arXiv subjects

Bernd R. Noack

Publications and source records attributed to Bernd R. Noack.

At least 55 records · Page 3Linked to original sources

arXiv2020

Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body

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 explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex method, the random restart variant, Latin hypercube sampling, Monte Carlo iterations and the genetic algorithm. EGM is applied to minimize the net drag power of the two-dimensional fluidic pinball benchmark with three cylinder rotations as actuation parameters. The net drag power is reduced by $40\%$ employing direct numerical simulations at a Reynolds number of $100$ based on the cylinder diameter. This optimal actuation leads to $98\%$ drag reduction employing Coanda forcing for boat tailing and partial stabilization of vortex shedding. The price is an actuation energy corresponding to $58\%$ of the unforced parasitic drag power. EGM is also used to minimize drag of the $35^\circ$ slanted Ahmed body employing distributed steady blowing with 10 inputs. $17\%$ drag reduction are achieved using Reynolds-Averaged Navier-Stokes simulations (RANS) at the Reynolds number $Re_H=1.9 \times 10^5$ based on the height of the Ahmed body. The optimal actuation emulates boat tailing by inward-directed blowing with velocities which are comparable to the oncoming velocity. We expect that EGM will be employed as efficient optimizer in many future active flow control plants.

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arXiv2020

Cluster-based network modeling -- automated robust modeling of complex dynamical systems

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 assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM only assumes smoothness of the dynamics in the state space, robustly describes short- and long-term behavior and is fully automatable as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict and control complex systems in all scientific fields.

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arXiv2020

Cluster-based network model

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 few centroids representable for the whole ensemble. The dynamics is conceptualized as a directed network, where the centroids represent nodes and the directed edges denote possible finite-time transitions. The transition probabilities and times are inferred from the snapshot data. The resulting cluster-based network model constitutes a deterministic-stochastic grey-box model resolving the coherent-structure evolution. This model is motivated by limit-cycle dynamics, illustrated for the chaotic Lorenz attractor and successfully demonstrated for the laminar two-dimensional mixing layer featuring Kelvin-Helmholtz vortices and vortex pairing, and for an actuated turbulent boundary layer with complex dynamics. Cluster-based network modelling opens a promising new avenue with unique advantages over other model-order reductions based on clustering or proper orthogonal decomposition.

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arXiv2020

Towards human-interpretable, automated learning of feedback control for the mixing layer

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 maps control laws to performance including extrema and ridge-lines, (2) a catalogue of representative flow states and their contribution to cost function for investigated control laws and (3) a visualization of the dynamics. Key enablers are classification and feature extraction methods of machine learning. The analysis is successfully applied to the stabilization of a mixing layer with sensor-based feedback driving an upstream actuator. The fluctuation energy is reduced by 26\%. The control replaces unforced Kelvin-Helmholtz vortices with subsequent vortex pairing by higher-frequency Kelvin-Helmholtz structures of lower energy. These efforts target a human interpretable, fully automated analysis of MLC identifying qualitatively different actuation regimes, distilling corresponding coherent structures, and developing a digital twin of the plant.

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arXiv2020

Artificial intelligence control of a turbulent jet

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-frequency open-loop forcing, sensor-feedback and nonlinear combinations thereof. Mixing performance is quantified by the decay rate of the centreline mean velocity of jet. Intriguingly, the learning process of AI control discovers the classical forcings, i.e. axisymmetric, helical and flapping achievable from conventional control techniques, one by one in the order of increased performance, and finally converges to a hitherto unexplored forcing. Careful examination of the control landscape unveils typical control laws, generated in the learning process, and their evolutions. The best AI forcing produces a complex turbulent flow structure that is characterized by periodically generated mushroom structures, helical motion and oscillating jet column, all enhancing the mixing rate and vastly outperforming others. Being never reported before, this flow structure is examined in various aspects, including the velocity spectra, mean and fluctuating velocity fields and their downstream evolution, and flow visualization images in three orthogonal planes, all compared with other classical flow structures. Along with the knowledge of the minijet-produced flow and its effect on the initial condition of the main jet, these aspects cast valuable insight into the physics behind the highly effective mixing of this newly found flow structure. The results point to the great potential of AI in conquering the vast opportunity space of control laws for many actuators and sensors and in optimizing turbulence.

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arXiv2019

Actuation response model from sparse data for wall turbulence drag reduction

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 parameterized by wavelength, amplitude, and period. The drag reduction for the set of actuation parameters is modeled using 71 large-eddy simulations (LES). This drag model allows to extrapolate outside the actuation domain for larger wavelengths and amplitudes. The modeling novelty is based on combining support vector regression for interpolation, a parameterized ridgeline leading out of the data domain, scaling from Tomiyama and Fukagata (2013), and a discovered self-similar structure of the actuation effect. The model yields high prediction accuracy outside the training data range.

