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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
RESEARCH PAPER

Abstract

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 %.

Keywords

Wind turbine blades RBDO Wind load uncertainty Reliability analysis Fatigue life 

Abbreviations

CDF

Cumulative distribution function

CoV

Coefficient of variation

DDO

Deterministic design optimization

DKG

Dynamic Kriging

DoE

Design of experiment

FE

Finite element

FORM

First-order reliability method

MCS

Monte Carlo simulation

MLE

Maximum likelihood estimation

NRMSE

Normalized root mean square error

PDF

Probability density function

RBDO

Reliability-based design optimization

SORM

Second-order reliability method

SQP

Sequential Quadratic Programming

UKG

Universal Kriging

a,a

Shape parameter and random vector of shape parameter of Gamma distribution

b,b

Scale parameter and random vector of scale parameter of Gamma distribution

C

Scale parameter of Weibull distribution / total cost of composite materials

C

Random vector of scale parameter of Weibull distribution

c

Copula density function for V 10 and Σ 10

D10

10-min fatigue damage

D1year

One-year fatigue damage

D20year

20-year fatigue damage

d

Design variable vector in DDO

k,k

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

fVI

Joint PDF of V 10 and I 10

I10,i10

10-min turbulence intensity and its realization

PVIi,j

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

Ti

Laminate thickness random variable

V10, v10

10-min mean wind speed and its realization

X

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

μ

Random design variable vector in RBDO

Notes

Acknowledgments

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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