The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.

Machine Learning for Fluid Mechanics

This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and from requirements of non-linear, non-convex search in continuous domain.

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The CMA Evolution Strategy: A Tutorial

Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

This paper presents natural evolution strategies (NES), a novel algorithm for performing real-valued dasiablack boxpsila function optimization: optimizing an unknown objective function where algorithm-selected function measurements constitute the only information accessible to the method. Natural evolution strategies search the fitness landscape using a multivariate normal distribution with a self-adapting mutation matrix to generate correlated mutations in promising regions. NES shares this property with covariance matrix adaption (CMA), an evolution strategy (ES) which has been shown to perform well on a variety of high-precision optimization tasks. The natural evolution strategies algorithm, however, is simpler, less ad-hoc and more principled. Self-adaptation of the mutation matrix is derived using a Monte Carlo estimate of the natural gradient towards better expected fitness. By following the natural gradient instead of the dasiavanillapsila gradient, we can ensure efficient update steps while preventing early convergence due to overly greedy updates, resulting in reduced sensitivity to local suboptima. We show NES has competitive performance with CMA on unimodal tasks, while outperforming it on several multimodal tasks that are rich in deceptive local optima.

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Natural Evolution Strategies

Closed-Loop Turbulence Control: Progress and Challenges

We present a novel method for handling uncertainty in evolutionary optimization. The method entails quantification and treatment of uncertainty and relies on the rank based selection operator of evolutionary algorithms. The proposed uncertainty handling is implemented in the context of the covariance matrix adaptation evolution strategy (CMA-ES) and verified on test functions. The present method is independent of the uncertainty distribution, prevents premature convergence of the evolution strategy and is well suited for online optimization as it requires only a small number of additional function evaluations. The algorithm is applied in an experimental setup to the online optimization of feedback controllers of thermoacoustic instabilities of gas turbine combustors. In order to mitigate these instabilities, gain-delay or model-based H infin controllers sense the pressure and command secondary fuel injectors. The parameters of these controllers are usually specified via a trial and error procedure. We demonstrate that their online optimization with the proposed methodology enhances, in an automated fashion, the online performance of the controllers, even under highly unsteady operating conditions, and it also compensates for uncertainties in the model-building and design process.

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A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion

We present the system identification and the online optimization of feedback controllers applied to combustion systems using evolutionary algorithms. The algorithmis applied to gas turbine combustors that are susceptible to thermoacoustic instabilities resulting in imperfect combustion and decreased lifetime. In order to mitigate these pressure oscillations, feedback controllers sense the pressure and command secondary fuel injectors. The controllers are optimized online with an extension of the CMA evolution strategy capable of handling noise associated with the uncertainties in the pressure measurements. The presented method is independent of the specific noise distribution and prevents premature convergence of the evolution strategy. The proposed algorithm needs only two additional function evaluations per generation and is therefore particularly suitable for online optimization. The algorithm is experimentally verified on a gas turbine combustor test rig. The results show that the algorithm can improve the performance of controllers online and is able to cope with a variety of time dependent operating conditions.

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Evolutionary Optimization of Feedback Controllers for Thermoacoustic Instabilities

This paper describes the suppression of thermoacoustic instabilities in a swirl-stabilized test rig. To that end, a high-bandwidth secondary fuel injector is installed and commanded with robust H infin and simpler gain-delay controllers. Depending on the operating condition, several distinct flame types occur, which are investigated with OH chemiluminescence. A model of the plant is obtained by means of closed-loop identification experiments. The model-based H infin approach confers more design freedom to the engineer and gives better results. In particular, the sensitivity can be distributed arbitrarily to target specific and separate frequency ranges. The pressure spectrum reductions achieved are compared with the predictions of the design process and are found to agree well. The influence of the injected natural gas on the flame is studied through OH chemiluminescence. Experiments show that the controlled flame assumes a position similar to the one of a flame being in a stable operating condition.

Thermoacoustic Instability Suppression by Gain-Delay and ${\cal H}_{\infty}$ Controllers Designed for Secondary Fuel Injection

This paper describes the identification and modeling of a test rig designed to study thermoacoustic instabilities. Various operating conditions with different flame structures are identified. Physics-based models are used in a network model in order to advance the understanding of the phenomena involved. The parameters identified of the flame correlate well with the observed flame shapes. The transfer function from a loudspeaker input to a pressure reading is assembled and compared to measurements. Reflection coefficients are introduced to study the amplifying frequency ranges of the flame, which correspond to the highest peaks in the pressure spectrum.

https://journals.sagepub.com/doi/pdf/10.1260/175682709788083380

André S.P. Niederberger

Papers

A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion

Evolutionary Optimization of Feedback Controllers for Thermoacoustic Instabilities

Thermoacoustic Instability Suppression by Gain-Delay and ${\cal H}_{\infty}$ Controllers Designed for Secondary Fuel Injection

Parameter Identification for a Low-Order Network Model of Combustion Instabilities:

Modeling and active control of thermoacoustic instabilities