list of content structural reliability and risk analysis ... mare wint sept.20131 structural...

T.Moan MARE WINT Sept.20131

Structural reliability and risk analysisof «offshore structures»By Torgeir Moan, CeSOS and Department of Marine Technology, NTNU


List of content Introduction - Facilities- Regulatory framework - Accident/failure experiences

- Safety ManagementStructural Reliability Analysis

- Introduction- Estimation of failure probability of components- Uncertainties in Load effect (S) and Resistance (R)- System reliability- Time variant Reliability- Summary of Reliability methods- Practical use of Structural Reliability Analysis- Guidelines for Reliability Analysis

Reliability-base-Calibration of codes for new applications - Relation between prob. Of failure and safert factors- Reliability based Calibration of safety factorsFatigue reliability- Background- Fatigue life models (based on SN- and Fracture Mechanics)- Reliability updating approaches


List of content - continuedFatigue reliability - continued- Inspection scheduling - Calibration of fatigue design criteria- Fatigue reliability of gear components

Quantitative risk assessment- Risk Analysis Framework- Internal and external hazards- ALS design check- Ship Collision risk- Accidental Actions on wind turbines

T.Moan MARE WINT Sept.20134Wind turbines vs other marine structures

Facilities for wind vs oil and gas technology

• Number of units – one of a kind versus mass production.

• Safety issues:No hydro carbons and people on board wind turbines

• The wind energy sector is a “marginal business”

• Return are more sensitive to IMMR (O&M) costs (access)

Integratingknowledge

4Introduction


Regulatory framework - general

5

to avoid:• Fatalities or injury• Environmental damage• Property damage

Regulatory regime (depends on economy; accident potential):

Regulatory principles- Goal-setting viz. prescriptive- Probabilistic viz. deterministic- First principles viz.

purely experientialOverall stability Strength Escapeways/ lifeboats

Offshore oil and gas Wind turbines- National regulatory

bodies; - Industry: API, NORSOK, - Classification soc. - ISO/IMO

- National Regulatorybodies

- Classification societies ??- IEC

Introduction


Introduction

ExperiencesOil and gas platforms- significance of the oil and gas industry to the world econmy- need for technology development for deeper water, challengingnatural and industrial environment,…

- ageing facilitiesWind turbines

CeSOS NTNU

Gathering of experiences – development of procedures/methods/data

Failure - and accident dataSafety management procedure- safety criteria, (limit states) – including accidental limit state- risk and reliability analysis of design, inspection/monitoring

Methods (hydrodynamics, structural analysis)Data (strength data for tubular joints)

5


A Case of structural failure - due to ”natural hazards” ?

Severe damage caused by hurricane Lilli in the Gulf ofMexico

Technical-physical causes:Observation: Wave forces exceeded the

structural resistance

Human – organizational factors:Design- Inadequate wave conditions or load calculationor strength formulation or safety factors

Fabrication deficiencies

due to- inadequate state of art in offshoreengineeringor,

- errors and omission during design or fabrication!

CeSOS NTNU

6Introduction


a) Alexander L. Kielland – fatigue failure, progressive failure and capsizing, North Sea, 1980

c) Piper Alpha fire and explosion, NorthSea, 1988

b) Ocean Ranger, flooding and capsizing, New Foundland, 1982.(Model during survival testing)

d) P - 36 explosion, flooding and capsizing, Brazil, 2001

Lessons learnt from total losses of platformsIntroduction


0

2

4

6

8

10

12

14

16

18

20

Blow

out

Colis

ion/co

ntac

tDr

oppe

d ob

ject

Explo

sion

Fire

Grou

ndin

gSp

ill/re

lease

Stru

ctur

al da

mag

eCa

psize

/foun

derin

g/lis

t

MobileFixed

(World wide in the period 1980-95, Source: WOAD 1996)

Accident experiences for mobile drilling and fixed production platforms(Number of accidents per 1000 platform years)

Operational errors

Design orFabricationerrors

CeSOS NTNU

7Introduction


In-service experiences with cracks in fixed offshore platforms (See Vårdal, Moan et al, 1997...)

Data basis- 30 North Sea platforms, with a service time of 5 to 25 years- 3411 inspections on jackets- 690 observations of cracks

The predicted frequency of crack occurrence was foundto be 3 times larger than the observed frequency; i.e.conservative prediction methods

On the other hand:- Cracks which are not predicted, do occur. Hence, 13 % of observed fatigue cracks occurred in jointswith characteristic fatigue life exceeding 800 years; due to - abnormal fabrication defects(initial crack size ≥ 0.1 mm !)

