RELIABILITY OF WIND TURBINES AND WAVE ENERGY DEVICES · RELIABILITY OF WIND TURBINES AND WAVE ENERGY DEVICES ... OM and Risk assessment ... Vol. 24, 2009, pp. 504–10.

RELIABILITY OF WIND TURBINES ANDWAVE ENERGY DEVICES

JOHN DALSGAARD SØRENSEN

• Introduction• Reliability modeling of wind turbine and wave energy device

components • Structural reliability theory (FORM) - introduction• Probabilistic design of wind turbines, OM and Risk assessment• Example: Reliability-based calibration of material partial factors• Example: Reliability-based calibration of safety factors for fatigue

design of welded details in offshore wind turbines• Example: Grouted connections• Summary / Conclusions

Outline

Introduction – wind energy

www.siemens.com

• Oscillating water column dev.

• Overtopping dev.

• Point absorbers

• Wave turbines

• And many others ...

Introduction – wave energy devices

4

Development / qualification phases:

From Carbon Trust (DnV) 2005

Introduction

Reliability assessment – WED vs WT

Wave energy devices (WED): ratio between structural loadings in extreme and production conditions is in most cases very high

Wind turbines (WT): ratio is significantly smaller, as wind turbine blades are pitched out of the wind in extreme conditions, making extreme loadings of the same order of magnitude as production loads.

As extreme loadings and survivability drive the costs of the devices, and as income is only generated in everyday production conditions, it is of tremendous importance for WED to increase reliability and reduce cost.

6

Introduction

Minimize the Total Expected Life-Cycle Costs

Minimize Cost Of Energy (COE)

• Dependent on Reliability Level Initial Costs

• Dependent on O&M Strategy, Availability and ReliabilityOperation &

Maintenance Costs

• Dependent on ReliabilityFailure Costs

Introduction

Failure rates and downtime (examples – onshore wind turbines):

ISET 2006

Observed failure ratesClassical reliability theory

Probabilistic models for failure events Structural Reliability Theory

Mechanical / electricalcomponents

Structural components

Introduction

Failu

re Rate

Time

‘Burn‐in’ failuresImprove quality control

Wear outInspections Robustness

Random failure Improve reliability

Constant failure rate= 1 / Mean Time Between Failure

Bath tub curve

Reliability – elec. / mech. components

10

• Use Structural Reliability Methods• ULS: Extreme loads

• Stand‐still• Operation

• FAT: Fatigue • ALS: Accidental situations• SLS: Serviceability

• Damage tolerant / robustness

• Calibration of ‘Partial safety factors’

Reliability – structural components

Limit state equation:

Probability of failure:

Requirements:• Formulation of limit state equation• Stochastic modeling of uncertain parameters

• Physical uncertainties• Statistical uncertainties• Model uncertainties• Measurement uncertainties

0xg

0XgPPF

Probabilityof failure,

10‐2 10‐3 10‐4 10‐5 10‐6 10‐7

Reliabilityindex,

2,3 3,1 3,7 4,3 4,8 5,2FP

Reliability – structural components – time invariant

Structural Reliability - introduction

Structural Reliability




FORM – First Order Reliability Method



u 2

g ( u ) = 0

s

f

l ( u ) = 0

u*

0 u 1

region of most contribution to probability integral

n ( u ) = const

Summary: FORM – First Order Reliability Method

FORM – General transformation

• Reliability index – FORM (First Order Reliability Method)• Reliability index – SORM (Second Order Reliability Method)

• Simulation methods• Crude Monte Carlo simulation• Importance sampling• Directional simulation • Asymptotic sampling• Subset simulation• …


Crude Monte Carlo simulation

x1

x2

0

s

f

g ( x ) = 0

f X ( x ) = const.

u 2

Gg( u ) =

s

f

0 u 1

n ( u ) = const

u*

Importance sampling

(u)Sf

)()() 1 nuuf (uU

Other simulation techniques

• Asymptotic samplingBucher C: Asymptotic sampling for high-dimensional reliability analysis. Probabilistic Engineering Mechanics. Vol. 24, 2009, pp. 504–10.

