Articles | Volume 7, issue 5
https://doi.org/10.5194/wes-7-2135-2022
© 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-7-2135-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Gaussian mixture model for extreme wind turbulence estimation
Technical University of Denmark, Department of Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
Anand Natarajan
Technical University of Denmark, Department of Wind and Energy Systems, Frederiksborgvej 399, 4000 Roskilde, Denmark
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This study demonstrates lifetime assessments of a wind turbine structural component as the tower and rotating components as the main bearings using the controller data, measurements, and no blade design information, representing a realistic scenario for operating turbines. A tower bottom virtual load sensor framework based on neural networks was proposed using different input combinations to replace the tower sensor. The estimated lifetime was considerably longer than the design lifetime.
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Wind turbine extreme response estimation based on statistical extrapolation necessitates using a small number of simulations to calculate a low exceedance probability. This is a challenging task especially if we require small prediction error. We propose the use of a Gaussian mixture model as it is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, having flexibility in modeling the distributions of varying response variables.
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Preprint under review for WES
Short summary
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This study demonstrates lifetime assessments of a wind turbine structural component as the tower and rotating components as the main bearings using the controller data, measurements, and no blade design information, representing a realistic scenario for operating turbines. A tower bottom virtual load sensor framework based on neural networks was proposed using different input combinations to replace the tower sensor. The estimated lifetime was considerably longer than the design lifetime.
Xiaodong Zhang and Nikolay Dimitrov
Wind Energ. Sci., 8, 1613–1623, https://doi.org/10.5194/wes-8-1613-2023, https://doi.org/10.5194/wes-8-1613-2023, 2023
Short summary
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Wind turbine extreme response estimation based on statistical extrapolation necessitates using a small number of simulations to calculate a low exceedance probability. This is a challenging task especially if we require small prediction error. We propose the use of a Gaussian mixture model as it is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, having flexibility in modeling the distributions of varying response variables.
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Wind Energ. Sci., 7, 1171–1181, https://doi.org/10.5194/wes-7-1171-2022, https://doi.org/10.5194/wes-7-1171-2022, 2022
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The article delineates a novel procedure to use 10 min measurement statistics with few known parameters of the wind turbine to determine the long-term fatigue damage probability and compare this with the expected damage levels from the design to provide an indicator of structural reliability and remaining life. The results are validated with load measurements from a wind turbine within an offshore wind farm.
Cited articles
Abdallah, I.: Assessment of extreme design loads for modern wind turbines using the probabilistic approach, DTU Wind Energy, ISBN 8793278322, ISBN 9788793278325, 2015. a
Abdallah, I., Natarajan, A., and Sørensen, J. D.: Influence of the control
system on wind turbine loads during power production in extreme turbulence:
Structural reliability, Renew. Energy, 87, 464–477,
https://doi.org/10.1016/j.renene.2015.10.044, 2016. a
Akaike, H.: Information theory and an extension of the maximum likelihood
principle, in: Selected papers of hirotugu akaike, Springer, New York, 199–213, https://doi.org/10.1007/978-1-4612-1694-0_15, 1998. a
Arthur, D. and Vassilvitskii, S.: k-means : The advantages of careful seeding, Tech. rep., Society for Industrial and Applied Mathematics, Stanford, USA, 1027–1035, ISBN 978-0-89871-624-5, 2006. a
Bouyé, E., Durrleman, V., Nikeghbali, A., Riboulet, G., and Roncalli, T.:
Copulas for finance – a reading guide and some applications, SSRN Electron. J., https://doi.org/10.2139/ssrn.1032533, 2011. a
Chang, G. W., Lu, H. J., Wang, P. K., Chang, Y. R., and Lee, Y. D.: Gaussian
mixture model-based neural network for short-term wind power forecast, Int. T. Elect. Energ. Syst., 27, e2320, https://doi.org/10.1002/etep.2320, 2017. a
Cui, M., Feng, C., Wang, Z., and Zhang, J.: Statistical representation of wind power ramps using a generalized Gaussian mixture model, IEEE T. Sustain. Energ., 9, 261–272, https://doi.org/10.1109/TSTE.2017.2727321, 2018. a
Dempster, A. P., Laird, N. M., and Rubin, D. B.: Maximum likelihood from
incomplete data via the EM algorithm, J. Roy. Stat. Soc. Ser. B, 39, 1–38,
1977. a
Dimitrov, N. K., Natarajan, A., and Mann, J.: Effects of normal and extreme