- inadequate inspectionCeSOS NTNU

8Introduction


Failure Rates and Down Times of Wind Turbines

Availability- 96 - 98 % on land- 80 % for early wind

farms offshore

-Need for robust design,(reliable and fewcomponents) & smart maintenance, but also improvedaccessibility

- Larger turbine size? ( > 5 - 20 MW)

Courtesy: Fraunhofer

- Predict, monitor and measure degradation

(Courtesy: Fraunhofer)

Introduction


Risk Control MeasuresCause of failure Safety measure

Inadequate design check toaccount for normal variability

−Increase safety factors or uselower Rc and higher Sc

Human error and omission─ Design─ Fabrication─ Operation

Unknown phenomena

In general:-improve the quality of the initial job.-implement proper QA/QC

−possible ALS design check−ALS design checkR&D

Introduction


Safety management (ISO 2394, ISO19900, etc)

ULSFLS: D = Σni/Ni ≤ DallowableALS

• Measures to maintain acceptable risk- Life Cycle Approachdesign, fabrication and operational criteria

- QA/QC of engineering design process- QA/QC of the as-fabricated structure- QA/QC during operation

(structural inspection )

- Event control of accidental events

- Evacuation and Escape

CeSOS NTNU

9Introduction


Safety with respect to - Fatalities- Environmental damage- Property damage

Floatability / stability

Structural strength of the hull

Strength of (possible) mooring system

Escapeways and lifeboatstationes etc for evacuation

Regulatory requirements: - National Regulatory bodies;

(MMS, HSE, NPD- Industry : API, NORSOK,…- Class societies/IACS- IMO/ISO/(CEN)

OR modeltests

Introduction


Safety criteria for design and reassessment(with focus on structural failure modes) ISO

Limit states Physical appearance of failure mode

Remarks

Ultimate (ULS)- Ultimate strength of structure, mooring or possible foundation

Component design check

Fatigue (FLS)- Failure of welded jointsdue to repetitive loads

Component design check depending on residual system strength andaccess for inspection

Accidental collapse (ALS)- Ultimate capacity1) of damaged structure with “credible” damage

Plate thick-ness

Collapsedcylinder

Jack-up collapsed

Fatiguecrack

CeSOS NTNU

10Introduction


Accidental Collapse Limit State for Structures (NPD, 1984)

• Estimate the damage due to accidental loads (A) at an annual exceedance probability of 10-4

- and likely fabrication errors

• Check survival of the structure with damage under functional (F) and environmental loads (E) -at an annual exceedance probability of 10-2.

• Load & resistance factors equal to 1.0E

P,F

P,F

A

CeSOS NTNU

11Introduction


Ocean environment

Analysis for demonstrating compliance with design criteria

Functional loads- dead loads- -pay loads

Accidentalloads

Piper AlphaResponseanalysis- dynamic v.s.quasi-static/quasi-dynamic

Sea loads

Design criteria

Load effects

Collapseresistance

SN-curve/fracturemechanics

Ultimateglobalresistance

Extrememoment (M)andaxial force (N)

Localstressrangehistory

Extremeglobalforce

Designcheck

ULS:

FLS:

ALS:Damagedstructure

Analysis ofdamage

IndustrialandOperationalConditions

CeSOS NTNU

Defined probability level

12Introduction


Risk and reliability assessment

Definition• Reliability:

Probability of a component/system to perform a required function

• Risk: Expected loss (probability times consequences)

Recognised in the oil and gas industry- calibration of LFRD design approaches (1970s, 1980s)- RBI (Risk/Reliability Based Inspection)

(methods in 1980s-; industry adoption in 1990s-)

rational mechanics methods for design of structures, foundationsloads and resistances are subjected to uncertainties- normal variability and uncertainty; gross errorsdesign is decision under uncertainty :- rational treatment of uncertainty (range, mean+st.dev. etc)- implying probabilistic methodsespecially in connection with new technology, no standards

CeSOS NTNU

ALARPprinciple

13Introduction


Estimation of Failure Probability of componentsA simple example: The probability of failure , Pf , for

a time-invariant reliability problem, is

- R is the resistance - S is the loading

The main issues in the following will be to- describe the R and S as random variables- derive the expression for the Pf and generalise it for more complex problems

Notionalprobaility,

not true, actuarial

[ ] [ ][ ] ( )

fP P R S 0 P ln R ln S 0

.... P R ' S' 0 '