• Subset SimulationAu, S. K. & J. L. Beck: First excursion robabilities for linear systems by very efficient importance sampling. Probabilistic Engineering Mechanics. Vol. 16, 2001, pp. 193–207.

Structural Reliability – computer programs

• rcp, Munich: STRUREL: STATREL, COMREL & SYSREL

• DnV: Proban

• FERUM (Matlab)

• …

ULS limit states: • Fatigue failure of welded details• Mooring failure by sliding of anchor• Mooring failure by breaking of mooring line(s)• Failure of structural element, leading to disintegration/change of

geometry/loss of part(s)• Local structural failure due to wave impact (slamming) (potentially leading

to capsizing/sinking)• Wear out of hinged connections• ...

Reliability – WED structural components

Blades

Gearbox, …

Power electronics:

Reliability – WT structural components

Tower & Substructures:

Foundation:


Reliability – Uncertainty modelling / Reliability / Risk

• Using models and principles by JCSS (Joint Committee on Structural Safety)

Uncertainty Modelling• Resistance• Loads• Models

Reliability Assessment• Probability of failure• Calibration of safety factors

Risk Analysis• Consequences• Rational decision making


Stochastic modeling of loads:• Wind• Waves• Currentso Control system / aerodynamics

Stochastic modeling of resistances / material parameters: • Blades: composite materials• Hub: cast steel• Tower: structural steel• Foundation: soil

Probabilistic Design of Wind Turbines

Overall design approach:

• Combination of• Theoretical computational models• Test of components / materials• Measurements of climatic conditions• Full-scale measurements

• Information are subject to physical, model, statistical and measurement uncertainties

• Uncertainties can be assessed and combined by use of Bayesian statistical methods for use in probabilistic design

www.lmwindpower.com

Probabilistic Design of Wind Turbines

Probabilistic Design of Wind Turbines (Tower)

Failure modes for wind turbine towers:• Buckling failure• Yield strength• Fatigue properties• Bolted/welded connections

ECCS 2008www.bladt.dk

Probabilistic Design of Wind Turbines (Blades)

Uncertainties for wind turbine blades:• Complex material structure (damage tolerance).• Manufacturing process (imperfections).• Loading conditions (site dependency)• Structural analysis (instability).• Failure criteria (ultimate/fatigue).

www.gurit.com


Design of wind turbine blades can typically be characterized by a combination / sequence of tests:• Coupon tests• Computational / numerical calculations• One full-scale test – proof loading

102 103 104 105 106 107100

200

300

400R = 0.1

cycles to failure N

stre

ss ra

nge


Uncertainties related to fatigue design of composite structures:• Linear SN-curve• Constant life diagram• Miners rule

Miners sum at failure

102 103 104 105 106 107100

200

300

400

500600700800

R = -1.0

cycles to failure N

stre

ss ra

nge

Spectrum Tests n Mean Std. COV

Wisper 10 0.90 0.54 0.60

Wisperx 13 0.28 0.20 0.72

Reverse Wisper 2 0.20 - -

Reverse Wisperx 10 0.32 0.16 0.50

All 35 0.46 0.42 0.91

All values 1 31 0.33 0.21 0.64

Probabilistic Design of Wind Turbines (Foundations)

Design of foundations for offshore wind farms:• Geotechnical field measurements are carried out at the location of each

turbine (usually as CPT)• Characteristic values of the material properties are determined (usually

as 5% quantile values or “cautious estimates”)• The soil is assumed to consist of a number of well defined layers• Within each detected layer the soil is regarded as a homogeneous

material• The application of partial safety factors then provides the design values,

and a deterministic design of each foundation is performed


• Three possible structural design regimes – offshore wind turbines• Soft–soft (f1 < 1P)• Soft–stiff (1P < f1 < 3P)• Stiff–stiff (3P < f1)

• Note• f1: First natural frequency• 1P: Rotor rate• 3P: Blade passage rate

• Main design problem• Obtain enough stiffness• Estimate stiffness correctly



• Example: Stochastic model for monopile foundation

www.wmc.eu

Computational model

Soil properties as stochastic

variables

Realisticproperties of

structure

Response (rotations and deflections at the pile cap)

