Bernd R. Noack

• National Talent Professor
• Professor at Harbin Institute of Technology

We optimize jet mixing using large eddy simulations (LES) at a Reynolds number of 3000. Key methodological enablers consist of Bayesian optimization, a surrogate model enhanced by deep learning and persistent data topology for physical interpretation. The mixing performance is characterized by an equivalent jet radius ( 𝑅𝑒𝑞 ) derived from the strea...

xPDT is the third volume of this ‘Machine Learning Tools in Fluids Mechanics’ Series and focuses on Persistent Data Topology (PDT). The objectives of this book are twofold: First, provide an introduction to PDT for students, researchers, and newcomers on the field; and second, share an open-source code, xPDT, to automatically extract the topologica...

This experimental work is conducted to manipulate the wake to reduce aerodynamic drag using the actuations on the trailing edges of a bluff body at a yaw angle of 10°. Two loudspeakers are separately installed into the vertical trailing edges of the vertical base, creating a zero-net mass-flux jet through vertical slots. A maximum drag reduction of...

We mitigate the drag and lift forces of a square cylinder at three Reynolds numbers of 500, 1000, and 2000 using deep reinforcement learning (DRL) and two different positions of a zero flux jet actuator couple based on computational fluid dynamics simulations. The jet actuators are symmetrically deployed at the leading and trailing corners of the s...

Experimental assessment of safe and precise flight control algorithms for unmanned aerial vehicles under gusty wind conditions requires the capability to generate a large range of velocity profiles. In this study, we employ a small fan-array wind generator that can generate flows with large spatial and temporal variabilities. We perform a thorough...

Experimental assessment of safe and precise flight control algorithms for unmanned aerial vehicles (UAVs) under gusty wind conditions requires the capability to generate a large range of velocity profiles. In this study, we employ a small fan array wind generator which can generate flows with large spatial and temporal variability. We perform a tho...

This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning as the starting point. DRL performance is significantly improved by lifting the sensor signals to dynamic features (DF), w...

Contra-rotating rotors are widely adopted for multicopters due to the advantage of compactness and redundancy. Unlike traditional contra-rotating propellers or rotors with fixed rotation speeds, contra-rotating rotors of multicopters are driven by individual electrical motors, allowing for independent rotation speeds. This enables the optimization...

Contra-rotating rotors have the advantage of compactness and redundancy, which can be observed in many unmanned aerial vehicles. One significant installation parameter for the contra-rotating rotors is the axial distance between the upper and lower rotors, which influences both the time-averaged and unsteady loading of the rotors, as well as the ae...

We mitigate vortex-induced vibrations of a square cylinder at a Reynolds number of 100 using deep reinforcement learning (DRL)-based active flow control (AFC). The proposed method exploits the powerful nonlinear and high-dimensional problem-solving capabilities of DRL, overcoming limitations of linear and model-based control approaches. Three posit...

We develop and apply a novel shape optimization exemplified for a two-blade rotor with respect to the figure of merit. This topologically assisted optimization contains two steps. First, a global evolutionary optimization is performed for the shape parameters, and then a topological analysis reveals the local and global extrema of the objective fun...

Combustion instabilities have been a plaguing challenge in lean-conditioned propulsion systems. An open-loop control system was developed using machine learning to suppress pressure fluctuations and NO x emissions simultaneously. The open-loop control is realized by regulating the solenoid valve to modulate the methane supply. Control laws comprisi...

We present the first machine-learned multiple-input multiple-output aerodynamic feedback control under varying operating conditions. Closed-loop control is relevant to many fluid dynamic applications ranging from gust mitigation to drag reduction. Existing machine learning control investigations have been mainly applied under steady conditions. The...

Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control. Flu...

Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science, statistics, optimization, signal processing, pattern recognition, nonlinear dynamics, and control. Flu...

We improve convergence speed by two orders of magnitude and the global exploration capabilities of particle swarm optimization (PSO) through targeted position-mutated elitism (TPME). The proposed fast-converging TPME operator requires a fitness-based classification technique to categorize the particles. The introduced classification is motivated by...

