We propose a data-driven model to predict the short-term fatigue Damage Equivalent Loads (DEL) on a wake-affected wind turbine based on wind field inflow sensors and/or loads sensors deployed on an adjacent up-wind wind turbine. Gaussian Process Regression (GPR) with Bayesian hyperparameters calibration is proposed to obtain a surrogate from input random variables to output DELs in the blades and towers of the up-wind and wake-affected wind turbines. A sensitivity analysis based on the hyperparameters of the GPR and Kullback-Leibler divergence is conducted to assess the effect of different input on the obtained DELs. We provide qualitative recommendations for a minimal set of necessary and sufficient input random variables to minimize the error in the DEL predictions on the wake-affected wind turbine. Extensive simulations are performed comprising different random variables, including wind speed, turbulence intensity, shear exponent and inflow horizontal skewness. Furthermore, we include random variables related to the blades lift and drag coefficients with direct impact on the rotor aerodynamic induction, which governs the evolution and transport of the meandering wake. In addition, different spacing between the wind turbines and W\u00f6hler exponents for calculation of DELs are considered. The maximum prediction normalized mean squared error, obtained in the tower base DELs in the fore-aft direction of the wake affected wind turbine, is less than 4%. In the case of the blade root DELs, the overall prediction error is less than 1%. The proposed scheme promotes utilization of sparse structural monitoring (loads) measurements for improving diagnostics on wake-affected turbines.
", "keywords": ["bepress|Physical Sciences and Mathematics|Physics|Engineering Physics", "engrXiv|Engineering|Risk Analysis", "engrXiv|Engineering|Other Engineering", "bepress|Engineering", "engrXiv|Engineering|Mechanical Engineering|Fluid Mechanics", "bepress|Engineering|Mechanical Engineering", "engrXiv|Engineering|Mechanical Engineering", "bepress|Engineering|Mechanical Engineering|Applied Mechanics", "Gaussian Process Regression", "02 engineering and technology", "7. Clean energy", "Virtual sensing", "wind turbine", "bepress|Engineering|Computational Engineering", "engrXiv|Engineering|Civil and Environmental Engineering", "0202 electrical engineering", " electronic engineering", " information engineering", "uncertainty", "Fatigue", "wake", "engrXiv|Engineering|Civil and Environmental Engineering|Structural Engineering", "Uncertainty", "engrXiv|Engineering|Mechanical Engineering|Applied Mechanics", "Bayesian Calibration", "engrXiv|Engineering|Engineering Physics", "bepress|Engineering|Risk Analysis", "engrXiv|Engineering", "bepress|Engineering|Civil and Environmental Engineering", "engrXiv|Engineering|Computational Engineering", "Wake", "bepress|Engineering|Aerospace Engineering|Aerodynamics and Fluid Mechanics", "bepress|Engineering|Civil and Environmental Engineering|Structural Engineering", "fatigue", "bepress|Engineering|Other Engineering", "Sensitivity analysis", "Wind turbine", "Bayesian Gaussian process regression"]}, "links": [{"href": "https://doi.org/10.1016/j.renene.2021.02.003"}, {"rel": "related", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main/items/Renewable%20Energy", "name": "related record", "description": "related record", "type": "application/json"}, {"rel": "self", "type": "application/geo+json", "title": "10.1016/j.renene.2021.02.003", "name": "item", "description": "10.1016/j.renene.2021.02.003", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main/items/10.1016/j.renene.2021.02.003"}, {"rel": "collection", "type": "application/json", "title": "Collection", "name": "collection", "description": "Collection", "href": "https://repository.soilwise-he.eu/cat/collections/metadata:main"}], "time": {"date": "2020-11-05T00:00:00Z"}}, {"id": "10.3929/ethz-b-000445427", "type": "Feature", "geometry": null, "properties": {"updated": "2026-07-25T16:21:19Z", "type": "Journal Article", "created": "2020-09-08", "title": "GP-ARX-Based Structural Damage Detection and Localization under Varying Environmental Conditions", "description": "The representation of structural dynamics in the absence of physics-based models, is often accomplished through the identification of parametric models, such as the autoregressive with exogenous inputs, e.g. ARX models. When the structure is amenable to environmental variations, parameter-varying extensions of the original ARX model can be implemented, allowing for tracking of the operational variability. Yet, the latter occurs in sufficiently longer time-scales (days, weeks, months), as compared to system dynamics. For inferring a \uffe2\uff80\uff9cglobal\uffe2\uff80\uff9d, long time-scale varying ARX model, data from a full operational cycle has to typically become available. In addition, when the sensor network comprises multiple nodes, the identification of long time-scale varying, vector ARX models grow in complexity. We address these issues by proposing a distributed framework for structural identification, damage detection and localization. Its main features are: (i) the individual estimation of local, single-input-single-output ARX models at every operational point; (ii) the long time-scale representation of each individual ARX coefficient via a Gaussian process regression, which captures dependency on varying Environmental and Operational Conditions (EOCs); (iii) the establishment of a distributed residual generation algorithm for damage detection, which produces time-series of well-defined stationary statistics, with detected discrepancies used for damage diagnosis; and, (iv) exploitation of ARX-inferred mode shape curvatures, obtained via ARX-inferred global state-space models, of the healthy and damaged states, for damage localization. The method is assessed via application on two numerical case studies of different complexity, with the results confirming its efficacy for diagnostics under varying EOCs.
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