29/07/2014


• Sample random field simulation results

0.000E+00 50.000E+03100.000E+03150.000E+03200.000E+03250.000E+03300.000E+03350.000E+03400.000E+03450.000E+03500.000E+03 1.879E+06

Job simulates the monopileODB: Simulation10.odb Abaqus/Standard 6.11−2 Sat Sep 01 18:02:26 Romance Daylight Time 2012

XY

Z

0.000E+00940.456E−03 1.881E+00 2.821E+00 3.762E+00 4.702E+00 5.643E+00 6.583E+00 7.524E+00 8.464E+00

Job simulates the monopileODB: Simulation10.odb Abaqus/Standard 6.11−2 Sat Sep 01 18:02:26 Romance Daylight Time 2012

XY

Z

Mapping of the three-dimensional random field in the finite-element model

Plastic strains at fully developed failure mechanism


• Cumulative distribution of bearing capcity is found by crude Monte Carlo simulation with 1000 realizations

350 400 450 500 550 6000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bearing capacity, qu (kN/m2)

Cum

ulat

ive

dist

ribut

ion

func

tion

(CD

F)

MCS using 1000 realizationsLognormal distribution

Operation & Maintenance (OM)

Risk-based methods be used to optimal planning of:• Quality control / NDI• Future inspections / monitoring (time / type)• Decisions on maintenance / repair on basis of (unknown) observations from

future inspections / monitoring

taking into account uncertainty and costs

www.siemens.co.uk www.renewbl.com

Operation & Maintenance (OM)

Maintenance strategies:• Corrective (unplanned):

exchange / repair of failed components • Preventive (planned):

Timetabled: Inspections / service after predefined scheme Conditioned: Monitor condition of system and decide next inspection based

on degree of deteriorationBased on Pre-posterior Bayesian decision model

D0 D1

FC1

Ins1

R1

RC1

D2

FC2

Ins2

R2

RC2

F1 F2A1 A2

MU MU1 MU2

www.vestas.com

Risk Analysis - example

How close to roads can wind turbines be placed?

Load cases for Wave Energy Devices (WEDs)

The following load cases are generally of importance:• Extreme wave and wind loads during normal operation.• Extreme wave and wind loads during operation simultaneous

with a fault of • electrical component.• mechanical component.• control system.

• Extreme wave and wind loads when the WED is in ‘parked’ position.

• Extreme loads during Transport & Installation• Fatigue failure due to wave and wind loads.

48

Design load cases in IEC 61400:• Normal operation – power production (DLC 1)• Power production plus occurrence of fault (DLC 2)• Start up (DLC 3)• Normal shut down (DLC 4)• Emergency shut Down (DLC 5)• Parked (standing still or idling) (DLC 6)• Parked and fault Conditions (DLC 7)• Transport, assembly, maintenance and Repair (DLC 8)

Reliability modeling of WT structural components

50

Load cases – offshore wind turbines

Reliability modeling - Wind turbine components …

Power curve:

Rated speed

Reliability assessment in normal operation (DLC 1)

Loads on wind turbines depends on:• Structural dynamics• Aerodynamics• Control system• Wind climate

www.dongenergy.dk


0 100 200 300 400 500 6000

5000

10000

15000Blade - Out-of-plane Bending Moment - 21m/s

Time [s]

Mom

ent [

kNm

]

0 100 200 300 400 500 600-4000

-2000

0

2000

4000

6000

8000Blade - Inplane Bending Moment - 21m/s

Time [s]

Mom

ent [

kNm

]

0 100 200 300 400 500 6002500

3000

3500

4000

4500

5000Low Speed Shaft - Torsional Moment - 21m/s

Time [s]

Mom

ent [

kNm

]


Stochastic model for annual maximum load:

L extreme load effect based on ‘Load extrapolation’: typically assumed Weibull distributed


LXXXXP straerodyn exp

Fit of load effect for each wind speed: Aggregated fit of load effect for all wind speeds:

