Articles | Volume 7, issue 3
https://doi.org/10.5194/wes-7-1289-2022
© Author(s) 2022. 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-7-1289-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
27 Jun 2022
Research article |
| 27 Jun 2022
| 27 Jun 2022
Surrogate models for the blade element momentum aerodynamic model using non-intrusive polynomial chaos expansions
Department of Mechanical Engineering, Institute for Integrated Energy Systems, University of Victoria, British Columbia, Canada
Curran Crawford
Department of Mechanical Engineering, Institute for Integrated Energy Systems, University of Victoria, British Columbia, Canada
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Cited articles
Ashuri, T., Zhang, T., Qian, D., and Rotea, M.: Uncertainty quantification of
the levelized cost of energy for a 20 MW research wind turbine model, in:
34th Wind Energy Symposium, p. 1998, https://doi.org/10.2514/6.2016-1998, 2016. a
Barlas, T., Ramos-García, N., Pirrung, G. R., and González Horcas, S.: Surrogate-based aeroelastic design optimization of tip extensions on a modern 10 MW wind turbine, Wind Energ. Sci., 6, 491–504, https://doi.org/10.5194/wes-6-491-2021, 2021. a
Basu, A., Shioya, H., and Park, C.: Statistical Inference: The Minimum Distance
Approach, Chapman & Hall/CRC Monographs on Statistics & Applied
Probability, CRC Press, https://doi.org/10.1201/b10956, 2011. a
Bossanyi, E., Burton, T., Sharpe, D., and Jenkins, N.: Wind energy handbook, Wiley,
New York, https://doi.org/10.1002/9781119992714, 2011. a, b
Dimitrov, N.: Surrogate models for parameterized representation of wake-induced
loads in wind farms, Wind Energy, 22, 1371–1389, 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
DNV GL: Bladed User Manual Version 4.9, Garrad Hassan & Partners Ltd, Bristol, UK, https://www.dnv.com/services/wind-turbine-design-software-bladed-3775 (last access: 22 June 2022), 2018. a
Eldred, M. and Burkardt, J.: Comparison of non-intrusive polynomial chaos and
stochastic collocation methods for uncertainty quantification, in: 47th AIAA
Aerospace Sciences Meeting including The New Horizons Forum and Aerospace
Exposition, p. 976, https://doi.org/10.2514/6.2009-976, 2009. a
Eldred, M., Webster, C., and Constantine, P.: Evaluation of non-intrusive
approaches for Wiener-Askey generalized polynomial chaos, in: 10th AIAA
Non-Deterministic Approaches Conference, p. 1892, https://doi.org/10.2514/6.2008-1892, 2008. a
Fluck, M. and Crawford, C.: Fast analysis of unsteady wing aerodynamics via
stochastic models, AIAA J., 55, 719–728, 2016a. a
Fluck, M. and Crawford, C.: A stochastic aerodynamic model for stationary
blades in unsteady 3D wind fields, J. Phys. Conf. Ser.,
753, 082009, https://doi.org/10.1088/1742-6596/753/8/082009, 2016b. a, b, c
Fluck, M. and Crawford, C.: An engineering model for 3-D turbulent wind inflow based on a limited set of random variables, Wind Energ. Sci., 2, 507–520, https://doi.org/10.5194/wes-2-507-2017, 2017. a, b, c, d
Ghanem, R., Higdon, D., and Owhadi, H.: Handbook of uncertainty quantification,
Springer, https://doi.org/10.1007/978-3-319-12385-1, 2017. a
Ghanem, R. G. and Spanos, P. D.: Stochastic finite elements: a spectral
approach, Courier Corporation, https://doi.org/10.1007/978-1-4612-3094-6, 2003. a, b
Guo, Q. and Ganapathysubramanian, B.: Incorporating a stochastic data-driven
inflow model for uncertainty quantification of wind turbine performance, Wind
Energy, 20, 1551–1567, 2017. a
Hellinger, E.: Neue begründung der theorie quadratischer formen von
unendlichvielen veränderlichen, J. Reine Angew.
