Reduced-order models for closed-loop wake control

Tadmor, Gilead; Lehmann, Oliver; Noack, Bernd R.; Cordier, Laurent; Delville, J.; Bonnet, Jean-Paul; Morzyński, Marek

doi:10.1098/rsta.2010.0367

Cited by 42 publications

(44 citation statements)

References 40 publications

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“…We opted for dynamic mode-1 in our experiments as it gave us the best results by cross validation. This is supported by the literature [12], [13], [14], [15], [16], [17] which indicates that the first dynamic mode captures the largest dynamic scale or principal motion that is present in the sequence of images. In the next subsection, we assess the choice of LBP on the classification performance.…”

Section: B Selection Of Dmd Modessupporting

confidence: 74%

“…Pan's method [33] and [34] Optical flow Inside face changes (e.g., eye blinking) versus outside face (the scene context) Pinto's visual rhythm [5] Multiple video spectra represented by graylevel co-occurrence matrices represented by 12 sequence and the resultant scores, one from each image, are combined via a fixed operator such as mean or a second-level classifier that combines the statistics (e.g. [37]).…”

Section: B Data-driven Methodsmentioning

confidence: 99%

“…No specific spatial arrangement of the image data is assumed and there are no parameters to be tuned. The first dynamic mode captures the largest scale dynamics that is present in the sequence of frames [12], [13], [14], [15], [16], [17].…”

Section: Algorithm 1 Dynamic Mode Decompositionmentioning

confidence: 99%

“…Gaining a deep and accurate understanding of complex flow behaviour requires a form of reduced order models [12] or mode decomposition [13]. The mode decomposition of the form that we are interested is commonly used in the area of computational fluid dynamics (CFD) [14].…”

Section: Motivation For Dmdmentioning

confidence: 99%

See 3 more Smart Citations

Detection of Face Spoofing Using Visual Dynamics

Tirunagari

Poh

Windridge

et al. 2015

IEEE Trans.Inform.Forensic Secur.

226

111

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Abstract-Rendering a face recognition system robust is vital in order to safeguard it against spoof attacks carried out by using printed pictures of a victim (also known as print attack) or a replayed video of the person (replay attack). A key property in distinguishing a live, valid access from printed media or replayed videos is by exploiting the information dynamics of the video content, such as blinking eyes, moving lips, and facial dynamics. We advance the state of the art in facial anti-spoofing by applying a recently developed algorithm called Dynamic Mode Decomposition (DMD) as a general-purpose, entirely data-driven approach to capture the above liveness cues. We propose a classification pipeline consisting of DMD, Local Binary Patterns (LBP), and Support Vector Machines (SVM) with a histogram intersection kernel. A unique property of DMD is its ability to conveniently represent the temporal information of the entire video as a single image with the same dimensions as those images contained in the video. The pipeline of DMD+LBP+SVM proves to be efficient, convenient to use, and effective. In fact only the spatial configuration for LBP needs to be tuned. The effectiveness of the methodology was demonstrated using three publicly available databases: print-attack, replay-attack, and CASIA-FASD, attaining comparable results with the state of the art, following the respective published experimental protocols.

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Section: B Selection Of Dmd Modessupporting

confidence: 74%

Section: B Data-driven Methodsmentioning

confidence: 99%

Section: Algorithm 1 Dynamic Mode Decompositionmentioning

confidence: 99%

Section: Motivation For Dmdmentioning

confidence: 99%

See 2 more Smart Citations

Detection of Face Spoofing Using Visual Dynamics

Tirunagari

Poh

Windridge

et al. 2015

IEEE Trans.Inform.Forensic Secur.