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arXiv2019

Drag Reduction and Energy Saving by Spanwise Traveling Transversal Surface Waves for Flat Plate Flow

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 based Reynolds number of $Re_θ= 1000$. The results show a strong decrease of friction drag of up to $26\,\%$ and considerable net power saving of up to $10\,\%$. However, the highest net power saving does not occur at the maximum drag reduction. The drag reduction is modeled as a function of the actuation parameters by support vector regression using the LES data. A substantial attenuation of the near-wall turbulence intensity and especially a weakening of the near-wall velocity streaks are observed. Similarities between the current actuation technique and the method of a spanwise oscillating wall without any normal surface deflection are reported. In particular, the generation of a directional spanwise oscillating Stokes layer is found to be related to skin-friction reduction.

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arXiv2019

Locally linear embedding for transient cylinder wakes

Reduced-order representations of an ensemble of cylinder wake transients are investigated. Locally linear embedding identifies a two-dimensional manifold with a maximum error of 1% from new snapshot data. This representation outperforms a 50-dimensional POD expansion from the same data and is not obtainable with cluster-based coarse graining of similar order. This manifold resolves the steady solution, the stability eigenmodes, the first post-transient POD modes, the intermediate vortex shedding structure as well as higher harmonics. The snapshot data are generated by a direct numerical simulation of the two-dimensional wake behind a circular cylinder at a Reynolds number of 100. The initial conditions of the 16 transients start near the steady solution and converge to the period vortex shedding. Many oscillatory flows can be expected to be characterized on two- or low-dimensional manifolds identifiable with locally linear embedding. These manifolds have unexplored potential for prediction, estimation and control.

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arXiv2018

Cluster-based feedback control of turbulent post-stall separated flows

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only $O(10)$ iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.

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arXiv2018

Metric for attractor overlap

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshots to snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse-graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids, and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by few representative centroids. We employ MAO for two quite different actuated flow configurations: (1) a two-dimensional wake of the fluidic pinball with vortices in a narrow frequency range and (2) three-dimensional wall turbulence with broadband frequency spectrum manipulated by spanwise traveling transversal surface waves. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.

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arXiv2018

Bluff body drag manipulation using pulsed jets and Coanda effect

The impact of fluidic actuation on the wake and drag of a three-dimensional blunt body is investigated experimentally. Jets blowing tangentially to the main flow allow to force the wake with variable frequency and amplitude. Depending on the forcing conditions, two flow regimes can be distinguished. First, in case of broadband actuation with frequencies comprising the natural wake time scale, the convection of the jet structures enhances wake entrainment, shortens the length of the recirculating flow and increases drag. Secondly, at higher actuation frequencies, shear-layer deviation leads to fluidic boat-tailing of the wake. It additionally lowers its turbulent kinetic energy thus reducing the entrainment of momentum towards the recirculating flow. The combination of both mechanisms produces a raise of the base pressure and reduces the drag of the model. Both actuation regimes are characterized by complementary velocity, pressure and drag measurements at several upstream conditions and control parameters. By adding curved surfaces to deviate the jets by the Coanda effect, periodic actuation is reinforced and drag reductions of about 20% are achieved. The unsteady Coanda blowing not only intensifies the flow deviation and the base pressure recovery but also preserves the unsteady high-frequency forcing effect on the turbulent field. The present results encourage further development of fluidic control to improve the aerodynamics of road vehicles and provide a complementary insight into the relation between wake dynamics and drag.

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arXiv2018

Unstable Periodically Forced Navier-Stokes Solutions---Towards Nonlinear First-Principle Reduced-Order Modeling of Actuator Performance

We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of more damped higher-order eigenmodes. This challenge is addressed by a novel method to compute unstable periodically forced solutions of the linearized Navier-Stokes solution. This method utilizes two key enablers. First, the linear dynamics is transformed by a complex shift of the eigenvalues amplifying the flow response at the given frequency of interest. Second, the growth rate is obtained from an iteration procedure. The method is demonstrated for several wake flows around a circular cylinder, a fluidic pinball, i.e. the wake behind a cluster of cylinders, a wall-mounted cylinder, a sphere and a delta wing. The example of flow control with periodic wake actuation and forced physical modes paves the way for applications of physical modal expansions. These results encourage Galerkin models of three-dimensional flows utilizing Navier-Stokes based modes.