= − ≤ = − ≤ =

= − ≤ = Φ −β

22

ln

2121ln

21

21ln

SR

S

R

SR

R

S

S

R

VVVV

V

V

+≈

⎟⎠⎞⎜

⎝⎛ +⎟

⎠⎞⎜

⎝⎛ +

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+

+⋅

=′μ

μμμ

β

where Φ ( ) is the standard normal density function

φ(u)

( ) ( )u

u t dtφ−∞

Φ = ∫


β Pf Pf β

12

2.53

3.54

4.55

5.56

1.59 ·10-1

2.27·10-2

6.21·10-3

1.35·10-3

2.33·10-4

3.17·10-5

3.40 ·10-6

2.90 ·10-7

1.90·10-8

1.00·10-9

10-1

10-2

10-3

10-4

10-5

10-6

10-7

10-8

10-9

10-10

1.292.323.093.724.274.755.205.616.006.36

Relation between Pf and β

1.2 1.4( ) 10 ββ −Φ − ≈=fPA rough approximation:

Estimation of Failure Probability


General methods to determine Pf The probability of failure , Pf , for a time-invariant reliability problem, is

( ) ( )( ) 0

0 ( )≤

⎡ ⎤= ≤ = = Φ −⎣ ⎦ ∫∫fg

P P g f d βxx

x x x

- g(x) is the limit state function, i.e. g(x) = R - S - X is the set of n random variables - fx(x) in the joint probability density of the vector X.

- Pf is determined by calculating the integral byMC simulation or FORM/SORM methods (Avoid FOSM methods etc)

Main issue: Modelling load effects andresistance in terms of: fx(x)

Notionalprobaility,

not true, actuarial



General formulation for two variablesAn approach which represents a first step towards a general formulation can be based on

Volume: fRS(r,s)drds is per definition the probability that s and r lies in the interval(s, s+ds) and (r, r+dr), respectively

Formulation of failure probability , which can be generalizedNOTE: The probability density function for independent variables is )()( sfrf SR ⋅



FORM/ SORM

Instead of integrating the probability density in the domain of physical variable R and S, the integral may be transformed into a domain of independent standard normal variables, u1 and u2. This is done here for the simple problem where

Transformation of variables

Transformtion of failure function

1

2

R

R

S

S

RU

SU

μσ

μσ

− ⎫= ⎪⎪⎬− ⎪=⎪⎭

[ ] [ ] [ ]P P R S P R S 0 P M 0 f = ≤ = − ≤ = ≤

( )2,R RR N μ σ= ( )2,S SS N μ σ=

'1 2( ) ( )R R S SM R S U Uσ μ σ μ= − = + − +

1

( ) ( )

( ( ))−

Φ =

= Φx

x

u F xx F u

In general transformation of (independent variables) x into variables u is :



( )d cfr. previous definitionμ − μ= → β

σ + σR S

2 2R S

1 2' '

'1 2 1 2 1 2 1 2

( 0) ( 0)

0 ( ) ( ). ( ) ( )f U UM M

P P M f u u du du u u du duφ φ β≤ ≤

⎡ ⎤= ≤ = = = Φ −⎣ ⎦ ∫∫ ∫∫

Distance d:

Failure probability

The same answer as before.The advantage of this method is when multiple variables are needed.

R,S space U-space



Monte Carlo simulationInstead of using integration, the failure probability may be determined by using Monte Carlo simulation and interpreting probability as relative frequency.

This approach is described in the following for the simple case specified by:

with independent variables R and S given by probability density function fR(r)and fS(s), respectively.pf may be determined as follows:

1) Generate n sample of pair (R,S) from fR(r) and fS(s), respectively

[ ]0= ≤

= −fp P M

M R S

( )( )( )

( )

1 1

2 2

3 3

n n

ˆ ˆr , sˆ ˆr , sˆ ˆr , s

ˆ ˆr , s



Samples for a variable X with a distribution function FX(x) ora density fX(x) may be generated by , where pi is asample of a variable which is uniformly distributed in the interval[0,1]. can then be obtained by using tables of random number or standard subroutines in computers.

2) Determine for all pairs.