We propose a novel nonlinear manifold learning from snapshot data and demonstrate its superiority over proper orthogonal decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap, as encoder and, $K$ -nearest neighbours ( $K$ NN) algorithm as decoder. The proposed technique is applied to numerical an...

We stabilize an open cavity flow experiment to 1 % of its original fluctuation level. For the first time, a multi-modal feedback control is automatically learned for this configuration. The key enabler is automatic in situ optimization of control laws with machine learning augmented by a gradient descent algorithm, named gradient-enriched machine l...

We propose a cluster-based control (CBC) strategy for model-free feedback drag reduction with multiple actuators and full-state feedback. CBC consists of three steps. First, the input of the feedback law is clustered from unforced flow data. Second, the feedback law is interpolated with actuation commands associated with the cluster centroids. Thus...

Symmetry is ubiquitous in nature, physics, and mathematics. However, a classical symmetry-agnostic Reinforcement Learning (RL) approach cannot guarantee to respect symmetry. Researchers have shown that if the symmetry of a system cannot be respected, the performance of a symmetry-agnostic RL approach can be inhibited. To this end, this paper develo...

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tr...

We propose the first machine-learned control-oriented flow estimation for multiple-input, multiple-output plants. The starting point is constant actuation with open-loop actuation commands leading to a database with simultaneously recorded actuation commands, sensor signals and flow fields. A key enabler is an estimator input vector comprising sens...

Deep learning has been widely utilized to accurately estimate the flow state from the sparse sensor measurements. Yet there is still a lack of understanding of the actual dimension of this type of regression problem. In this study, we propose an Autoencoder (AE) based estimation method to tackle the control-oriented, sensor-based flow estimation pr...

xMLC is the second book of this `Machine Learning Tools in Fluid Mechanics' Series and focuses on Machine Learning Control (MLC). The objectives of this book are two-fold: First, provide an introduction to MLC for students, researchers, and newcomers on the field; and second, share an open-source code, xMLC, to automatically learn open- and closed-...

We propose an open-source python platform for applications of Deep Reinforcement Learning (DRL) in fluid mechanics. DRL has been widely used in optimizing decision-making in nonlinear and high-dimensional problems. Here, an agent maximizes a cumulative reward by learning a feedback policy by acting in an environment. In control theory terms, the cu...

We propose a novel trajectory-optimized Cluster-based Network Model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. ["Cluster-based network model," J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering which minimizes the represen...

We dramatically improve convergence speed and global exploration capabilities of particle swarm optimization (PSO) through a targeted position-mutated elitism (PSO-TPME). The three key innovations address particle classification, elitism, and mutation in the cognitive and social model. PSO-TPME is benchmarked against five popular PSO variants for m...

We propose an open-source python platform for applications of Deep Reinforcement Learning (DRL) in fluid mechanics. DRL has been widely used in optimizing decision-making in nonlinear and high-dimensional problems. Here, an agent maximizes a cumulative reward with learning a feedback policy by acting in an environment. In control theory terms, the...

We propose the first machine-learned control-oriented flow estimation for multiple-input multiple-output plants. Starting point are experiments or simulations with representative steady actuation commands leading to a database with simultaneously recorded actuation commands, sensor signals and flow fields. A key enabler is an estimator input vector...

We propose a novel trajectory-optimized Cluster-based Network Model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. ["Cluster-based network model, " J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering which minimizes the represe...

A comparative assessment of machine-learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number ( Re = 100). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylind...

We propose a novel non-linear manifold learning from snapshot data and demonstrate its superiority over Proper Orthogonal Decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap (Tenenbaum et al., 2000), as encoder and K-nearest neighbours (KNN) algorithm as decoder. The proposed technique is appli...

