reliability-based calibration of partial safety factors for wind turbine blades

Department of Civil Engineering Division of Structural Mechanics

EWEA 2011 – 16 March 2011 www.civil.aau.dk

1

Reliability-based Calibration of Partial Safety Factors for Wind Turbine Blades

Henrik Stensgaard Toft(1)

Kim Branner(2)

Peter Berring(2)

John Dalsgaard Sørensen(1,2)

(1)Aalborg University, Denmark(2)Risø-DTU, Denmark



2

Outline of Presentation

• Introduction

• Reliability-based design

• Modelling of uncertainties

• Illustrative example: Reliability of wind turbine blade

• Conclusions & Future work

[www.lmwindpower.com]



3

Wind Turbine Blades

Wind turbine blades consist normally of a main spar and an aerodynamic shell.

• Blades are typically made of glass fiber reinforced epoxy, but carbon fibers are also used.

• Optimal structural design of the blades will lead to load reduction on other major wind turbine component (e.g. tower and foundation).




4

Observed Annual Failure Rates and Downtime

[ISET, 2008]



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Reliability-based Design

• Limit state equation:

• Probability of failure:

• Reliability index:

Reliability Estimation based on Finite Element Analysis

Evaluation of large and nonlinear FE models is very time consuming. This

demands for a simple and fast way to estimate the reliability.

• Smart simulation methods (e.g. importance sampling).

• First or Second Order Reliability methods (FORM/SORM).

• Response-surface method

g R S

FP P R S

1FP

f R, f

S

R, SRc

Sc

R ~ ResistanceS ~ Load



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Design and Limit State Equation

• Design equation according to IEC 61400-1:

• Limit state equation:

• Response surface technique:

The constants a, bi and ci are determined by evaluating the limit state equation (FE-

model) in the points for each stochastic variable Xi.

The partial safety factors can be calibrated in order to obtain a target reliability

index t for each failure mode.

,1 mat cf c

n m

G R L

x

R matg X R Q X

Partial Safety Factors (IEC 61400-1) ULS

n – Consequences of failure 1.00

m – Material properties (brittle failure) 1.30

f – Load (normal operation) 1.25

2

1 1

n n

i i i ii i

g a b x c x

x

i i i ix X f



7

Modelling of Uncertainties

The uncertainties can be divided into the following four groups:

• Physical uncertainty (aleatory)

• Measurement uncertainty (epistemic)

• Statistical uncertainty (epistemic)

• Model uncertainty (epistemic)

The uncertainties are modelled by stochastic variables.




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Uncertainty – Material Properties

• Stochastic models for the material properties have been modelled from micro-scale using the properties of the fiber and matrix (model uncertainty included).

• Scatter between the uncertainties in the literature is observed due to e.g. variations in the manufacturing procedure and basic material.

[Lekou & Philippidis] [DNV-OS-C501] Micro-scale modelingincl. model uncertainty

Variable Distribution COV COV Distribution Mean COV

E1 [GPa] Weibull 0.089 0.050 Lognormal 39.90 0.106

E2 [GPa] Extreme Type I 0.148 0.100 Lognormal 13.62 0.136

G12 [GPa] Gamma 0.249 0.100 Lognormal 4.23 0.129

12 [-] Weibull 0.187 0.100 Lognormal 0.290 0.107

XT [MPa] Weibull 0.151 0.050 Normal 795.7 0.138

XC [MPa] Lognormal 0.101 0.050 Normal 529.7 0.143

YT [MPa] Extreme Type I 0.150 0.100 Weibull 54.0 0.104

YC [MPa] Extreme Type I 0.135 0.150 Weibull 162.6 0.112

S [MPa] Weibull 0.181 0.100 Weibull 55.8 0.106



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Uncertainty – Load-effect

• The uncertainty related to the load-effect corresponds to DLC 1.1 in IEC 61400-1 (normal operation – blade out-of-plane bending).