Stochastic model for annual maximum load based on ‘Load extrapolation’:

Xdyn uncertainty related to modeling of the dynamic response, including uncertainty in damping ratios and eigenfrequencies

Xexp uncertainty related to the modeling of the exposure (site assessment) -such as the terrain roughness and the landscape topography

Xaero uncertainty in assessment of lift and drag coefficients and additionally utilization of BEM, dynamic stall models, etc

Xstr uncertainty related to the computation of the load-effects given external load

Limit state equation for structural component:



LXXXXRzg straerodyn exp

Stochastic model for annual maximum load based on ‘Load extrapolation’:

L extreme load effect from wind pressure: Gumbel distributed

Limit state equation for structural component:

Reliability assessment in parked position (DLC 6)



Probability of failure of structural component i when fault (e.g. electrical component):

Reliability assessment with faults (DLC 2)

faultfault, annualiif PFPP

probability of failure of structural component i given fault

annual probability of fault

Annual failure rate for structural component i when grid loss and occurrence of an EOG (Extreme Operating Gust) – DLC 2.3:

probability of failure for a specific structural failure mode given a mean wind speed in the range I1 , e.g. [8-15 m/s] and occurrence of an EOG

mean annual rate of occurrence of grid loss

Reliability assessment with fault - example

loss grid

22

11

EOG EOGloss grid

EOGloss grid1

PIVPIVFP

IVPIVFP

i

iF

EOGloss grid1 IVFP

loss gridd

Extreme Operating Gust:

Reliability level

• Building codes: e.g. Eurocode EN1990:2002:annual PF = 10-6 or β = 4.7

• Fixed steel offshore structures: e.g. ISO 19902:2004manned: annual PF ~ 3 10-5 or β = 4.0unmanned: annual PF ~ 5 10-4 or β = 3.3

• Observation of failure rates for wind turbines 1984 – 2000Failure of blades: approx. 2.010-3 per year (decreasing)Wind turbine collapse: approx. 0.810-3 per year (decreasing)

Assumptions:• A systematic reconstruction policy is used (a new wind turbine is erected in

case of failure or expiry of lifetime).• Consequences of a failure are ‘only’ economic (no fatalities and no pollution).• Wind turbines are designed to a certain wind turbine class, i.e. not all wind

turbines are ‘designed to the limit’.

Target reliability level corresponding to an annual nominal probability of failure:

5 10-4 (annual reliability index equal to 3.3)

Application of this target value assumes that the risk of human lives is negligible in case of failure of a structural element.

Corresponds to minor / moderate consequences of failure and moderate / high cost of safety measure (JCSS)

Reliability level

• Example 1: calibration of material partial safety factors for revision of IEC 61400-1

• Example 2: calibration of safety factors for fatigue of welded details in substructures for offshore wind turbines

Reliability-based calibration of safety factors

Load bearing capacity:

Design values:

Model 1: and

Model 2:

Model 3:

Example: Reliability-based calibration of material partial safety factors

model uncertainty

conversion factor, accounting for bias in R ( ), scale effects, time duration effects, failure type, etc.

aRbY X,

),( ddd

aXRRm

kd

XX

M

kkd

aXRR

), (

M

kd

RR

For calibration it is assumed that• no bias (hidden safety) in calculation of load effects• no bias (hidden safety) in calculation of load bearing capacities• no scale effects, time duration effects,…i.e. η = 1 and b = 1


Design equation:



0 kf

R

k LRz

Characteristic value for R: 5% quantileCharacteristic value of model uncertainty: mean value


35.1f


Model 1: and Approximately:

Model 2:

Model 3:

b Bias

Partial safety factor for material parameters:


b

bR

M

RM

bR

M m

Example: Buckling - EN1993 calculation modelAssumptions:• No internal stiffners in the cylinder• Boundary conditions BC 2• Bending moment applied – No axial force• Quality class B in EN 1993-1-6• Yield strength: fyk = 235MPa (COV=5%)• E-module: 210.000MPa

• Test results only based on axial loading. EN 1993 calculation model: COV=13%, b = 1 / 0,85

• The bias is normally slightly less for bending. The COV for bending is unknown.