Understanding the mechanism of particle transport and sedimentation in pulmonary alveolus is important for deciphering the causes of respiratory diseases and helping the development of drug delivery. In this study, taking advantage of the microfluidic technique, an experimental platform was developed to study particle behavior in a rhythmically exp...

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant shedding and...

Thrust and/or efficiency of a pitching foil (mimicking a tail of swimming fish) can be enhanced by tweaking the pitching waveform. The literature, however, show that non-sinusoidal pitching waveforms can enhance either thrust or efficiency but not both simultaneously. With the knowledge and inspiration from nature, we devised and implemented a nove...

A comparative assessment of machine learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional K\'arm\'an vortex street past a circular cylinder at a moderate Reynolds number ($Re=100$). The flow is manipulated with two blowing/suction actuators on the upper and lower side of...

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called the explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hyperc...

We stabilize an open cavity flow experiment to 1% of its original fluctuation level. For the first time, a multi-modal feedback control is automatically learned for this configuration. The key enabler is automatic in-situ optimization of control laws with machine learning augmented by a gradient descent algorithm, named gradient-enriched machine le...

Recent progress in machine learning and big data not only forms a new research paradigm, but also provides opportunity to solve grand challenges in fluid mechanics. Following the disciplinary development, this thematic issue of artificial intelligence (AI) in fluid mechanics came into being. This perspective briefly summarizes the development trend...

A key question in flow control is that of the design of optimal controllers when the control space is high-dimensional and the experimental or computational budget is limited. We address this formidable challenge using a particular flavor of machine learning and present the first application of Bayesian optimization to the design of open-loop contr...

An artificial intelligence (AI) open-loop control system is developed to manipulate a turbulent boundary layer (TBL) over a flat plate, with a view to reducing friction drag. The system comprises six synthetic jets, two wall-wire sensors, and genetic algorithm for the unsupervised learning of optimal control law. Each of the synthetic jets through...

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the unforced fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant she...

Generically, a local bifurcation only affects a single solution branch. However, branches that are quite different may nonetheless share certain eigenvectors and eigenvalues, leading to coincident bifurcations. For the fluidic pinball, two supercritical pitchfork bifurcations, of the equilibrium and the periodic solutions, occur at nearly the same...

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Kármán vortex street is one of the most prominent. Subsequent ROMs typically relied on first principl...

The transfer of internal energy fluctuation is numerically investigated for the stationary compressible isotropic turbulence in vibrational non-equilibrium with large-scale thermal forcing. We observe the spectra of velocity, solenoidal pressure component, density and temperatures all exhibiting the k −5/3 scaling in the inertial range. The Helmhol...

In this work, we report on a closed-loop flow control strategy that consistently reduces the drag of a D-shaped bluff body under variable freestream velocity conditions. The control strategy is guided by open-loop tests with pulsed Coanda blowing at two freestream velocities that yield optimal frequencies (Strouhal number of 0.33 and 1.3), which re...

For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr-Sommerfeld stability equation (1907) and numerous vortex models, of which the von K\'arm\'an vortex street (1911) is one of the most prominent. Subsequent ROMs typically relied...

We stabilize the flow past a cluster of three rotating cylinders-the fluidic pinball-with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open-and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three succ...

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assu...

Up to 40% drag reduction was achieved for a D-shaped cylinder in an experiment with robust model-based closed-loop control. The flow is actuated with on-off jet slots blowing in the stream-wise direction over the top and bottom edge. These jets are deflected inward with Coanda surfaces, thus realizing drag reduction by aerodynamic boat tailing. The...

An artificial intelligence (AI) control system is developed to manipulate a turbulent jet targeting maximal mixing. The control system consists of sensors (two hot-wires), genetic programming for evolving the control law and actuators (6 unsteady radial minijets). The mixing performance is quantified by the jet centerline mean velocity. AI control...

Minijet is one of the most promising active methods for the enhancement of jet mixing. The injection of minijets into a turbulent jet before the jet exit may have multiple impacts on the jet mixing structure. This work aims to understand the jet flow structure controlled by multiple unsteady minijets, especially the effect of the minijet phases on...

