On Stochastic Reduced-Order and LES-based Models of Offshore Wind Turbine Wakes

Paskyabi, Mostafa Bakhoday; Krutova, Maria; Nielsen, Finn Gunnar; Reuder, Joachim; Guernaoui, Omar El

doi:10.1088/1742-6596/1669/1/012018

“…Examples include partial differential equations with random coefficients ( [18], [19], [42], [45]), parametric closure models for the stochastic Burgers' equation ( [77]), or a variance reduction method for SDEs ( [20]). Stochastic reduced models were also used as noisy perturbations of deterministic reduced models in order to account for unresolved small-scale features ( [12], [35], [78], [89]). However, to the best of our knowledge the adaptation of the POD method to SDEs driven by a Wiener process has been much less investigated.…”

Section: Data-driven Structure-preserving Model Reduction 221mentioning

confidence: 99%

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Tyranowski

2024

JCD

0

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In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and the large number of independent Monte Carlo runs. We also extend the proper symplectic decomposition method to stochastic Hamiltonian systems, both with and without external forcing, and argue that preserving the underlying symplectic or variational structures results in more accurate and stable solutions that conserve energy better than when the non-geometric approach is used. We validate our proposed techniques with numerical experiments for a semi-discretization of the stochastic nonlinear Schrödinger equation and the Kubo oscillator.

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“…We will show that the computational cost of both these tasks can be alleviated by adapting the POD method to the stochastic setting. A number of reduced basis methods have been applied to stochastic systems in various contexts-see [1], [17], [21], [24], [25], [26], [47], [62], [67], [68], [104], [105], [117], [119], [150] and the references therein-but to the best of our knowledge the adaptation of the POD method to SDEs driven by a Wiener process has been much less investigated. An application of the POD method which is similar in spirit to our approach appears in [85] and [157], but only in the specific context of solving the stochastic Burgers equation, empirical approximation of the nonlinear term is not addressed, and only low-order integration in time is used (see also [31]).…”

Section: Introductionmentioning

confidence: 99%

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Tyranowski¹

2022

Preprint

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In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the computational cost arising from both the high dimension of the considered stochastic system and the large number of independent Monte Carlo runs. We also extend the proper symplectic decomposition method to stochastic Hamiltonian systems, both with and without external forcing, and argue that preserving the underlying symplectic or variational structures results in more accurate and stable solutions that conserve energy better than when the non-geometric approach is used. We validate our proposed techniques with numerical experiments for a semi-discretization of the stochastic nonlinear Schrödinger equation and the Kubo oscillator.

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A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Li,

Ge,

Li

et al. 2024

Physics of Fluids

6

0

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Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

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On Stochastic Reduced-Order and LES-based Models of Offshore Wind Turbine Wakes

Cited by 4 publications

References 12 publications

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

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