Variational assimilation of POD low-order dynamical systems

D’Adamo, Juan; Papadakis, Nicolas; Mémin, Étienne; Artana, Guillermo

doi:10.1080/14685240701242385

Cited by 22 publications

(25 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method extends a similar technique we proposed recently [10]. This technique was formulated also as a weakly constrained optimal control problem incorporating an additive uncertainty function [10]. We will show that considering for the control variables an additional uncertainty function or the dynamical system's coefficients corresponds indeed to different assumptions on the reduced dynamical model.…”

Section: Introductionmentioning

confidence: 80%

“…It is nevertheless formulated slightly differently as an optimal control problem with an explicit constraint on the initial condition and on the system's coefficients and relies on general norms weighted by appropriate covariance matrices. The method extends a similar technique we proposed recently [10]. This technique was formulated also as a weakly constrained optimal control problem incorporating an additive uncertainty function [10].…”

Section: Introductionmentioning

confidence: 93%

“…The first method, which corresponds to a refinement of a method detailed in [10], consists in performing an assimilation of the temporal modes considering an additive uncertainty function on the reduced dynamical model. The coefficients of the dynamical system are here first assumed to be directly provided by the data.…”

Section: Application To Low Order Dynamical Systemsmentioning

confidence: 99%

“…4.1 Recovery of the temporal modes trajectory with a weak constraint assimilation This first technique corresponds to a continuation of the work developed in [10]. For this assimilation problem, we consider the dynamics of the temporal POD modes defined in equations (3)(4) and augmented by an additive uncertainty function, ω(t) ≃ ξ(t) + ϑ(t), encoding both the contribution of the component of the fluctuating pressure belonging to the complement space of the subspace spanned by the POD temporal modes, ξ(t) (10) and the interaction between the modes of the reduced POD basis and the secondary modes that have been truncated, ϑ(t) (19):…”

Section: Application To Low Order Dynamical Systemsmentioning

confidence: 99%

See 3 more Smart Citations

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Artana¹,

Cammilleri²,

Carlier³

et al. 2012

Journal of Computational Physics

View full text Add to dashboard Cite

In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed differ in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coefficients constitute the control variables. Both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data.

show abstract

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 93%

Section: Application To Low Order Dynamical Systemsmentioning

confidence: 99%

Section: Application To Low Order Dynamical Systemsmentioning

confidence: 99%

See 2 more Smart Citations

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Artana¹,

Cammilleri²,

Carlier³

et al. 2012

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…This technique has been also used recently to recover the parameters of a reduced dynamical system obtained from a POD-Galerkin techniqes (D'Adamo et al, 2007). Compared to traditional approaches this technique allows an improved accuracy and stability of the estimated reduced system.…”

Section: Non-local Temporal Contextmentioning

confidence: 99%

Variational fluid flow measurements from image sequences: synopsis and perspectives

2009

Self Cite

View full text Add to dashboard Cite

Variational approaches to image motion segmentation has been an active field of study in image processing and computer vision for two decades. We present a short overview over basic estimation schemes and report in more detail recent modifications and applications to fluid flow estimation. Key properties of these approaches are illustrated by numerical examples. We outline promising research directions and point out the potential of variational techniques in combination with correlation-based PIV methods, for improving the consistency of fluid flow estimation and simulation.

show abstract

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

et al. 2018

View full text Add to dashboard Cite

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 ...

show abstract

Variational assimilation of POD low-order dynamical systems

Cited by 22 publications

References 15 publications

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Variational fluid flow measurements from image sequences: synopsis and perspectives

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

Contact Info

Product

Resources

About