In this work, we are interested in the transient dynamics of a fluid configuration consisting of three fixed cylinders whose axes distribute over an equilateral triangle in transverse flow << fluidic pinball >>. As the Reynolds number is increased on the route to chaos, its transient dynamics tell us about the contribution of the elementary degrees...

Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new opportunities to these two processes and is revolutionising traditional methods. We show a framework to obtain a spa...

The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can independen...

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a seconda...

Genetic Algorithms (GAs) are an excellent approach for mining high-utility itemsets (HUIs) as they can discover most of the HUIs in a fraction of the time spent by exact algorithms. A key feature of GAs is crossover operators, which allow individuals in a population to communicate and exchange information with each other. However, the usefulness of...

This experimental work aims to investigate the manipulation of a bluff body flow with a yaw angle of 10 based on a genetic algorithm optimization. Two loudspeakers are used to generate zero-net mass-flux jets through streamwise slots, which span a large portion of the rounded A-pillars of the bluff body. The actuations produce a maximum drag reduct...

With the ever-increasing computational resources, numerical simulations of fluid flows have grown enormously in terms of mesh size and algorithmic complexity. The snapshots of a single detached eddy simulation (DES) may easily grow to hundreds of gigabytes of data. Processing and extracting information from such vast amounts of data has become a ch...

We model an actuated turbulent boundary layer with a cluster-based network model (CNM), an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into a few centroids representing the whole ensemble. The dynamics is conceptual...

We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into a few centroids representing the whole ensemble. The dynamics is conceptualized as a directed network, where the centroids represent nodes and the direc...

The present study investigates the lift gains generated by the superposition of a periodic actuation component onto a steady component on an airfoil with a highly deflected Coanda flap. The presented results are drawn from two experiments conduced in the water and in the wind tunnel. For the water tunnel experiment, periodic actuation is provided b...

This work aims to investigate experimentally the effect of Reynolds number Re on the mixing effectiveness of a turbulent jet manipulated using a single unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the turbulent jet. The control parameters include the duty cycle α, ratio fe/f0 of the m...

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering,...

A machine learning control (MLC) is proposed based on the explorative gradient method (EGM) for the optimization and sensitivity analysis of actuation parameters. This technique is applied to reduce the drag of a square-back Ahmed body at a Reynolds number Re = 1.7 × 10⁵. The MLC system consists of pulsed blowing along the periphery of the base, 25...

Reduced-order models are essential for the accurate and efficient prediction, estimation, and control of complex systems. This is especially true in fluid dynamics, where the fully resolved state space may easily contain millions or billions of degrees of freedom. Because these systems typically evolve on a low-dimensional attractor, model reductio...

The Reynolds transport theorem provides a generalized conservation law for the transport of a conserved quantity by fluid flow through a continuous connected control volume. It is close connected to the Liouville equation for the conservation of a local probability density function, which in turn leads to the Perron-Frobenius and Koopman evolution...

We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of a bluff-body flow. The force on this body is derived as a constant-linear-quadratic function of the mode ampl...

We stabilize the flow past a cluster of three rotating cylinders, the fluidic pinball, with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open- and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three s...

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assu...

We develop an open-loop control system using machine learning to destabilize and stabilize the mixing layer. The open-loop control law comprising harmonic functions is explored using the linear genetic programming in a purely data-driven and model-free manner. The best destabilization control law exhibits a square wave with two alternating duty cyc...

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding sub-optimal local minima. This challenge is addressed by a new optimizer, called explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube...

We propose a cavity as an actuator to actuate the supersonic mixing layer downstream a thick splitter plate. The cavity-actuated case at Re = 1.73 × 10⁵ is simulated using large eddy simulation. The forced dynamics is resolved by the cluster-based network model (CNM) from a probabilistic point of view. Introducing a cavity obtains a 50% increase in...

