Research Papers

Fast Estimation of the Damage Equivalent Load in Blade Geometry Multidisciplinar Optimization

[+] Author and Article Information
Fernando Echeverría Durá

ACCIONA Windpower,
Polígono industrial Barasoain parcela 2,
Barasoain 31395, Navarra, Spain
e-mail: FEcheverria@nordex-online.com

Fermín Mallor Gimenez

ACCIONA Windpower,
Avenida Innovación 3, Sarriguren,
Pamplona 31621, Spain;
UPNA Universidad Pública de Navarra (UPNA),
Sarriguren 31621, Navarra, Spain
e-mail: mallor@unavarra.es

Javier Sanz Corretge

ACCIONA Windpower,
Polígono industrial Barasoain parcela 2,
Barasoain 31395, Navarra, Spain
e-mail: FSanz@nordex-online.com

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received September 14, 2016; final manuscript received April 12, 2017; published online May 22, 2017. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 139(4), 041008 (May 22, 2017) (10 pages) Paper No: SOL-16-1407; doi: 10.1115/1.4036636 History: Received September 14, 2016; Revised April 12, 2017

Designing blade geometry as a multidisciplinary optimization presents important challenges due to the increment in the number of design variables and computational cost of calculating the constraints and objective function. Blades have an important impact on loads because they capture the kinetic energy in wind and transfer it to the rest of the wind turbine components. Thus, consideration of the fatigue response is necessary in the optimization problem. However, the calculation of the damage equivalent loads (DELs) implies time-consuming simulations that restrict the number of design variables due to the increment of the search space. This article proposes a frequency domain method to estimate the fatigue response, which produces an advantage in terms of computational cost. The method is based on wind turbine model linearization by means of an aero-elastic code and the subsequent calculation of a frequency response function (FRF), which serves to estimate the response of the wind turbine. The Dirlik method is then applied to infer the damage equivalent loads. This process, which is useful for variables that have a stochastic nature, provides rapid approximate prediction of the fatigue response. An alternative estimation is proposed for loads subjected to an important periodic component. The results show that the method is useful in the initial stages of design.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Drela, M. , 1998, “ Pros and Cons of Airfoil Optimization,” Frontiers Computational Fluid Dynamics, World Scientific, Singapore, pp. 363–381.
Fuglsang, P. , and Madsen, H. A. , 1999, “ Optimization Method for Wind Turbine Rotors,” J. Wind Eng. Ind. Aerodyn., 80(1–2), pp. 191–206. [CrossRef]
Lee, K.-H. , Kim, K.-H. , Lee, D.-H. , Lee, K.-T. , and Park, J.-P. , 2010, “ Two-Step Optimization for Wind Turbine Blade With Probability Approach,” ASME J. Sol. Energy Eng., 132(3), p. 034503. [CrossRef]
Buckley, H. P. , Zhou, B. Y. , and Zingg, D. W. , 2010, “ Airfoil Optimization Using Practical Aerodynamic Design Requirements,” J. Aircr., 47(5), pp. 1707–1719. [CrossRef]
Korte, J. , Weston, R. , and Zang, T. , 1997, “ Multidisciplinary Optimization Methods For Preliminary Design,” NASA Langley Technical Report Server, Technical Report No. AIAA Paper -94-4325-CP.
Bottasso, C. L. , Campagnolo, F. , and Croce, A. , 2012, “ Multi-Disciplinary Constrained Optimization of Wind Turbines,” Multibody Syst. Dyn., 27(1), pp. 21–53. [CrossRef]
Ashuri, T. , Zaaijer, M. B. , Martins, J. R. R. A. , van Bussel, G. J. W. , and van Kuik, G. A. M. , 2014, “ Multidisciplinary Design Optimization of Offshore Wind Turbines for Minimum Levelized Cost of Energy,” Renewable Energy, 68(C), pp. 893–905. [CrossRef]
Ning, A. S. , Damiani, R. , and Moriarty, P. J. , 2014, “ Objectives and Constraints for Wind Turbine Optimization,” ASME J. Sol. Energy Eng., 136(4), p. 041010. [CrossRef]
Toft, H. S. , Svenningsen, L. , Moser, W. , Sørensen, J. D. , and Thøgersen, M. L. , 2016, “ Wind Climate Parameters for Wind Turbine Fatigue Load Assessment,” ASME J. Sol. Energy Eng., 138(3), p. 031010. [CrossRef]
Passipoularidis, V. , and Brøndsted, P. , 2010, “ Fatigue Evaluation Algorithms: Review,” Technical University of Denmark, Risø National Laboratory for Sustainable Energy, Roskilde, Denmark.
Bellman, R. , 1957, Dynamic Programming, Princeton University Press, Princeton, NJ.
Chen, S. , Montgomery, J. , and Bolufe-Rohler, A. , 2015, “ Measuring the Curse of Dimensionality and Its Effects on Particle Swarm Optimization and Differential Evolution,” Appl. Intell., 42(3), pp. 514–526. [CrossRef]
