Articles | Volume 7, issue 2
https://doi.org/10.5194/wes-7-623-2022
© 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-7-623-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Mar 2022
Research article |
| 16 Mar 2022
| 16 Mar 2022
Model updating of a wind turbine blade finite element Timoshenko beam model with invertible neural networks
Pablo Noever-Castelos
CORRESPONDING AUTHOR
Institute for Wind Energy Systems, Leibniz University Hannover, Appelstr. 9A, 30167 Hanover, Germany
David Melcher
Department of Rotor Blades, Fraunhofer IWES, Fraunhofer Institute for Wind Energy Systems, Am Seedeich 45, 27572 Bremerhaven, Germany
Claudio Balzani
Institute for Wind Energy Systems, Leibniz University Hannover, Appelstr. 9A, 30167 Hanover, Germany
Related authors
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Wind turbine rotor blades consist of subcomponents that are glued together. Such connections are subject to fatigue loads. This paper analyzes the fatigue load characteristics of three different wind turbine rotor blades in trailing edge adhesive joints. It is shown that the fatigue loads have measurable degrees of non-proportionality and that the choice of the procedure to calculate the fatigue damage is crucial for designing reliable blades.
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Modern rotor blade designs depend on detailed numerical models and simulations. Thus, a validated modeling methodology is fundamental for reliable designs. This paper briefly presents a modeling algorithm for rotor blades, its validation against real-life full-scale blade tests, and the respective test data. The hybrid 3D shell/solid finite-element model is successfully validated against the conducted classical bending tests in flapwise and lead–lag direction as well as novel torsion tests.
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It is shown that conventional methods in rotor blade fatigue testing can lead to substantial under-testing across major blade areas, as the material fatigue behavior is not represented well. An improved approach based on strain proportional loads with mean load correction is proposed to define loads, which result in sufficient fatigue damage throughout all blade areas. The results suggest that this can require up to 16 % higher uniaxial fatigue test loads than conventional methods.
Claudio Balzani and Pablo Noever Castelos
Wind Energ. Sci., 10, 1249–1267, https://doi.org/10.5194/wes-10-1249-2025, https://doi.org/10.5194/wes-10-1249-2025, 2025
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Wind turbine rotor blades consist of subcomponents that are glued together. Such connections are subject to fatigue loads. This paper analyzes the fatigue load characteristics of three different wind turbine rotor blades in trailing edge adhesive joints. It is shown that the fatigue loads have measurable degrees of non-proportionality and that the choice of the procedure to calculate the fatigue damage is crucial for designing reliable blades.
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Wind Energ. Sci., 10, 679–694, https://doi.org/10.5194/wes-10-679-2025, https://doi.org/10.5194/wes-10-679-2025, 2025
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The amount of energy that can be extracted from wind depends primarily on the blade geometry, which can be affected by elastic deformations. This paper presents a first study analysing the influence of cross-sectional deformations of a 15 MW wind turbine blade on aero-elastic simulations. The results show that cross-sectional deformations have a minor influence on the internal loads of rotor blades in normal operation.
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Aeroelastic stability simulations are needed to guarantee the safety and overall robust design of wind turbines. To increase our confidence in these simulations in the future, the sensitivity of the stability analysis with respect to variability in the structural properties of the wind turbine blades is investigated. Multiple state-of-the-art tools are compared and the study shows that even though the tools predict similar stability behavior, the sensitivity might be significantly different.
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Wind Energ. Sci., 9, 1465–1481, https://doi.org/10.5194/wes-9-1465-2024, https://doi.org/10.5194/wes-9-1465-2024, 2024
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We provide a comprehensive overview showing available cross-sectional approaches and their properties in relation to derived requirements for the design of composite rotor blades. The Jung analytical approach shows the best results for accuracy of stiffness terms (coupling and transverse shear) and stress distributions. Improved performance compared to 2D finite element codes could be achieved, making the approach applicable for optimization problems with a high number of design variables.
Pablo Noever-Castelos, Bernd Haller, and Claudio Balzani
Wind Energ. Sci., 7, 105–127, https://doi.org/10.5194/wes-7-105-2022, https://doi.org/10.5194/wes-7-105-2022, 2022
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Modern rotor blade designs depend on detailed numerical models and simulations. Thus, a validated modeling methodology is fundamental for reliable designs. This paper briefly presents a modeling algorithm for rotor blades, its validation against real-life full-scale blade tests, and the respective test data. The hybrid 3D shell/solid finite-element model is successfully validated against the conducted classical bending tests in flapwise and lead–lag direction as well as novel torsion tests.