We propose an automated analysis of the flow control behaviour from an ensemble of control laws and associated time-resolved flow snapshots. The input may be the rich data base of machine learning control (MLC) optimizing a feedback law for a cost function in the plant. The proposed methodology provides (1) insights into control landscape which map...

Artificial intelligence control of a turbulent jet - Volume 897 - Yu Zhou, Dewei Fan, Bingfu Zhang, Ruiying Li, Bernd R. Noack

We compute, model, and predict drag reduction of an actuated turbulent boundary layer at a momentum-thickness-based Reynolds number of Reθ=1000. The actuation is performed using spanwise traveling transversal surface waves parametrized by wavelength, amplitude, and period. The drag reduction for the set of actuation parameters is modeled using 71 l...

Once stall has set in, lift collapses, drag increases and then both of these forces will fluctuate strongly. The result is higher fatigue loads and lower energy yield. In dynamic stall, separation first develops from the trailing edge up the leading edge. Eventually the shear layer rolls up, and then a coherent vortex forms and then sheds downstrea...

The control of bluff-body wakes for reduced drag and enhanced stability has traditionally relied on the so-called direct-wake control approach. By the use of actuators or passive devices, one can manipulate the aerodynamic loads that act on the rear of the model. An alternative approach for the manipulation of the flow is to move the position of th...

A fast triple-parameter extremum seeking method is applied for jet control based on the pioneering work of Gelbert et al. (J Process Control 22(4):700, 2012). The simultaneous adaptation of three input parameters takes less time than the single-input adaptation of each parameter combined. The key enablers are phase-shifted sinusoids for the input e...

Wall-resolved large-eddy simulations are performed to study the impact of spanwise traveling transversal surface waves in zero-pressure gradient turbulent boundary layer flow. Eighty variations of wavelength, period, and amplitude of the space- and time-dependent sinusoidal wall motion are considered for a boundary layer at a momentum thickness bas...

An artificial intelligence (AI) control system is developed to maximize the mixing rate of a turbulent jet. This system comprises six independently operated unsteady minijet actuators, two hot-wire sensors placed in the jet, and genetic programming for the unsupervised learning of a near-optimal control law. The ansatz of this law includes multi-fr...

As pioneered by Donzis and Maqui [J. Fluid Mech. 797, 181 (2016)] and Khurshid and Donzis [Phys. Fluids 31, 015103 (2019)], the compressible isotropic turbulence in thermal nonequilibrium is drawing attention in the fluid dynamics community. In the present study, the vibrational rate and the dissipation or production of vibrational energy fluctuati...

The Reynolds transport theorem provides a generalized conservation law for a conserved quantity carried by fluid flow through a continuous connected control volume. It is also intimately linked to the Liouville equation for the conservation of a local probability density function (pdf), and to the Perron-Frobenius and Koopman evolution operators. A...

The wake stabilization of a triangular cluster of three rotating cylinders is investigated. Experiments are performed at Reynolds number Re ∼ 2200. Flow control is realized using rotating cylinders spanning the wind-tunnel height. The cylinders are individually connected to identical brushless DC motors. Two-component planar particle image velocime...

We propose an automatable data-driven methodology for robust nonlinear reduced-order modeling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole ensemble. The dynamics is conceptualized as a directed network where the centroids represent nodes and the dire...

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from experiments, field measurements, and large-scale simulations at multiple spatiotemporal scales. Machine learning (ML) offers a wealth of techniques to extract information from data that can be translated into knowledge about the underlying fluid mechanic...

Low-order model for successive bifurcations of the fluidic pinball - Volume 884 - Nan Deng, Bernd R. Noack, Marek Morzyński, Luc R. Pastur

Large‐eddy simulations of spanwise traveling transversal surface waves in turbulent boundary layer flow are conducted. The parameter space of period, amplitude, and wavelength is investigated by 80 simulations. A maximum decrease of the averaged drag by 26 percent is obtained and an approximate scaling law for the decrease of the skin friction is f...