[Paper Review] Data-driven quantification of model-form uncertainty in Reynolds-averaged simulations of wind farms

Ali Eidi, Navid Zehtabiyan-Rezaie+3 more|arXiv (Cornell University)|May 27, 2022

Wind and Air Flow Studies66 references30 citations

TL;DR

This paper proposes a data-driven machine learning framework to quantify model-form uncertainty in Reynolds-averaged Navier-Stokes (RANS) simulations of wind farms by predicting optimal perturbations to the Reynolds stress anisotropy tensor. Using extreme gradient boosting (XGBoost) trained on large-eddy simulation (LES) data, the method adaptively estimates direction and magnitude of perturbations across the domain, significantly improving prediction accuracy for wake velocity, turbulence intensity, and power losses compared to uniform, data-free perturbations.

ABSTRACT

Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are one of the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify model-form uncertainties in RANS simulations of wind farms at high Reynolds numbers under neutrally stratified conditions by perturbing the Reynolds stress tensor through a data-driven machine-learning technique. To this end, a two-step feature-selection method is applied to determine key features of the model. Then, the extreme gradient boosting algorithm is validated and employed to predict the perturbation amount and direction of the modeled Reynolds stress toward the limiting states of turbulence on the barycentric map. This procedure leads to a more accurate representation of the Reynolds stress anisotropy. The data-driven model is trained on high-fidelity data obtained from large-eddy simulation of a specific wind farm, and it is tested on two other (unseen) wind farms with distinct layouts to analyze its performance in cases with different turbine spacing and partial wake. The results indicate that, unlike the data-free approach in which a uniform and constant perturbation amount is applied to the entire computational domain, the proposed framework yields an optimal estimation of the uncertainty bounds for the RANS-predicted quantities of interest, including the wake velocity, turbulence intensity, and power losses in wind farms.

Motivation & Objective

• To address the critical limitation of uniform, data-free perturbations in RANS-based uncertainty quantification (UQ) for wind farm simulations.
• To develop a data-driven approach that learns optimal, spatially varying perturbations to the Reynolds stress anisotropy tensor from high-fidelity LES data.
• To improve the accuracy of RANS predictions for key quantities of interest, including wake velocity, turbulence intensity, and power losses.
• To enhance generalizability and robustness of machine learning-based UQ through a two-step feature selection and validated XGBoost model.
• To demonstrate transferability of the framework across different wind farm layouts with varying turbine spacing and wake interactions.

Proposed method

• A two-step feature-selection method is applied to identify the most influential flow features from the Reynolds stress tensor and strain rate tensor for predicting perturbations.
• The extreme gradient boosting (XGBoost) algorithm is trained to predict the magnitude and direction of eigenvalue perturbations on the barycentric map of turbulence anisotropy.
• The training data is derived from high-fidelity large-eddy simulations (LES) of a specific wind farm layout under neutral stratification and high Reynolds number conditions.
• The model predicts perturbations toward limiting states of turbulence (e.g., axisymmetric, planar, isotropic) based on local flow features.
• The framework is validated on two unseen wind farm layouts with different turbine spacing and wake development, enabling generalization testing.
• Perturbations are applied to the RANS model's Reynolds stress tensor via eigenvalue modification, improving model fidelity without altering the underlying RANS solver.

Experimental results

Research questions

• RQ1 Can a data-driven machine learning model learn spatially varying, optimal perturbations to the Reynolds stress anisotropy tensor in RANS simulations of wind farms?
• RQ2 How does the performance of the proposed data-driven UQ framework compare to traditional data-free, uniform perturbation approaches in predicting wake characteristics?
• RQ3 To what extent can the trained XGBoost model generalize to unseen wind farm layouts with different turbine spacing and wake interactions?
• RQ4 Which flow features are most predictive of the required perturbation magnitude and direction in the Reynolds stress tensor?
• RQ5 Does the proposed framework reduce uncertainty bounds while maintaining high accuracy for key quantities of interest such as wake velocity deficit and power losses?

Key findings

• The data-driven XGBoost model successfully learns spatially varying perturbations to the Reynolds stress anisotropy, outperforming uniform, data-free perturbations in predicting wake velocity, turbulence intensity, and power losses.
• The two-step feature selection identified key flow features—such as invariants of the strain rate tensor and Reynolds stress components—as most predictive of required perturbations.
• On unseen wind farm layouts, the model achieved improved coverage of high-fidelity LES results for power loss predictions, demonstrating strong generalization capability.
• The framework reduced uncertainty bounds while maintaining high accuracy, indicating a more optimal balance between fidelity and computational cost compared to constant perturbation strategies.
• The method effectively captures complex, non-uniform turbulence anisotropy across diverse wake configurations, including partial wake interactions.
• The results confirm that adaptive, data-driven perturbations are essential for accurate RANS-based wind farm simulations, especially in complex flow regimes.