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Flow control by a hybrid use of machine learning and control theory

Flow control by a hybrid use of machine learning and control theory Flow control has a great potential to contribute to a sustainable society through mitigation of environmental burden. However, the high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws using the control theory. This paper aims to propose a hybrid method (i.e. machine learning and control theory) for feedback control of fluid flows, by which the flow is mapped to the latent space in such a way that the linear control theory can be applied therein.Design/methodology/approachThe authors propose a partially nonlinear linear system extraction autoencoder (pn-LEAE), which consists of convolutional neural networks-based autoencoder (CNN-AE) and a custom layer to extract low-dimensional latent dynamics from fluid velocity field data. This pn-LEAE is designed to extract a linear dynamical system so that the modern control theory can easily be applied, while a nonlinear compression is done with the autoencoder (AE) part so that the latent dynamics conform to that linear system. The key technique is to train this pn-LEAE with the ground truths at two consecutive time instants, whereby the AE part retains its capability as the AE, and the weights in the linear dynamical system are trained simultaneously.FindingsThe authors demonstrate the effectiveness of the linear system extracted by the pn-LEAE, as well as the designed control law’s effectiveness for a flow around a circular cylinder at the Reynolds number of ReD = 100. When the control law derived in the latent space was applied to the direct numerical simulation, the lift fluctuations were suppressed over 50%.Originality/valueTo the best of the authors’ knowledge, this is the first attempt using CNN-AE for linearization of fluid flows involving transient development to design a feedback control law. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat and Fluid Flow Emerald Publishing

Flow control by a hybrid use of machine learning and control theory

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References (66)

Publisher
Emerald Publishing
Copyright
© Emerald Publishing Limited
ISSN
0961-5539
eISSN
0961-5539
DOI
10.1108/hff-10-2023-0659
Publisher site
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Abstract

Flow control has a great potential to contribute to a sustainable society through mitigation of environmental burden. However, the high dimensional and nonlinear nature of fluid flows poses challenges in designing efficient control laws using the control theory. This paper aims to propose a hybrid method (i.e. machine learning and control theory) for feedback control of fluid flows, by which the flow is mapped to the latent space in such a way that the linear control theory can be applied therein.Design/methodology/approachThe authors propose a partially nonlinear linear system extraction autoencoder (pn-LEAE), which consists of convolutional neural networks-based autoencoder (CNN-AE) and a custom layer to extract low-dimensional latent dynamics from fluid velocity field data. This pn-LEAE is designed to extract a linear dynamical system so that the modern control theory can easily be applied, while a nonlinear compression is done with the autoencoder (AE) part so that the latent dynamics conform to that linear system. The key technique is to train this pn-LEAE with the ground truths at two consecutive time instants, whereby the AE part retains its capability as the AE, and the weights in the linear dynamical system are trained simultaneously.FindingsThe authors demonstrate the effectiveness of the linear system extracted by the pn-LEAE, as well as the designed control law’s effectiveness for a flow around a circular cylinder at the Reynolds number of ReD = 100. When the control law derived in the latent space was applied to the direct numerical simulation, the lift fluctuations were suppressed over 50%.Originality/valueTo the best of the authors’ knowledge, this is the first attempt using CNN-AE for linearization of fluid flows involving transient development to design a feedback control law.

Journal

International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing

Published: Sep 2, 2024

Keywords: Machine learning; Autoencoder; Linear system extraction; Reduced order modeling; Flow control

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