Sørensen, P. , Larsen, G. C. , and Christensen, C. J. , 1995, “ A Complex Frequency Domain Model of Wind Turbine Structures,” ASME J. Sol. Energy Eng., 117(4), pp. 311–317. [CrossRef]
Halfpenny, A. , 1998, “ Dynamics Both On and Offshore Wind Turbines Frequency Domain,” University College London, London, UK.
Ziegler, L. , Voormeeren, S. , Schafhirt, S. , and Muskulus, M. , 2015, “ Sensitivity Wave Fatigue Loads Offshore Wind Turbines Varying Site Conditions,” Energy Proc., 80, pp. 193–200. [CrossRef]
van der Tempel, J. , 2010, “ Design of Support Structures for Offshore Wind Turbines,” Technische Universiteit Delft, Delft, The Netherlands.
Dirlik, T. , 1985, “ Application of Computers in Fatigue Analysis,” University of Warwick, Coventry, UK.
Nocedal, J. , and Wright, S. J. , 2006, Numerical Optimization (Series in Operations Research Financial Engineering), Springer-Verlag, New York.
Han, X. , 2011, “ An Evolutionary Geometry Parametrization for Aerodynamic Shape Optimization,” University of Toronto, Toronto, ON, Canada.
Fuglsang, P. , and Dahl, K. S. , 1998, “ Design of the Wind Turbine Airfoil Family RISØ-A-XX,” Technical University of Denmark, Risø National Laboratory for Sustainable Energy, Roskilde, Denmark.
Obayashi, S. , Tsukahara, T. , and Nakamura, T. , 2000, “ Multiobjective Genetic Algorithm Applied to Aerodynamic Design Cascade Airfoils,” IEEE Trans. Ind. Electron., 47(1), pp. 211–216. [CrossRef]
Tegen, P. S. , Lantz, E. , Hand, M. , Maples, B. , Smith, A. , and Schwabe, P. , 2013, “ 2011 Cost Wind Energy Review,” National Renewable Energy Laboratory, Golden, CO.
Griffith, D. T. , and Johanns, W. , 2013, “ Carbon Design Studies for Large Blades: Performance and Cost Tradeoffs for the Sandia 100-Meter Wind Turbine Blade,” AIAA Paper No. 2013-1554.
IEC, 2005, “ Wind Turbines—Part 1: Design Requirements,” International Electrotechnical Commission, Geneva, Switzerland, Standard No. IEC 61400-1.
Garrad and Hassan & Partners, 2012, “ Bladed User Manual,” Garrad Hassan & Partners Ltd., Bristol, UK.
Jonkman, J., 2015, “ NWTC Information Portal (FAST),” National Renewable Energy Laboratory, Golden, CO, accessed May 11, 2016, https://nwtc.nrel.gov/FAST
Munteanu, I. , 2008, “ Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design,” Int. J. Robust Nonlinear Control, 18(7), pp. 796–797. [CrossRef]
Burlibasa, A. , and Ceanga, E. , 2013, “ Rotationally Sampled Spectrum Approach for Simulation of Wind Speed Turbulence in Large Wind Turbines,” Appl. Energy, 111, pp. 624–635. [CrossRef]
Ostergaard, K. Z. , Brath, P. , and Stoustrup, J. , 2007, “ Estimation of Effective Wind Speed,” J. Phys.: Conf. Ser., 75(1), p. 012082. [CrossRef]
Simley, E. , and Pao, L. , 2013, “ Correlation Between Rotating LIDAR Measurements and Blade Effective Wind Speed,” AIAA Paper No. 2013-0749.
Burton, T. , 2001, Windenergy Handbook, Wiley, Chichester, UK.
Larsen, C. E. , and Irvine, T. , 2015, “ Review of Spectral Methods for Variable Amplitude Fatigue Prediction and New Results,” Proc. Eng., 101, pp. 243–250. [CrossRef]
Ragan, P. , and Manuel, L. , 2007, “ Comparing Estimates of Wind Turbine Fatigue Loads Using Time-Domain Spectral Methods,” Wind Eng., 31(2), pp. 83–99. [CrossRef]
Mrsnik, M. , Boltezar, M. , and Slavic, J. , 2013, “ Frequency-Domain Methods for a Vibration Fatigue Life Estimation: Application to Real Data,” Int. J. Fatigue, 47, pp. 8–17. [CrossRef]
Zahle, F. , Tibaldi, C. , Verelst, D. R. , Bitche, R. , and Bak, C. , 2015, “ Aero-Elastic Optimization of a 10 MW Wind Turbine,” AIAA Paper No. 2015-0491.
Bortolotti, P. , Adolphs, G. , and Bottasso, C. L. , 2016, “ A Methodology to Guide the Selection of Composite Materials in a Wind Turbine Rotor Blade Design Process,” J. Phys.: Conf. Ser., 753(6), p. 062001.
Saltelli, A. , 2004, Sensitivity Analysis Practice: A Guide to Assessing Scientific Models, Wiley, Hoboken, NJ.
MATLAB, 2015, “ MATLAB. (R2015a),” The MathWorks Inc., Natick, MA.
Efron, B. , 1982, “ The Jackknife, the Bootstrap and Other Resampling Plans,” Society for Industrial and Applied Mathematics, Stanford, CA.
Drela, M. , 1989, “ XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,” Conference on Low Reynolds Number Aerodynamics, Notre Dame, IN, June 5–7.
Bir, G. , and Damiani, R. , 2004, “ Pre-Processor for Computing Composite Blade Properties,” Computer Software, National Renewable Energy Laboratory, Golden, CO, accessed May 9, 2017, https://nwtc.nrel.gov/PreComp
Boorsma, K. , and Bulder, B. H. , 2012, “ Silant,” Computer Software, Energy Research Centre of the Netherlands, Petten, The Netherlands, accessed May 9, 2017, https://www.ecn.nl/