turbulence spectral parameters on wind turbine loads, Renew. Energy, 101,
1180–1193, https://doi.org/10.1016/j.renene.2016.10.001, 2017. a, b
Hannesdóttir, Á., Kelly, M., and Dimitrov, N.: Extreme wind
fluctuations: Joint statistics, extreme turbulence, and impact on wind
turbine loads, Wind Energ. Sci., 4, 325–342, https://doi.org/10.5194/wes-4-325-2019, 2019. a, b
Janouek, J., Gajdo, P., Radecky, M., and Snasel, V.: Gaussian mixture model
cluster forest, in: Proceedings – 2015 IEEE 14th International Conference on
Machine Learning and Applications, Icmla, Miami, Florida, USA, 1019–1023, https://doi.org/10.1109/ICMLA.2015.12, 2015. a
Li, T., Wang, Y., and Zhang, N.: Combining probability density forecasts for
power electrical loads, IEEE T. Smart Grid, 11, 1679–1690,
https://doi.org/10.1109/TSG.2019.2942024, 2020. a
Low, Y. M.: A new distribution for fitting four moments and its applications to reliability analysis, Struct. Safe., 42, 12–25,
https://doi.org/10.1016/j.strusafe.2013.01.007, 2013. a
Mann, J.: The spatial structure of neutral atmospheric surface-layer
turbulence, J. Fluid Mech., 273, 141–168, https://doi.org/10.1017/S0022112094001886, 1994. a
McLachlan, G. J., Lee, S. X., and Rathnayake, S. I.: Finite mixture models, Annu. Rev. Stat. Appl., 6, 355–378, https://doi.org/10.1146/annurev-statistics-031017-100325, 2019. a, b
Miyazaki, B., Izumi, K., Toriumi, F., and Takahashi, R.: Change detection of
orders in stock markets using a Gaussian mixture model, Intel. Syst. Account. Financ. Manage., 21, 169–191, https://doi.org/10.1002/isaf.1356, 2014. a
Monahan, A. H.: Idealized models of the joint probability distribution of wind speeds, Nonlin. Processes Geophys., 25, 335–353,
https://doi.org/10.5194/npg-25-335-2018, 2018. a
Peña Diaz, A., Floors, R. R., Sathe, A., Gryning, S.-E., Wagner, R., Courtney, M., Larsén, X. G., Hahmann, A. N., and Hasager, C. B.: Ten years of boundary-layer and wind-power meteorology at Høvsøre, Denmark, Bound.-Lay. Meteorol., 158, 1–26, https://doi.org/10.1007/s10546-015-0079-8, 2016. a
Permuter, H., Francos, J., and Jermyn, I. H.: Gaussian mixture models of
texture and colour for image database retrieval, in: Icassp, IEEE International Conference on Acoustics, Speech and Signal Processing – Proceedings, 3, 6–10 April 2003, Hong Kong, China, 569–572, https://doi.org/10.1109/ICASSP.2003.1199538, 2003. a
Prabakaran, I., Wu, Z., Lee, C., Tong, B., Steeman, S., Koo, G., Zhang, P. J., and Guvakova, M. A.: Gaussian mixture models for probabilistic classification of breast cancer, Cancer Res., 79, 3492–3502,
https://doi.org/10.1158/0008-5472.CAN-19-0573, 2019.
a
Reynolds, D. and Rose, R.: Robust text-independent speaker identification using Gaussian mixture speaker models, IEEE T. Speech Audio Process., 3, 72–83, https://doi.org/10.1109/89.365379, 1995. a
Schwarz, G.: Estimating the dimension of a model, Ann. Stat., 6, 461–464, https://doi.org/10.1214/aos/1176344136, 1978. a
Srbinovski, B., Temko, A., Leahy, P., Pakrashi, V., and Popovici, E.: Gaussian mixture models for site-specific wind turbine power curves, Proc. Inst. Mech. Eng. Pt. A, 235, 494–505, https://doi.org/10.1177/0957650920931729, 2021. a
Steinhoff, C., Müller, T., Nuber, U. A., and Vingron, M.: Gaussian mixture density estimation applied to microarray data, Lect. Notes Comput. Sci., 2810, 418–429, https://doi.org/10.1007/978-3-540-45231-7_39, 2003. a, b
Wahbah, M., Alhussein, O., El-Fouly, T. H., Zahawi, B., and Muhaidat, S.:
Evaluation of parametric statistical models for wind speed probability
density estimation, in: 2018 IEEE Electrical Power and Energy Conference, Epec 2018, Toronto, Ontario, 8598283, https://doi.org/10.1109/EPEC.2018.8598283, 2018. a
Xiao, Q.: Evaluating correlation coefficient for Nataf transformation,
Probabil. Eng. Mech., 37, 1–6, https://doi.org/10.1016/j.probengmech.2014.03.010, 2014. a, b
Zhang, J., Yan, J., Infield, D., Liu, Y., and sang Lien, F.: Short-term
forecasting and uncertainty analysis of wind turbine power based on long
short-term memory network and Gaussian Mixture Model, Appl. Energy, 241, 229–244, https://doi.org/10.1016/j.apenergy.2019.03.044, 2019. a
Zhang, X., Low, Y. M., and Koh, C. G.: Maximum entropy distribution with
fractional moments for reliability analysis, Struct. Safe., 83, 101904,
https://doi.org/10.1016/j.strusafe.2019.101904, 2020. a
Zhang, Y., Li, M., Wang, S., Dai, S., Luo, L., Zhu, E., Xu, H., Zhu, X., Yao,
C., and Zhou, H.: Gaussian mixture model clustering with incomplete data, ACM
T. Multimed. Comput. Commun. Appl., 17, 1–14, 2021. a
Short summary
Joint probability distribution of 10 min mean wind speed and the standard deviation is proposed using the Gaussian mixture model and has been shown to agree well with 15 years of measurements. The environmental contour with a 50-year return period (extreme turbulence) is estimated. The results from the model could be taken as inputs for structural reliability analysis and uncertainty quantification of wind turbine design loads.
Joint probability distribution of 10 min mean wind speed and the standard deviation is proposed...
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