Math., 1909, 210–271, 1909. a
Hosder, S., Walters, R., and Balch, M.: Efficient sampling for non-intrusive
polynomial chaos applications with multiple uncertain input variables, in:
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference, p. 1939, https://doi.org/10.2514/6.2008-1892, 2012. a, b
Jonkman, J., Butterfield, S., Musial, W., and Scott, G.: Definition of a 5-MW
reference wind turbine for offshore system development, Tech. rep., National
Renewable Energy Lab.(NREL), Golden, CO, USA, https://doi.org/10.2172/947422, 2009. a, b, c
Jonkman, J. M. and Buhl Jr., M. L.: FAST User's Guide – Updated August 2005, U.S. Department of Energy
Office of Scientific and Technical Information, https://doi.org/10.2172/15020796, 2005. a
Kaintura, A., Dhaene, T., and Spina, D.: Review of Polynomial Chaos-Based
Methods for Uncertainty Quantification in Modern Integrated Circuits,
Electronics, 7, 30, https://doi.org/10.3390/electronics7030030, 2018. a
Kim, S. H. and Boukouvala, F.: Machine learning-based surrogate modeling for data-driven optimization: a comparison of subset selection for regression techniques, Optim. Lett., 14, 989–1010, https://doi.org/10.1007/s11590-019-01428-7, 2020. a
Kucherenko, S., Albrecht, D., and Saltelli, A.: Exploring multi-dimensional
spaces: a Comparison of Latin Hypercube and Quasi Monte Carlo Sampling
Techniques, arXiv, https://doi.org/10.48550/arXiv.1505.02350, 2015. a
Larsen, T. J. and Hansen, A. M.: How 2 HAWC2, the user's manual, DTU, ISBN 978-87-550-3583-6, 2007. a
Le Maître, O. and Knio, O. M.: Spectral methods for uncertainty
quantification: with applications to computational fluid dynamics, Springer
Science & Business Media, https://doi.org/10.1007/978-90-481-3520-2, 2010. a, b
Lupton, R.: Frequency-domain modelling of floating wind turbines, PhD thesis,
University of Cambridge, https://doi.org/10.17863/CAM.14119, 2015. 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. Energ.,
119, 910–922, 2018. a
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods,
Society for Industrial and Applied Mathematics, SIAM,
https://doi.org/10.1137/1.9781611970081, 1992. a
Owen, N. E., Challenor, P., Menon, P. P., and Bennani, S.: Comparison of
surrogate-based uncertainty quantification methods for computationally
expensive simulators, SIAM/ASA Journal on Uncertainty Quantification, 5,
403–435, 2017. a
Rao, S. S.: A course in time series analysis, https://web.stat.tamu.edu/~suhasini/teaching673/time_series.pdf
(last access: 22 June 2022), 2008. a
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
Schröder, L., Dimitrov, N. K., and Sørensen, J. A.: Uncertainty
propagation and sensitivity analysis of an artificial neural network used as
wind turbine load surrogate model, J. Phys. Conf. Ser.,
1618, 042040, https://doi.org/10.1088/1742-6596/1618/4/042040, 2020a. a
Schröder, L., Dimitrov, N. K., and Verelst, D. R.: A surrogate model approach for associating wind farm load variations with turbine failures, Wind Energ. Sci., 5, 1007–1022, https://doi.org/10.5194/wes-5-1007-2020, 2020b. a
Slot, R. M., Sørensen, J. D., Sudret, B., Svenningsen, L., and Thøgersen,
M. L.: Surrogate model uncertainty in wind turbine reliability assessment,
Renew. Energ., 151, 1150–1162, 2020. a
Smolyak, S.: Quadrature and interpolation formulas for tensor products of
certain classes of functions, in: Doklady Akademii Nauk, Russian Academy of Sciences, 148, 1042–1045,
1963. a
Sobol, I. M.: On the distribution of points in a cube and the approximate
evaluation of integrals, Zhurnal Vychislitel'noi Matematiki i Matematicheskoi
Fiziki, 7, 784–802, https://doi.org/10.1016/0041-5553(67)90144-9, 1967. a
Sudret, B.: Uncertainty propagation and sensitivity analysis in mechanical
models – Contributions to structural reliability and stochastic spectral
methods, PhD thesis, Universite Blaise Pascal – Clermont II, https://ethz.ch/content/dam/ethz/special-interest/baug/ibk/risk-safety-and-uncertainty-dam/publications/reports/HDRSudret.pdf
(last access: 22 June 2022),
2007. a, b, c, d, e
Sudret, B.: Polynomial chaos expansions and stochastic finite element methods,
Risk and reliability in geotechnical engineering, edited by: Phoon, K.-K. and Ching, J., 265–300, https://doi.org/10.1201/b17970, 2015.
a
Tyson, S., Donovan, D., Thompson, B., Lynch, S., and Tas, M.: Uncertainty
Modelling with Polynomial Chaos Expansion: Stage 1 – Final Report, The University of Queensland,
ISBN 978-1-74272-173-6, 2015. a
van den Bos, L., Sanderse, B., Blonk, L., Bierbooms, W., and van Bussel, G.:
Efficient ultimate load estimation for offshore wind turbines using
interpolating surrogate models, J. Phys. Conf. Ser.,
1037, 062017, https://doi.org/10.1088/1742-6596/1037/6/062017, 2018. a
van Garrel, A.: Development of a Wind Turbine Aerodynamics Simulation Module,
Tech. rep., Energy research Centre of the Netherlands,
https://doi.org/10.13140/RG.2.1.2773.8000, 2003. a
Wang, H., Jiang, X., Chao, Y., Li, Q., Li, M., Chen, T., and Ouyang, W.:
Numerical optimization of horizontal-axis wind turbine blades with surrogate
model, P. I. Mech. Eng. A-J. Pow., 235, 1173–1186, https://doi.org/10.1177/0957650920976743, 2020. a
Xiu, D. and Karniadakis, G. E.: The Wiener–Askey polynomial chaos for
stochastic differential equations, SIAM J. Sci. Comput., 24,
619–644, 2002. a
Xiu, D., Lucor, D., Su, C.-H., and Karniadakis, G. E.: Stochastic modeling of
flow-structure interactions using generalized polynomial chaos, J.
Fluids Eng., 124, 51–59, 2002. a
Short summary
Based on the IEC standards, a limited number of simulations is sufficient to calculate the extreme and fatigue loads on a wind turbine. However, this means inaccuracy in the output statistics. This paper aims to build a surrogate model on blade element momentum aerodynamic model simulation output employing non-intrusive polynomial chaos expansion. The surrogate model is then used in a large number of Monte Carlo simulations to provide an accurate statistical estimate of the loads.
Based on the IEC standards, a limited number of simulations is sufficient to calculate the...
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