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Leveraging reduced-order models for state estimation using deep learning

Published online by Cambridge University Press:  09 June 2020

Nirmal J. Nair Open the ORCID record for Nirmal J. Nair [Opens in a new window]  and
Andres Goza Open the ORCID record for Andres Goza [Opens in a new window]
Nirmal J. Nair*
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana IL 61801, USA
Andres Goza
Affiliation:
Department of Aerospace Engineering, University of Illinois at Urbana–Champaign, Urbana IL 61801, USA
*
†Email address for correspondence: [email protected]
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Abstract

State estimation is key to both analysing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When desired, the full state can be recovered via the ROM.) Current methods in this category nearly always use a linear model to relate the sensor data to the reduced state, which often leads to restrictions on sensor locations and has inherent limitations in representing the generally nonlinear relationship between the measurements and reduced state. We propose an alternative methodology whereby a neural network architecture is used to learn this nonlinear relationship. A neural network is a natural choice for this estimation problem, as a physical interpretation of the reduced state–sensor measurement relationship is rarely obvious. The proposed estimation framework is agnostic to the ROM employed, and can be incorporated into any choice of ROMs derived on a linear subspace (e.g. proper orthogonal decomposition) or a nonlinear manifold. The proposed approach is demonstrated on a two-dimensional model problem of separated flow around a flat plate, and is found to outperform common linear estimation alternatives.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Mathematical Foundations: Computational methods Vortex Flows: Vortex shedding
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 897 , 25 August 2020 , R1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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