Cited articles
Akima, H.: A New Method of Interpolation and Smooth Curve Fitting Based on
Local Procedures, J. ACM, 17, 589–602, https://doi.org/10.1145/321607.321609, 1970. a
Ardizzone, L., Mackowiak, R., Rother, C., and Köthe, U.: Training
Normalizing Flows with the Information Bottleneck for Competitive Generative
Classification, in: 32nd Conference on Neural Information Processing Systems
(NeurIPS 2018), vol. 33, 7828–7840, https://researchr.org/publication/nips-2020 (last access: 14 March 2022), 2018. a
Ardizzone, L., Kruse, J., Wirkert, S., Rahner, D., Pellegrini, E. W., Klessen, R. S., Maier-Hein, L., Rother, C., and Köthe, U.: Analyzing Inverse Problems with Invertible Neural Networks, in: Seventh International
Conference on Learning Representations, https://doi.org/10.48550/arXiv.1808.04730, 2019a. a, b
Augustyn, D., Smolka, U., Tygesen, U. T., Ulriksen, M. D., and Sørensen, J. D.: Data-driven model updating of an offshore wind jacket substructure,
Appl. Ocean Res., 104, 102366, https://doi.org/10.1016/j.apor.2020.102366, 2020. a, b
Blasques, J. P. and Stolpe, M.: Multi-material topology optimization of
laminated composite beam cross sections, Compos. Struct., 94, 3278–3289, https://doi.org/10.1016/j.compstruct.2012.05.002, 2012. a, b, c, d
Bruns, M., Hofmeister, B., Grießmann, T., and Rolfes, R.: Comparative Study of Parameterizations for Damage Localization with Finite Element Model
Updating, in: Proceedings of the 29th European Safety and Reliability
Conference (ESREL), edited by: Beer, M. and Zio, E., 1125–1132, Research
Publishing Services, Singapore, https://doi.org/10.3850/978-981-11-2724-3_0713-cd, 2019. a, b, c
Chakroborty, S. and Saha, G.: Feature selection using singular value
decomposition and QR factorization with column pivoting for text-independent
speaker identification, Speech Commun., 52, 693–709,
https://doi.org/10.1016/j.specom.2010.04.002, 2010. a, b, c, d
Chopard, B. and Tomassini, M. (Eds.): An Introduction to Metaheuristics for
Optimization, Natural Computing Series, Springer International Publishing,
Cham, https://doi.org/10.1007/978-3-319-93073-2, 2018. a
Dick, J. and Pillichshammer, F.: Digital nets and sequences: Discrepancy theory and quasi-Monte Carlo integration, Cambridge Univ. Press, Cambrigde, ISBN 9780511761188, 2010. a
Duchi, J., Hazan, E., and Singer, Y.: Adaptive Subgradient Methods for Online
Learning and Stochastic Optimization, J. Mach. Learn. Res., 12, 2121–2159, 2011. a
Grieves, M. W.: Virtually Intelligent Product Systems: Digital and Physical
Twins, in: Complex Systems Engineering: Theory and Practice, vol. 411, edited by: Flumerfelt, S., Schwartz, K. G., Mavris, D., and Briceno, S., American Institute of Aeronautics and Astronautics, Inc, Reston, VA, 175–200, https://doi.org/10.2514/5.9781624105654.0175.0200, 2019. a
Gundlach, J. and Govers, Y.: Experimental modal analysis of aeroelastic
tailored rotor blades in different boundary conditions, J. Phys.: Conf. Ser., 1356, 012023, https://doi.org/10.1088/1742-6596/1356/1/012023, 2019. a
He, K., Zhang, X., Ren, S., and Sun, J.: Delving Deep into Rectifiers:
Surpassing Human-Level Performance on ImageNet Classification, https://doi.org/10.48550/arXiv.1502.01852, 2015. a
Herman, J. and Usher, W.: SALib: An open-source Python library for Sensitivity Analysis, J. Open Source Softw., 2, 97, https://doi.org/10.21105/joss.00097, 2017. a
Hofmeister, B., Bruns, M., and Rolfes, R.: Finite element model updating using deterministic optimisation: A global pattern search approach, Eng. Struct., 195, 373–381, https://doi.org/10.1016/j.engstruct.2019.05.047, 2019. a
Knebusch, J., Gundlach, J., and Govers, Y.: A systematic investigation of
common gradient based model updating approaches applied to high-fidelity
test-data of a wind turbine rotor blade, in: Proceedings of the XI International Conference on Structural Dynamics, EASDAthens,
2159–2174, https://doi.org/10.47964/1120.9175.19508, 2020. a, b
Lin, J., Leung, L. K., Xu, Y.-L., Zhan, S., and Zhu, S.: Field measurement,
model updating, and response prediction of a large-scale straight-bladed
vertical axis wind turbine structure, Measurement, 130, 57–70,
https://doi.org/10.1016/j.measurement.2018.07.057, 2018. a
Liu, X., Leimbach, K. R., and Hartmann, D.: System identification of a wind
turbine using robust model updating strategy, in: Proceedings of 19th International Conference on the Application of Computer Science and
Mathematics in Architecture and Civil Enrineering, Weimar, 250–260,
https://e-pub.uni-weimar.de/opus4/frontdoor/deliver/index/docId/2457/file/IKM2012_pdfa.pdf
(last access: 14 March 2022), 2012. a
Luczak, M., Manzato, S., Peeters, B., Branner, K., Berring, P., and Kahsin, M.: Updating Finite Element Model of a Wind Turbine Blade Section Using
Experimental Modal Analysis Results, Shock Vibrat., 2014, 1–12,
https://doi.org/10.1155/2014/684786, 2014. a, b
Marwala, T., Boulkaibet, I., and Adhikari, S.: Probabilistic Finite Element
Model Updating Using Bayesian Statistics, John Wiley & Sons, Ltd, Chichester, UK, https://doi.org/10.1002/9781119153023, 2016. a, b
Noever-Castelos, P.: IWES-LUH/Beam-ModelUpdating-cINN, Zenodo [code],
https://doi.org/10.5281/zenodo.6351906, 2022a. a
Noever-Castelos, P.: Training data and models for cINN model updating of finite element beam models of wind turbine blades, Research Data Repository of the Leibniz Universität Hannover [data set], https://doi.org/10.25835/0042221, 2022b. a
Noever-Castelos, P., Haller, B., and Balzani, C.: Validation of a modeling methodology for wind turbine rotor blades based on a full-scale blade test, Wind Energ. Sci., 7, 105–127, https://doi.org/10.5194/wes-7-105-2022, 2022.
