Articles | Volume 9, issue 10
https://doi.org/10.5194/wes-9-1885-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-9-1885-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
07 Oct 2024
Research article |
| 07 Oct 2024
| 07 Oct 2024
Probabilistic surrogate modeling of damage equivalent loads on onshore and offshore wind turbines using mixture density networks
Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Richard Dwight
Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
Axelle Viré
Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, the Netherlands
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Cited articles
Abdallah, I., Lataniotis, C., and Sudret, B.: Parametric hierarchical kriging for multi-fidelity aero-servo-elastic simulators – Application to extreme loads on wind turbines, Probabilistic Eng. Mech., 55, 67–77, https://doi.org/10.1016/j.probengmech.2018.10.001, 2019. a
Avendaño-Valencia, L. D., Abdallah, I., and Chatzi, E.: Virtual fatigue diagnostics of wake-affected wind turbine via Gaussian process regression, Renew. Energy, 170, 539–561, https://doi.org/10.1016/j.renene.2021.02.003, 2021. a
Bishop, C. M.: Pattern Recognition and Machine Learning, Springer New York, https://doi.org/10.1007/978-3-030-57077-4_11, 2006. a
Blei, D. M., Kucukelbir, A., and McAuliffe, J. D.: Variational Inference: A Review for Statisticians, J. Am. Stat. Assoc., 112, 859–877, https://doi.org/10.1080/01621459.2017.1285773, 2017. a
Bortolotti, P., Tarres, H. C., Dykes, K. L., Merz, K., Sethuraman, L., Verelst, D., and Zahle, F.: IEA Wind TCP Task 37: Systems engineering in wind energy – WP2.1 Reference Wind Turbines, Tech. Rep. NREL/TP-5000-73492, National Renewable Energy Lab., Colorado, https://doi.org/10.2172/1529216, 2019. a, b, c
Couturier, P. J. and Skjoldan, P. F.: Implementation of an advanced beam model in BHawC, J. Phys. Conf. Ser., 1037, 0–10, https://doi.org/10.1088/1742-6596/1037/6/062015, 2018. a
Dimitrov, N.: Surrogate models for parameterized representation of wake‐induced loads in wind farms, Wind Energy, 22, 1371–1389, https://doi.org/10.1002/we.2362, 2019. a
Dimitrov, N. and Natarajan, A.: From SCADA to lifetime assessment and performance optimization: how to use models and machine learning to extract useful insights from limited data, J. Phys. Conf. Ser., 1222, 012032, https://doi.org/10.1088/1742-6596/1222/1/012032, 2019. a
Dimitrov, N., Kelly, M. C., Vignaroli, A., and Berg, J.: From wind to loads: wind turbine site-specific load estimation with surrogate models trained on high-fidelity load databases, Wind Energ. Sci., 3, 767–790, https://doi.org/10.5194/wes-3-767-2018, 2018. a, b, c, d
Gasparis, G., Lio, W. H., and Meng, F.: Surrogate models for wind turbine electrical power and fatigue loads in wind farm, Energies, 13, 6360, https://doi.org/10.3390/en13236360, 2020. a
Hlaing, N., Morato, P. G., Santos, F. d. N., Weijtjens, W., Devriendt, C., and Rigo, P.: Farm-wide virtual load monitoring for offshore wind structures via Bayesian neural networks, Struct. Health Monit., 23, 1641–1663, https://doi.org/10.1177/14759217231186048, 2024. a
IEC 61400-3-1: Wind energy generation systems – Part 3-1: Design requirements for fixed offshore wind turbines, Standard, IEC, Geneva, CH, ISBN 9782832276099, 2019. a
Jiang, P., Zhou, Q., and Shao, X.: Surrogate-model-based design and optimization, Springer Nature Singapore Pte Ltd, https://doi.org/10.1007/978-981-15-0731-1_7, 2020. a
Jonkman, B. J. and Buhl, M. L., J.: TurbSim User's Guide: Revised February 2007 for Version 1.21, https://doi.org/10.2172/903075, 2007. a
Jonkman, J.: The New Modularization Framework for the FAST Wind Turbine CAE Tool, AIAA, https://doi.org/10.2514/6.2013-202, 2013. a, b
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, arXiv [preprint], https://doi.org/10.48550/arXiv.1412.6980, 2017. a
