fourth, a generalized feature-based modal decomposition identifies coherent structures that are most dynamically correlated with the linear and nonlinear interaction terms in the sparse model, adding interpretability. Steps 1 and 2 define a black-box model. Optional steps 3 and 4 lift the black-box dynamics to a grey-box model in terms of the identified coherent structures, if non-time-resolved full-state data are available. This grey-box modelling strategy is successfully applied to the transient and post-transient laminar cylinder wake, and compares favourably with a proper orthogonal decomposition model. We foresee numerous applications of this highly flexible modelling strategy, including estimation, prediction and control. Moreover, the feature space may be based on intrinsic coordinates, which are unaffected by a key challenge of modal expansion: the slow change of low-dimensional coherent structures with changing geometry and varying parameters.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 459 - 490
Copyright
© 2018 Cambridge University Press 

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