3) Determine no. of cases (k) where - which correspond to failure.Then

This estimate is accurate for large n. to determine a pf of (10-4-10-6) requires an n of the order (10-5-10-7)

{ }ix̂( )1−=i X iˆ ˆx F v

iv̂

= −i i iˆ ˆ ˆM r s

0<iM̂

fkpn

≅

v


FORM in a general case

(linearization)

( ),= Φ −Pf β



Calculation of probability of unions and intersections

So far, the failure probability pf

Pf = P[g( ) ≤ 0] or P[M ≤ 0]

has been addressed, where: g( ) ≤ 0 expresses failure

In general, the following type of expressions are needed:

Pf = P[(g1( ) ≤ 0) ∪ (g2( ) ≤ 0) ∪ … ]

Pf = P[(g1( ) ≤ 0) ∩ (g2( ) ≤ 0) ∪ … ]

Pf = P[{(g1( ) ≤ 0) ∩ (g2( ) ≤ 0)} ∪ {… }]

etc

Methods

- FORM/SORM,

- Monte Carlo Simulation can be applied.

Note that the conditional probabilityPf = P[g( ) ≤ 0| I( )<0] = P[M1 ≤ 0| M2 ≤ 0]

= P[(M1 ≤ 0) ∩ (M2<0)] / P[M2 ≤ 0]



System reliabilitySystem failure may imply fatalitiesA system may - fail due to overload or fatigue failures (at

multiple crack initiation sites), but may have - reserve capacity beyond first component

failure

Simplified system model for frame type structures:

Pf,SYS = P[FSYS] = P[FSYS(U)] + Σ P[FSYS(U)| Fi] P [Fi]

- P [Fi] probability of fatigue failure

- P[FSYS(U)|Fi] conditional probability of ultimate failure

[ ] ( )( )(...)

1 1

0= =

⎡ ⎤= = ≤⎢ ⎥

⎣ ⎦∪∩ j

N k

FSYS ii j

P P FSYS P g

P[FSYS(U)]=P[Rsys - Ssys ≤ 0)]



Illustration of calculation of failure probability for a time-variant load and resistance



Failure probability in time period, T:

Example:Wave loads (due to inertia forces) in North Sea:

(ratio of loads prop. to ratio of wave heights)

VS = 0.30 for both cases (incl. statistical + model uncertainty)Resistance

μR = 100, VR = 0.10 For lognormal variables

[ ]= ≤ maxfP P R S

( ) )100(8.01 maxmax yearsSyear S ⋅≈

)100(8.0)1( yearsSmaxyearSmax μμ ⋅=

μs yearsmax( )10050= 40

)1max(=

yearsμ

( )β ′−Φ=fP ln

22SR

S

R

VV +≈′ μ

μ

β

18.2)100( =′ yearsβ ( ) 246.1100: −≈ EyearsPf

89.2)1( =′ yearβ ( ) 393.11: −≈ EyearPf

7~31093.1

21046.1)1(

)100(

−⋅

−⋅=

yearP

yearsP

f

f

What is the probability offailure in 20 years comparedto the failure prob. in 1 year ?


Structural Reliability Analysis Procedure- Aim: Estimate Pf

- Formulate the reliability problem (time invariant problems) - Define failure function: g( ) ≤ 0- Define properties of random variables xi

(type of distribution, mean value, st. dev.)- Calculate

- Failure probability, Pf (reliability index, β) by appropriate method (FORM/SORM, Monte Carlo simulation)

- Sensitivity of Pf (β) to parameter, θ- Time variant reliability- Systems reliability

- Uncertainty modelling- random variables- stochastic process


Uncertainties in Load effects (S) and Resistance(R): Classification of uncertainties according to their “nature”

Normal Uncertainties or, Variability

─ Fundamental (natural) VariabilityExample - Wave elevation/

- Loading/- Load effects

─ Lack of Knowledge e.g. - model uncertainty

- statistical uncertainty (due to limited data)

⇓

Wave elevation (loads) time


Characterisation of a random variable, X- Mean, μx

- ; or

- probability density function (fX(x) /distribution (FX(x))Fundamental uncertainty in wave elevation and corresponding wave-induced loads and load effects by stochastic methods Model uncertainty, X of a method:Estimate by obtaining a sample of:─ Predicted value (for a given set of parameters: PV─ True value (e.g. based on obs. or accurate analyses): TV

Model uncertainty for observation i: Xi = TVi/PVi

Establish statistics for X by a sample {Xi}n

NOTES:- Gross Errors are not considered in SRA as such- Unknown phenomena that can cause failures, cannot be treated withprobabilistic methods simply because they are unknown !

x

xCOVμ

σ==

ValueMean Dev. Stand.


Uncertainties according to theirphysical source – associated with wave loads- wave height, period, current velocity (including variability, limited amount of data, etc.)