Kingma, D. P. and Welling, M.: Auto-encoding variational bayes, 2nd International Conference on Learning Representations, ICLR 2014 – Conference Track Proceedings, Banff, AB, Canada, 14–16 April 2014, 14 pp., https://hdl.handle.net/11245/1.434281 (last access: 26 September 2024), 2014. a
Kneib, T.: Beyond mean regression, Stat. Model., 13, 275–303, https://doi.org/10.1177/1471082X13494159, 2013. a
Koenker, R. and Hallock, K. F.: Quantile Regression, J. Econ. Perspect., 15, 143–156, https://doi.org/10.1257/jep.15.4.143, 2001. a
Larsen, T. and Hansen, A.: How 2 HAWC2, the user's manual, no. 1597(ver. 3-1)(EN) in Denmark, Forskningscenter Risoe, Risoe-R, Risø National Laboratory, ISBN 978-87-550-3583-6, 2007. a
Li, X. and Zhang, W.: Probabilistic Fatigue Evaluation of Floating Wind Turbine using Combination of Surrogate Model and Copula Model, AIAA, AIAA 2019-0247, https://doi.org/10.2514/6.2019-0247, 2019. a, b
Li, X. and Zhang, W.: Long-term fatigue damage assessment for a floating offshore wind turbine under realistic environmental conditions, Renew. Energy, 159, 570–584, https://doi.org/10.1016/j.renene.2020.06.043, 2020. a
Liew, J. and Larsen, G. C.: How does the quantity, resolution, and scaling of turbulence boxes affect aeroelastic simulation convergence?, J. Phys. Conf. Ser., 2265, 032 049, https://doi.org/10.1088/1742-6596/2265/3/032049, 2022. a
Matsuishi, M. and Endo, T.: Fatigue of metals subjected to varying stress, Japan Society of Mechanical Engineers, Fukuoka, Japan, 68, 37–40, 1968. a
Meinshausen, N.: Quantile Regression Forests, J. Mach. Learn. Res., 7, 983–999, 2006. a
Montavon, G., Orr, G. B., and Müller, K.-R., (Eds.): Neural networks: Tricks of the trade, Springer Berlin, Heidelberg, 2 edn., https://doi.org/10.1007/978-3-642-35289-8, 2012. a
Müller, K. and Cheng, P. W.: Application of a Monte Carlo procedure for probabilistic fatigue design of floating offshore wind turbines, Wind Energ. Sci., 3, 149–162, https://doi.org/10.5194/wes-3-149-2018, 2018. a
Murcia, J. P., Réthoré, P.-E., Dimitrov, N., Natarajan, A., Sørensen, J. D., Graf, P., and Kim, T.: Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates, Renew. Energy, 119, 910–922, https://doi.org/10.1016/j.renene.2017.07.070, 2018. a
Ng, A. Y.: Feature Selection, L1 vs. L2 Regularization, and Rotational Invariance, in: Proceedings of the Twenty-First International Conference on Machine Learning, ICML '04, p. 78, Association for Computing Machinery, New York, NY, USA, https://doi.org/10.1145/1015330.1015435, 2004. a
NREL: OpenFAST, Version 2.4.0, GitHub [code], https://github.com/OpenFAST/openfast (last access: 29 September 2022), 2022. a
Olivier, A., Shields, M. D., and Graham-Brady, L.: Bayesian neural networks for uncertainty quantification in data-driven materials modeling, Comput. Methods Appl. Mech. Eng., 386, 114079, https://doi.org/10.1016/j.cma.2021.114079, 2021. a
Peyré, G. and Cuturi, M.: Computational optimal transport: With applications to data Science, Foundations and Trends in Machine Learning, 11, 355–607, https://doi.org/10.1561/2200000073, 2019. a
Ramdas, A., Garcia, N., and Cuturi, M.: On Wasserstein two sample testing and related families of nonparametric tests, arXiv [preprint], https://doi.org/10.48550/arxiv.1509.02237, 2015. a
Rasmussen, C. E. and Williams, C. K. I.: Gaussian processes for machine learning, Adaptive computation and machine learning, MIT Press, Cambridge, Mass., ISBN 9780262256834, https://doi.org/10.7551/mitpress/3206.001.0001, 2006. a, b, c
Schröder, L., Dimitrov, N. K., Verelst, D. R., and Sørensen, J. A.: Wind turbine site-specific load estimation using artificial neural networks calibrated by means of high-fidelity load simulations, J. Phys. Conf. Ser., 1037, 062027, https://doi.org/10.1088/1742-6596/1037/6/062027, 2018. a