• The physical uncertainty related to the load-effect is estimated from statistical load extrapolation for the NREL 5MW reference wind turbine.

expdyn st aero str simQ X X X X X X L

Variable Description Distribution Mean COV

Xdyn Dynamics Lognormal 1.00 0.05

Xexp Exposure Lognormal 1.00 0.20

Xst Limited wind data Lognormal 1.00 0.10

Xaero Aerodynamics Gumbel 1.00 0.10

Xstr Load-effect (model) Lognormal 1.00 0.03

Xsim Limited simulations Normal 1.00 0.05

L Load-effect (physical) Weibull - 0.15



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Uncertainty – Failure Prediction

• Failure of the blade is estimated by First Ply Failure (no redundancy and damage tolerance).

• Ply failure is estimated by the Tsai-Wu criteria.

• The uncertainty related to failure predictions is estimated from test results in the World Wide Failure Exercise.• Based on UD and MD-laminates.• Final failure - degradation of the structure is taken into account.

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

Ratio (test capacity / estimated capacity) [-]

Cum

ulat

ive

Pro

babi

lity

[-]

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Ratio (test capacity / estimated capacity) [-]

Cum

ulat

ive

Pro

babi

lity

[-]

Part A: XR~LN(1.31; 0.40) Part B: XR~LN(1.14; 0.30)



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Illustrative Example: Reliability Wind Turbine Blade

• Blade for a 1.5MW pitch controlled wind turbine (shortened after 25.4m).

• Geometrical nonlinear finite element analysis (mesh size 40x40mm).

• Load case: Combined edgewise and flapwise loading (normal operation).



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• Buckling of main spar cap at 3.4m, 9.0m, 11.6 and 13.6m.

• First ply failure (Tsai-Wu) in UD-lamina due to high strains in transverse direction (9m from blade root).

• Failure mode seems robust related to changes of the material properties.

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Distance from Root z [m]

Tsa

i-W

u C

rite

ria

[-]



13


The annual reliability is estimated using the response surface technique and Monte Carlo simulation / FORM.

Method / Parameters PF

Response surface, Monte Carlo, XR~LN(1.14,0.30) 2.7 3.210-3

Response surface, Monte Carlo, XR~LN(1.00,0.30) 2.6 4.810-3

Response surface, FORM, XR~LN(1.14,0.30) 3.1 0.910-3

Implicit target reliability in IEC 61400-1: =3.1 corresponding to PF=10-3.

0 5 10 15 20 25

3

4

5

6

7

8

9

Distance from Root z [m]

Ann

ual R

elia

bilit

y In

dex

[-

]



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The most important stochastic variables are determined from the-vectorestimated by FORM:

• Model uncertainty failure criteria XR (2=0.60).• Model uncertainty exposure Xexp (2=0.26).• The material properties has in general only a small influence.

The estimated reliability varies significantly dependent on the points which is used

for estimating the response surface. Especially the points for the load and failure

criteria are important. i i i ix X f

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

Load Level [-]

Tsa

i-W

u C

rite

ria

[-]

z = 3.44mz = 9.00mz =11.60mz =13.72m



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Conclusion

• Stochastic models for the uncertainty related to the material properties, load-effect and failure prediction for wind turbine blades have been proposed.

• The reliability have of the blade have been estimated using the response surface technique based on nonlinear finite element analysis.

• The estimated reliability level is slightly lower than the target reliability in IEC 61400-1.

Future Work

• The uncertainty related to failure prediction should be studied further in order to improve the stochastic models.

• The reliability is sensitive to the points used for evaluating the response surface. This demands for a more robust way of estimating the response surface.

• Estimate the influence of system effects (redundancy) and damage tolerance.



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Reliability-based Calibration of Partial Safety Factors for Wind Turbine Blades

Henrik Stensgaard Toft(1)

Kim Branner(2)

Peter Berring(2)

John Dalsgaard Sørensen(1,2)

(1)Aalborg University, Denmark(2)Risø-DTU, Denmark

reliability-based calibration of partial safety factors for wind turbine blades

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