Purpose

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/approach

The 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.

Findings

The 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 Re_D = 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/value

To 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.

中文翻译：

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混合使用机器学习和控制理论进行流量控制

 目的

流量控制具有通过减轻环境负担为可持续社会做出贡献的巨大潜力。然而，流体流动的高维和非线性特性对使用控制理论设计有效的控制律提出了挑战。本文旨在提出一种用于流体流动反馈控制的混合方法（即机器学习和控制理论），通过该方法将流动映射到潜在空间，从而可以在其中应用线性控制理论。

设计/方法论/途径

作者提出了一种部分非线性线性系统提取自动编码器（pn-LEAE），它由基于卷积神经网络的自动编码器（CNN-AE）和一个自定义层组成，用于从流体速度场数据中提取低维潜在动力学。该 pn-LEAE 旨在提取线性动态系统，以便可以轻松应用现代控制理论，同时使用自动编码器（AE）部分进行非线性压缩，以便潜在动态符合该线性系统。关键技术是在两个连续时刻用真实情况训练 pn-LEAE，从而 AE 部分保留其作为 AE 的能力，并且线性动力系统中的权重同时训练。

 发现

作者证明了 pn-LEAE 提取的线性系统的有效性，以及所设计的控制律对于雷诺数 Re _D = 100 时的圆柱绕流的有效性。当控制律在潜在空间中导出时应用到直接数值模拟中，升力波动被抑制了50%以上。

 原创性/价值

据作者所知，这是首次尝试使用 CNN-AE 对涉及瞬态发展的流体流动进行线性化，以设计反馈控制律。