• γR = 1,31• γM = 1,31 * 0,85 ~ 1,1


Cases considered for offshore wind turbine substructure:

• Wave load dominated detail

• Wind load dominated detail• Single wind turbine• Wind farm

Example: Reliability-based calibration of safety factors for fatigue of welded details in offshore wind turbines

• Linear SN-curve: N = K Δσm

• Single wind turbine - Free wind flowDesign equation:

Standard deviation of stress ranges:


0; 1)(

dUUfUmDK

TFDFzG UL

U

U C

Lout

in

dsUsfsmD mL )(;

0

zUUU u

ˆ)(

mudline bending moment

Stress range density function

Mean wind speed

Characteristic value of turbulence



dUdUfUf

zUUmDXXK

ttg

uUu

uL

U

U

mSCFW

u

out

in

/;)(0

Stochastic variables

• Wind turbines in wind farm – with wake effects


• Linear SN-curve• Wind turbines in wind farm – with wake effects

Design equation:

0/ˆ; 1)( ,

dUUfzUUmDK

TFDFzG UeffuL

U

U C

Lout

in

2

2

2

, ˆ/3.05.1

9.0)(ˆ u

j

jucUd

UU

mN

j

mjuw

muwweffu

W

ppNU1

1,, ˆˆ)1()(ˆ


• Linear SN-curve• Wind turbines in wind farm – with wake effects


dUdUfUf

zUUmDpzUUmDpN

XXK

ttg

uUu

N

jjuLWuLWW

U

U

mSCFW

u

W

out

in

/;/;1

)(

1,

0

2

2

2

,/3.05.1

)( u

j

wakejucUd

UXU


Wave load dominating• Design lifetime = 20 year• Number of stress ranges per year is = 5 ×106

• Acceptable annual probability of failure: 10-4 - 10-3


• Linear SN-curve with m = 3• Required FDF and corresponding partial safety factors γm γf in ( )

for given ( )

• = 3.5:

FATmin, FATFP max,,

FATmin,


Wind load dominating – single WT• Linear SN-curve with m = 3• Number of stress ranges per year is = 5 ×107

• Required FDF and corresponding partial safety factors γm γf in ( ) for given ( )FATmin, FATFP max,,


Wind load dominating – wind farm• Linear SN-curve with m = 3• Required FDF and corresponding partial safety factors γm γf in ( )

for given ( )FATmin, FATFP max,,


Calibration with inspections• Risk Based Inspection planning has been developed during the last

10-15 years- used for inspection planning for fatigue cracks in

e.g. oil & gas jacket structures

• Fracture mechanics model calibrated to SN model such that same reliability level is obtained

• POD-curve: • Equidistant inspection times

xxPOD exp1)(


• Linear SN-curve with m = 3, • Wind load dominating - Single wind turbine:

• Wind load dominating – wind farm:

• Wave load dominating:

5.3min, FAT


• Monopiles including grouted connection between Monopiles (MP) and Transition pieces (TP) have been widely used for wind turbine structures since 2002

• In Europe: 600? OWT’s using grouted connections• Unexpected behavior of grouted connections between MP and TP

Example: Grouted connections

From the Journal ”Ingeniøren” in Denmark, Spring 2010

Repair / Mitigation options• Elastomer spring bearings• …• Perform inspections and ’wait-and-see’

based on Risk-based Inspection Planning

Example: Grouted connections

(Illustration: Dong Energy)

(Dong Energy)

• Reliability of wind turbine (WT) and wave energy device (WED) components are very important for decreasing Levelised Cost Of Energy (LCOE)

• Structural reliability methods (time in-variant)

• General model presented for modeling reliability of structural, mechanical or electrical component.

• Reliability models presented for different components• Example: reliability based calibration of material partial safety factors for IEC

61400-1• Example: reliability-based calibration of partial safety factors for fatigue critical

details in offshore wind turbine substructures

Summary

Literature - More information

• Sørensen, J.D.: Framework for risk-based planning of operation and maintenance for offshore wind turbines. Wind Energy, Vol. 12, 2009, pp. 493-506.