226

111

View full text Add to dashboard Cite

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“…Holmes et al (1996); Berkooz et al (1993);Sirovich (1987)). Improved variants of POD have also been developed based on linear-operator-theoretic model reduction methods, such as the balanced POD Lall et al (2002); Ma et al (2010) and the bilateral coupling between variations in the ‡uctuation growth rate and the mean ‡ow variations Tadmor et al (2010Tadmor et al ( , 2011. In all of the above methods however, the static character of the employed modes does not allow for an e¢ cient setup of a low-dimensional but adaptive reduced order model that can reproduce important features of the original system such as strongly non-Gaussian statistics and transient instabilities.…”

Section: Introductionmentioning

confidence: 99%

Global analysis of Navier–Stokes and Boussinesq stochastic flows using dynamical orthogonality

2013

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We provide a new framework for the study of ‡uid ‡ows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal …eld equations. By numerically solving these equations we evolve in a fully coupled way the mean ‡ow and the statistical and spatial characteristics of the stochastic ‡uctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that reduce considerably the computational cost. We analyze the transformation of energy from stochastic modes to mean dynamics, and vice-versa, by deriving exact expressions that quantify the interaction among di¤erent components of the ‡ow. The developed framework is illustrated through speci…c ‡ows in unstable regimes. In particular we consider the ‡ow behind a disk and the Rayleigh-Bénard convection for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for di¤erent parameters associated with the considered ‡ows and we reveal the low-dimensionality of the underlying stochastic attractor.

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A generalized framework for reduced‐order modeling of a wind turbine wake

et al. 2018

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A reduced-order model for a wind turbine wake is sought from large eddy simulation data. Fluctuating velocity fields are combined in the correlation tensor to form the kernel of the proper orthogonal decomposition (POD). Proper orthogonal decomposition modes resulting from the decomposition represent the spatially coherent turbulence structures in the wind turbine wake; eigenvalues delineate the relative amount of turbulent kinetic energy associated with each mode.Back-projecting the POD modes onto the velocity snapshots produces dynamic coefficients that express the amplitude of each mode in time. A reduced-order model of the wind turbine wake (wakeROM) is defined through a series of polynomial parameters that quantify mode interaction and the evolution of each POD mode coefficients. The resulting system of ordinary differential equations models the wind turbine wake composed only of the large-scale turbulent dynamics identified by the POD. Tikhonov regularization is used to recalibrate the dynamical system by adding additional constraints to the minimization seeking polynomial parameters, reducing error in the modeled mode coefficients. The wakeROM is periodically reinitialized with new initial conditions found by relating the incoming turbulent velocity to the POD mode coefficients through a series of open-loop transfer functions. The wakeROM reproduces mode coefficients to within 25.2%, quantified through the normalized root-mean-square error. A high-level view of the modeling approach is provided as a platform to discuss promising research directions, alternate processes that could benefit stability and efficiency, and desired extensions of the wakeROM. KEYWORDSdynamical system, proper orthogonal decomposition, reduced-order model, wind turbine wake INTRODUCTIONPerformance of wind farms is highly correlated with the wake following a given wind turbine. 1,2 However, for the sake of design efficiency, wakes and wind plants are typically modeled with simplified engineering or empirical relationships. Wind turbine wakes are highly variable, combining effects from the atmospheric boundary layer, interacting with large rotating structures, and often subject to wake-to-wake interaction within a wind plant. 3 Further, wakes evolving from individual turbines are asymmetrical due to the inherent shear in the atmospheric boundary layer and reflect the specific nature of incoming inflow events that vary significantly with diurnal and seasonal cycles and affect the performance of other turbines in a wind plant. 4 Given the complexity of the wind turbine wake, a computationally efficient means of correctly modeling wake dynamics and interaction is crucial to meet the rapid pace at which wind energy is being adopted globally and to address persistent wind plant underperformance.Reduced-order modeling describes a wide range of approaches that approximate complex system dynamics of large or infinite degrees of freedom with a limited, and more manageable, number of degrees of freedom. For applications in turbulence, the goal ...

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Reduced-order models for closed-loop wake control

Cited by 42 publications

References 40 publications

Detection of Face Spoofing Using Visual Dynamics

Detection of Face Spoofing Using Visual Dynamics

Global analysis of Navier–Stokes and Boussinesq stochastic flows using dynamical orthogonality

A generalized framework for reduced‐order modeling of a wind turbine wake

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