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arXiv2018

Jet mixing optimization using machine learning control

We experimentally optimize mixing of a turbulent round jet using machine learning control (MLC) following Li et al (2017). The jet is manipulated with one unsteady minijet blowing in wall-normal direction close to the nozzle exit. The flow is monitored with two hotwire sensors. The first sensor is positioned on the centerline 5 jet diameters downstream of the nozzle exit, i.e. the end of the potential core, while the second is located 3 jet diameters downstream and displaced towards the shear-layer. The mixing performance is monitored with mean velocity at the first sensor. A reduction of this velocity correlates with increased entrainment near the potential core. Machine Learning Control (MLC) is employed to optimize sensor feedback, a general open-loop broadband frequency actuation and combinations of both. MLC has identified the optimal periodic forcing with a small duty cycle as the best control policy employing only 400 actuation measurements, each lasting for 5 seconds. This learning rate is comparable if not faster than typical optimization of periodic forcing with two free parameters (frequency and duty cycle). In addition, MLC results indicate that neither new frequencies nor sensor feedback improves mixing further-contrary to many of other turbulence control experiments. The optimality of pure periodic actuation may be attributed to the simple jet flapping mechanism in the minijet plane. The performance of sensor feedback is shown to face a challenge for small duty cycles. The jet mixing results demonstrate the untapped potential of MLC in quickly learning optimal general control policies, even deciding between open- and closed-loop control.

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arXiv2017

Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation

We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to a dynamic feature space. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to velocity fields is shown to be orders of magnitudes more accurate than optimal modal expansions of the same order. Fourth, a generalized feature-based modal decomposition identifies coherent structures that are most dynamically correlated with the linear and nonlinear interaction terms in the sparse model, adding interpretability. Steps 1 and 2 define a black-box model. Optional steps 3 and 4 lift the black-box dynamics to a 'gray-box' model of the coherent structures, if non-time-resolved full-state data is available. This gray-box modeling strategy is successfully applied to the transient and post-transient laminar cylinder wake, and compares favorably with a POD model. We foresee numerous applications of this highly flexible modeling strategy, including estimation, prediction and control. Moreover, the feature space may be based on intrinsic coordinates, which are unaffected by a key challenge of modal expansion: the slow change of low-dimensional coherent structures with changing geometry and varying parameters.

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arXiv2017

Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk

We advance Machine Learning Control (MLC), a recently proposed model-free control framework which explores and exploits strongly nonlinear dynamics in an unsupervised manner. The assumed plant has multiple actuators and sensors and its performance is measured by a cost functional. The control problem is to find a control logic which optimizes the given cost function. The corresponding regression problem for the control law is solved by employing linear genetic programming as an easy and simple regression solver in a high-dimensional control search space. This search space comprises open-loop actuation, sensor-based feedback and combinations thereof, thus generalizing former MLC studies. This methodology is denoted as linear genetic programming control (LGPC). Focus of this study is the frequency crosstalk between unforced unstable oscillation and the actuation at different frequencies. LGPC is first applied to the stabilization of a forced nonlinearly coupled three-oscillator model comprising open- and closed-loop frequency crosstalk mechanisms. LGPC performance is then demonstrated in a turbulence control experiment, achieving 22% drag reduction for a simplified car model. For both cases, LGPC identifies the best nonlinear control achieving the optimal performance by exploiting frequency crosstalk. Our control strategy is suited to complex control problems with multiple actuators and sensors featuring nonlinear actuation dynamics.

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arXiv2016

Drag reduction of a car model by linear genetic programming control

We investigate open- and closed-loop active control for aerodynamic drag reduction of a car model. Turbulent flow around a blunt-edged Ahmed body is examined at $Re_{H}\approx3\times10^{5}$ based on body height. The actuation is performed with pulsed jets at all trailing edges combined with a Coanda deflection surface. The flow is monitored with pressure sensors distributed at the rear side. We apply a model-free control strategy building on Dracopoulos & Kent (Neural Comput. & Applic., vol. 6, 1997, pp. 214-228) and Gautier et al. (J. Fluid Mech., vol. 770, 2015, pp. 442-457). The optimized control laws comprise periodic forcing, multi-frequency forcing and sensor-based feedback including also time-history information feedback and combination thereof. Key enabler is linear genetic programming as simple and efficient framework for multiple inputs (actuators) and multiple outputs (sensors). The proposed linear genetic programming control can select the best open- or closed-loop control in an unsupervised manner. Approximately 33% base pressure recovery associated with 22% drag reduction is achieved in all considered classes of control laws. Intriguingly, the feedback actuation emulates periodic high-frequency forcing by selecting one pressure sensor in the optimal control law. Our control strategy is, in principle, applicable to all multiple actuators and sensors experiments.

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arXiv2016

Cluster-based control of nonlinear dynamics

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. The approach is applied to a separating flow dominated by the Kelvin-Helmholtz shedding.

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arXiv2016

Prediction of Dynamical Systems by Symbolic Regression

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

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