• Sørensen, J.D. and Henrik S. Toft: Probabilistic design of wind turbines. Energies, Vol. 3, 2010, pp. 241-257.• Toft, H.S., J.D. Sørensen & D. Veldkamp: Assessment of Load Extrapolation Methods for Wind Turbines. Journal of

Solar Energy Engineering, Vol. 133, No. 2, 2011, pp. 1-8.• Toft, H.S., K. Branner, P. Berring & J.D. Sørensen: Defect Distribution and Reliability Assessment of Wind Turbine

Blades. Engineering Structures, Vol. 33, 2011, pp. 171-180.• Nielsen, J.J. & J.D. Sørensen: On Risk-Based Operation and Maintenance of Offshore Wind Turbine Components.

Journal for Reliability Engineering & System Safety, Vol.96, No. 1, 2011, pp. 218-229.• Toft, H.S. & J.D. Sørensen: Reliability-Based Design of Wind Turbine Blades. Structural Safety, Vol.33, No. 6, 2011, pp.

333-342.• Toft, H.S., A. Naess, N. Saha & J.D. Sørensen: Response load extrapolation for wind turbines during operation based

on average conditional exceedance rates. Wind Energy, Vol. 14, No. 6, 2011, pp. 749-766.• Andersen, L.V., M.J. Vahdatirad, M.T. Sichani and J.D. Sørensen: Natural frequencies of wind turbines on monopile

foundations in clayey soils — A probabilistic approach. Computers and Geotechnics, Vol. 43, 2012, pp 1-11.• Sørensen, J.D.: Reliability-based calibration of fatigue safety factors for offshore wind turbines. International Journal of

Offshore and Polar Engineering. Vol. 22, No. 3, 2012, pp. 234–241.• Toft, H.S., J.D. Sørensen, L. Mishnaevsky & K. Branner: Uncertainty Modeling and Code Calibration for Composite

Materials. Journal of Composite Materials, 2013.• Nielsen, J.S., R.P. van de Pieterman & J.D. Sørensen: Analysis of pitch system data for condition monitoring. Wind

Energy, 2013.• Kimiaeifar, A., E. Lund, O.T. Thomsen and J. D. Sørensen: Asymptotic Sampling for Reliability Analysis of Adhesive

Bonded Stepped Lap Composite Joints. Engineering Structures, Vol. 49, 2013, s. 655–663.• Vahdatirad, M.J., D.V. Griffiths, L.V. Andersen, J.D. Sørensen & G.A. Fenton: Reliability analysis of a gravity-based

foundation for wind turbines: a code-based design assessment. Géotechnique, Vol. 64, 2014.

Literature - More information

• Sørensen, J.D.: Notes in Structural Reliability Theory. Department of Civil Engineering, Aalborg University, 2011.

• Madsen, H.O. & S. Krenk & N.C. Lind: Methods of Structural Safety. Prentice-Hall, 1986.• Ditlevsen, O. & H.O. Madsen: Structural Reliability Methods. Wiley, 1996. Can be downloaded from www.• Thoft-Christensen, P. & M.J. Baker: Structural Reliability Theory and Its Applications. Springer Verlag,

1986. Can be downloaded from www.• Faber, M.H.: Statistics and Probability Theory: In Pursuit of Engineering Decision Support. Springer,

2012.• JCSS: www.jcss.byg.dtu.dk

Professor John Dalsgaard Sørensen, Aalborg University, Denmark [email protected]

Thank you for your attention!John Dalsgaard Sørensen

[email protected]

Acknowledgements:• NORCOWE: Norwegian Center for Offshore Wind Energy

(www.norcowe.no) supported by the Norwegian Research Council• “Reliability-based analysis applied for reduction of cost of energy for

offshore wind turbines” supported by the Danish Council for StrategicResearch

RELIABILITY OF WIND TURBINES AND WAVE ENERGY DEVICES · RELIABILITY OF WIND TURBINES AND WAVE ENERGY DEVICES ... OM and Risk assessment ... Vol. 24, 2009, pp. 504–10.

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