Grahic Jump Location
Fig. 1

Flow chart describing the DEL calculation in the frequency domain

Grahic Jump Location
Fig. 2

PSD Cumulative variance for the pitch rate signals. Three blades' and three seeds' conditions are shown.

Grahic Jump Location
Fig. 3

PSD Cumulative variance for the generator torque signals. Three blades' and three seeds' conditions are shown.

Grahic Jump Location
Fig. 4

Bode diagram (magnitude and phase) of the FRF that relates wind seed and moment My in hub

Grahic Jump Location
Fig. 5

PSD of effective wind seed (Veff). Excitation frequencies 1P, 3P, 6P, 9P, and 12P are presented in vertical lines.

Grahic Jump Location
Fig. 6

Spanwise distributions: (a) chord, (b) twist, and (c) relative thickness of the ten test blades

Grahic Jump Location
Fig. 7

DEL calculated in the frequency domain versus calculated in the time domain. Each point represents the result for one blade geometry (simulations with mean wind seed of 14 m/s). (a) Blade root Mx, (b) blade root My, (c) blade 75% span My, (d) hub Mx, (e) hub My in stationary axes, and (f) tower base My. The lines represent the linear regressions that minimize the least square error. Goodness of fitness R2 is also presented.

Grahic Jump Location
Fig. 8

DEL of stationary hub My with respect to blade. Values from thirty wind seeds and the mean are presented.

Grahic Jump Location
Fig. 9

Time series (a) and PSD (b) of moment Mx in root for two test blade models (id7 and id9)

Grahic Jump Location
Fig. 10

First-order mass function versus DEL in the time domain. Each point represents the results for one blade geometry. The dashed line represents the linear regression that minimizes the least square error. Goodness of fitness R2 is also presented. (a) Blade root Mx, (b) blade root My, (c) blade Mx (75% span), and (d) tower base Mx.

Grahic Jump Location
Fig. 11

Time series of (a) moment Mx in hub and (b) moment My in hub, for test blade models id7 and id9. The signals are divided into six periods of 100 s.

Grahic Jump Location
Fig. 12

DEL of the six periods and the total value for test blade id7 and id9. (a) Results for hub Mx and (b) results for hub My.

Grahic Jump Location
Fig. 13

Spanwise distributions: (a) chord, (b) twist, and (c) relative thickness of solutions from optimization scenario 1 and scenario 2

Grahic Jump Location
Fig. 14

Bending moment My in hub for baseline and solution (14 m/s mean wind seed)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In