a, b, c, d
Olufsen, M. S. and Ottesen, J. T.: A practical approach to parameter estimation applied to model predicting heart rate regulation, J. Math. Biol., 67, 39–68, https://doi.org/10.1007/s00285-012-0535-8, 2013. a, b
Omenzetter, P. and Turnbull, H.: Comparison of two optimization algorithms for fuzzy finite element model updating for damage detection in a wind turbine blade, in: Nondestructive Characterization and Monitoring of Advanced
Materials, Aerospace, Civil Infrastructure, and Transportation XII, edited by: Shull, P. J., SPIE, p. 60, https://doi.org/10.1117/12.2295314, 2018. a, b, c
Pastor, M., Binda, M., and Harčarik, T.: Modal Assurance Criterion,
Proced. Eng., 48, 543–548, https://doi.org/10.1016/j.proeng.2012.09.551, 2012. a, b
Patelli, E., Govers, Y., Broggi, M., Gomes, H. M., Link, M., and Mottershead,
J. E.: Sensitivity or Bayesian model updating: a comparison of techniques
using the DLR AIRMOD test data, Arch. Appl. Mech., 87, 905–925,
https://doi.org/10.1007/s00419-017-1233-1, 2017. a
Sayer, F., Antoniou, A., Goutianos, S., Gebauer, I., Branner, K., and Balzani, C.: ReliaBlade Project: A Material's Perspective towards the Digitalization of Wind Turbine Rotor Blades, IOP Conf. Ser.: Mater. Sci. Eng., 942, 012006, https://doi.org/10.1088/1757-899X/942/1/012006, 2020. a
Schröder, K., Grove, S., Tsiapoki, S., Gebhardt, C. G., and Rolfes, R.:
Structural Change Identification at a Wind Turbine Blade using Model
Updating, J. Phys.: Conf. Ser., 1104, 012030, https://doi.org/10.1088/1742-6596/1104/1/012030, 2018. a, b
Sehgal, S. and Kumar, H.: Structural Dynamic Model Updating Techniques: A State of the Art Review, Arch. Comput. Meth. Eng., 23, 515–533, https://doi.org/10.1007/s11831-015-9150-3, 2016. a
SmartBlades2: Fabrication, Testing, and Further Development of Smart Rotor
Blades, coordinated research project (project numbers 0324032A-H), supported
by the Federal Ministry for Economic Affairs and Energy of Germany due to a
decision of the German Bundestag, 2016–2020. a
Sobol', I. M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul., 55, 271–280, https://doi.org/10.1016/S0378-4754(00)00270-6, 2001. a
Velazquez, A. and Swartz, R. A.: Operational model updating of low-order
horizontal axis wind turbine models for structural health monitoring
applications, J. Intel. Mater. Syst. Struct., 26, 1739–1752, https://doi.org/10.1177/1045389X14563864, 2015. a
Visual Learning Lab Heidelberg: FrEIA – Framework for Easily Invertible
Architectures, GitHub, https://github.com/VLL-HD/FrEIA (last access: 14 March 2022), 2021. a
Short summary
In the wind energy industry, a digital twin is fast becoming a key instrument for the monitoring of a wind turbine blade's life cycle. Here, our introduced model updating with invertible neural networks provides an efficient and powerful technique to represent the real blade as built. This method is applied to a full finite element Timoshenko beam model of a blade to successfully update material and layup parameters. The advantage over state-of-the-art methods is the established inverse model.
In the wind energy industry, a digital twin is fast becoming a key instrument for the monitoring...
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