A method to construct reduced‐order parameter‐varying models

Annoni, Jennifer; Seiler, Peter

doi:10.1002/rnc.3586

Cited by 43 publications

(31 citation statements)

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“…Additionally, further development will be required to make a POD‐based dynamical system effective over the full parameter space of wind turbine operating conditions. Parameter‐varying reduced‐order models were explored for wind turbine wakes in Annoni and Seiler and shows promise for generalizing the wakeROM constructed above. Many alternate means of decomposition have been applied to turbulent velocity data such as the dynamical mode decomposition, balanced POD, and empirical mode decomposition to name a few.…”

Section: Discussion On Generalizing the Wakerommentioning

confidence: 99%

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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Section: Discussion On Generalizing the Wakerommentioning

confidence: 99%

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

et al. 2018

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“…To accelerate the computation of ioDMD-derived models, we follow [7,4] and reduce the order of the possibly high-dimensional state trajectories using a projection-based approach. The data matrices X 0 and X 1 are compressed using a truncated (Galerkin) projection Q ∈ R N ×n , n N , Q * Q = I:…”

Section: Reduced Order Dmdmentioning

confidence: 99%

On reduced input-output dynamic mode decomposition

Benner

Mitchell

2018

Adv Comput Math

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The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior of the data source. In this work, we consider the input-output dynamic mode decomposition method for system identification. We compare excitation approaches for the data-driven identification process and describe an optimization-based stabilization strategy for the identified systems.

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“…At this moment, research studies of reduced-order modeling methods of linear models have matured [1][2][3]. Also, these techniques have already been applied in some areas like optimization and control [4,5], uncertainty quantification [6], and parameter identification [7].…”

Section: Introductionmentioning

confidence: 99%

A Component‐Based Parametric Reduced‐Order Modeling Method Combined with Substructural Matrix Interpolation and Automatic Sampling

Liu

et al. 2019

Shock and Vibration

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An efficient parametric reduced-order modeling method combined with substructural matrix interpolation and automatic sampling procedure is proposed. is approach is based on the fixed-interface Craig-Bampton component mode synthesis method (CMS). e novel parametric reduced-order models (PROMs) are developed by interpolating substructural reducedorder matrices. To guarantee the compatibility of the coordinates, we develop a three-step adjustment procedure by reducing the local interface degrees of freedom (DOFs) and performing congruence transformation for the normal modes and interface reduced basis, respectively. In addition, an automatic sampling process is also introduced to dynamically fulfill the predefined error limits. It proceeds by first exploring the parameter space and identifying the sampling points with maximum error indicators for all the parameter-dependent substructures. e exact error of the assembled model at the optimal parameter point is subsequently calculated to determine whether the automatic sampling procedure reaches a desired error tolerance. e proposed framework is then applied to the moving coil of electrical-dynamic shaker to illustrate the advantage and validity. e results indicate that this new approach can significantly reduce both the offline database construction time and online calculation time. Besides, the automatic procedure can sample the parameter space efficiently and fulfill the stopping criterion dynamically with assurance of the resulting PROM accuracy.

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A method to construct reduced‐order parameter‐varying models

Cited by 43 publications

References 50 publications

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

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

On reduced input-output dynamic mode decomposition

A Component‐Based Parametric Reduced‐Order Modeling Method Combined with Substructural Matrix Interpolation and Automatic Sampling

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