Shaler, K., Jasa, J., and Barter, G. E.: Efficient Loads Surrogates for Waked Turbines in an Array, J. Phys. Conf. Ser., 2265, 032095, https://doi.org/10.1088/1742-6596/2265/3/032095, 2022. a, b, c
Singh, D.: Training and validation datasets for training probabilistic machine learning models on NREL's 10-MW reference wind turbine, 4TU.ResearchData [data set], https://doi.org/10.4121/21939995.V1, 2023. a
Singh, D., Dwight, R. P., Laugesen, K., Beaudet, L., and Viré, A.: Probabilistic surrogate modeling of offshore wind-turbine loads with chained Gaussian processes, J. Phys. Conf. Ser., 2265, 032070, https://doi.org/10.1088/1742-6596/2265/3/032070, 2022. a
Skjoldan, P.: Aeroelastic modal dynamics of wind turbines including anisotropic effects, Ph.D. thesis, Danmarks Tekniske Universitet, ISBN 978-87-550-3848-6, 2011. a
Slot, R. M., Sørensen, J. D., Sudret, B., Svenningsen, L., and Thøgersen, M. L.: Surrogate model uncertainty in wind turbine reliability assessment, Renew. Energy, 151, 1150–1162, https://doi.org/10.1016/j.renene.2019.11.101, 2020. a, b
Sobol, I. M.: On the distribution of points in a cube and the approximate evaluation of integrals, USSR Comp. Math. Math+, 7, 86–112, https://doi.org/10.1016/0041-5553(67)90144-9, 1967. a
Teixeira, R., O’Connor, A., Nogal, M., Krishnan, N., and Nichols, J.: Analysis of the design of experiments of offshore wind turbine fatigue reliability design with Kriging surfaces, Procedia Struct. Integr., 5, 951–958, https://doi.org/10.1016/j.prostr.2017.07.132, 2nd International Conference on Structural Integrity, ICSI 2017, 4-7 September 2017, Funchal, Madeira, Portugal, 2017. a
Tibshirani, R.: Regression Shrinkage and Selection via the Lasso, J. R. Stat. Soc. Ser. B Methodol., 58, 267–288, 1996. a
Vega, M. A. and Todd, M. D.: A variational Bayesian neural network for structural health monitoring and cost-informed decision-making in miter gates, Struct. Health Monit., 21, 4–18, https://doi.org/10.1177/1475921720904543, 2022. a
Villani, C.: The Wasserstein distances, in: Optimal Transport: Old and New, pp. 93–111, Springer Berlin Heidelberg, Berlin, Heidelberg, https://doi.org/10.1007/978-3-540-71050-9_6, 2009. a
Yang, Y. and Perdikaris, P.: Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems, Comput. Mech., 64, 417–434, https://doi.org/10.1007/s00466-019-01718-y, 2019. a
Yao, Y., Rosasco, L., and Caponnetto, A.: On Early Stopping in Gradient Descent Learning, Constr. Approx., 26, 289–315, https://doi.org/10.1007/s00365-006-0663-2, 2007. a
Zhu, C., Byrd, R. H., Lu, P., and Nocedal, J.: Algorithm 778: L-BFGS-B: Fortran Subroutines for Large-Scale Bound-Constrained Optimization, ACM Trans. Math. Softw., 23, 550–560, https://doi.org/10.1145/279232.279236, 1997. a
Zhu, X. and Sudret, B.: Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions, Int. J. Uncertain. Quan., 10, 249–275, https://doi.org.10.1615/Int.J.UncertaintyQuantification.2020033029, 2020. a
Zhu, X. and Sudret, B.: Emulation of Stochastic Simulators Using Generalized Lambda Models, SIAM/ASA J. Uncertain. Quantif., 9, 1345–1380, https://doi.org/10.1137/20M1337302, 2021. a, b
Zwick, D. and Muskulus, M.: The simulation error caused by input loading variability in offshore wind turbine structural analysis, Wind Energy, 18, 1421–1432, https://doi.org/10.1002/we.1767, 2015. a
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Short summary
The selection of a suitable site for the installation of a wind turbine plays an important role in ensuring a safe operating lifetime of the structure. In this study, we show that mixture density networks can accelerate this process by inferring functions from data that can accurately map the environmental conditions to the loads but also propagate the uncertainty from the inflow to the response.
The selection of a suitable site for the installation of a wind turbine plays an important role...
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