Structural and Multidisciplinary Optimization

, Volume 54, Issue 4, pp 953–970 | Cite as

Reliability-based design optimization of wind turbine blades for fatigue life under dynamic wind load uncertainty

  • Weifei Hu
  • K. K. ChoiEmail author
  • Hyunkyoo Cho


This paper studies reliability-based design optimization (RBDO) of a 5-MW wind turbine blade for designing reliable as well as economical wind turbine blades. A novel dynamic wind load uncertainty model has been developed using 249 groups of wind data to consider wind load variation over a large spatiotemporal range. The probability of fatigue failure during a 20-year service life is estimated using the uncertainty model in the RBDO process and is reduced to meet a desired target reliability. Meanwhile, the cost of composite materials used in the blade is minimized by optimizing the composite laminate thicknesses of the blade. In order to obtain the RBDO optimum design efficiently, deterministic design optimization (DDO) of the 5-MW wind turbine blade is carried out first using the mean wind load obtained from the wind load uncertainty model. The RBDO is then initiated from the DDO optimum. During the RBDO iterations, fatigue hotspots for RBDO are identified among the laminate section points. For an efficient RBDO process, surrogate models of 10-min fatigue damages D 10 at the hotspots are accurately created using the Kriging method. Using the wind load uncertainty model and surrogate models, probability of fatigue failure during a 20-year lifespan at the hotspots and the design sensitivities are calculated at given design points. Using the probability of fatigue failure and design sensitivity, RBDO of the 5-MW wind turbine blade has been successfully carried out, satisfying the target probability of failure of 2.275 %.


Wind turbine blades RBDO Wind load uncertainty Reliability analysis Fatigue life 



Cumulative distribution function


Coefficient of variation


Deterministic design optimization


Dynamic Kriging


Design of experiment


Finite element


First-order reliability method


Monte Carlo simulation


Maximum likelihood estimation


Normalized root mean square error


Probability density function


Reliability-based design optimization


Second-order reliability method


Sequential Quadratic Programming


Universal Kriging


Shape parameter and random vector of shape parameter of Gamma distribution


Scale parameter and random vector of scale parameter of Gamma distribution


Scale parameter of Weibull distribution / total cost of composite materials


Random vector of scale parameter of Weibull distribution


Copula density function for V 10 and Σ 10


10-min fatigue damage


One-year fatigue damage


20-year fatigue damage


Design variable vector in DDO


Shape parameter and random vector of shape parameter of Weibull distribution

fC, fk, fa, fb, fτ

Marginal PDF of C, k, a, b, τ

fV10, fI10, fΣ10

Marginal PDF of V 10, I 10, Σ 10


Joint PDF of V 10 and I 10


10-min turbulence intensity and its realization


Probability of the V 10 and I 10 in the (i, j) cell of wind load probability table

\( {\overline{P}}_{VI}^{i,j} \)

Mean probability of the V 10 and I 10 in the (i, j) cell of wind load probability table


Laminate thickness random variable

V10, v10

10-min mean wind speed and its realization


Random design vector

Σ10, σ10

10-min standard deviation of wind speed and its realization

τ, τ

Kendall’s tau and random vector of Kendall’s tau for V 10 and Σ 10


Random design variable vector in RBDO



This work is primarily supported by the Iowa Alliance Wind Innovation and Novel Development (IAWIND) 09-IPF-15 and by the National Science Foundation Experimental Program to Stimulate Competitive Research (EPSCoR) under Grant Number EPS-1101284. Any opinions, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the National Science Foundation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringThe University of IowaIowa CityUSA

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