- wave theory- drag and mass coefficient

Wave height: H100(100 year wave height)

Mean uncertainty ~ 1.0

Wave load model based on regular wave – relating to API/ISOMean uncertainty ~ 0.9 - 1.1 (1.0)COV ~ 0.25 - 0.35

Total uncertainty may be estimated by:F = ψ.c’.Hα

where ψ is the model uncertainty and the uncertainty in waveheight is represented by H.

⎩⎨⎧

−−

==GoM

SeaNorthCOV

H

H

20.015.015.010.0

μσ


Estimation of uncertainties of extreme loads on jackets (simplified approach)

Design Wave Approach• Kinematics : Stokes 5th order theory

particle velocity particle acceleration

• Wave loading

API (ISO) procedure will be referred to here

18m

→ F

c=18 m H=30m

70m

1F C v v C D aD M2 4 c H (approximation by regression fit)

π= ×ρ × × + × × ×

α≈ ×

2


Estimate of uncertainty in the global wave load on jackets – base shear force of the Magnus and Tern jackets:

i)predicted(F)measured(iF

μσ

Model uncertainty =

Mean = 1.06

COV = ≡ 25%

The Magnus platform

CeSOS NTNU

Keulegan-Carpenter number

ISO 19900load analysis procedure

21


Modelling of uncertainty in ultimate strength of beam-column

XA - parameter uncertainty in cross-section area Xfy - parameter uncertainty in yield strength fYXR- model uncertainty = Rtrue/Rpred:

Mean : CoV :

Model uncertainty of ECCS method for strength of tubular columns

N N

fyARcpred

ynom

y

nomRnomynom

predy

uRy

predy

uuu

XXXR

ff

AAXAf

ffAXf

ffAfNR

⋅⋅⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅⋅⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛=⋅⋅⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛=⋅==

)(

RX 1.00+0.10 for 0 2.0μ = λ < λ ≤

⎩⎨⎧

<≤≤

=0.26.0 for 08.0

6.0 for05.0λλλ

RXV

Slenderness, λ

u

y pred

ff

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

T.Moan MARE WINT Sept.201339 T.Moan MARE WINT Sept.201340

0

2

4

6

0 2 4 60

2

4

6

0 2 4 6

β LN

β M

β LN

β M

cov (S) cov (S)

0.2 0.4

0.2 0.4

cov (R) = 0.1, cov (S)-variable cov (R) = 0.2, cov (S)-variable

β LN : lognormal R and S β M : R lognormal and S lognormal

Tail sensitivity

(not analytical !)


Relation between reliability measure, (Pf ) and Safety Factors (γR , γS ) in ULS design check

( )2 2

1.2 1.4

2 2

ln

ln /( )

....... ( ) ( ) 10 ;β

μ μ

β −

≈ Φ −⎡ ⎤⎣ ⎦+

= Φ − = Φ − ≈+

= ≤ R Sf

R S

R R S S

R S

(B γ γ /B )

V V

V V

P P R S

Resistance R Load effect S

- Rc ; Sc - characteristic resistance and load effect

- γR ; γS - partial safety factors

Reliability analysis:R and S modelled as random variables;

e.g. by lognormal distributions

Semi-probabilistic design code:c R S cR /γ γ S≥

Goal: Implied Pf ≅ Pft

pdf

R,S

μ - denotes mean valueσ - denotes st. deviationV = σ/μ – coefficient of variationΦ(-β) = standard cumulative normal distr.

R R CB Rμ = S S CB Sμ =

μ μR R S S,V ); ,V )( (

≥ <R S;BB 1 1

14

0.85 0.7 logβ ≈ − fPT.Moan MARE WINT Sept.201342

Reliability - based ULS requirements

R — resistanceD, L, E — load effects due to

• permanent• live load effects• environmental

Reliability-based code calibrations:Offshore oil and gas- NPD/DNV; API/LRFD;- Conoco studies of TLPs ;

Wind turbines-IEC

RC/γR > γDDC + γLLC + γEEC Goal: The Implied

Pf = P(R>D+L+E)≅ Pft

Pf depends upon thesystematic and randomuncertainties in R; D, L, and E

Design equation

CeSOS NTNU

β

βT

WSD

LRFD

Load ratio, Ec/(Lc+Ec)

15


• Initial and modified inspection/monitoring plan- method, frequency

Safety against fatigue or other degradationfailure is achieved by design, inspection and repair

• Design criteria: FLS

ALS

.... 0.1 1.0

= ≤

= −

∑ iallowable

i

nD DN

Bracewall

Ground

Chordwall

CeSOS NTNU

NDE diver inspection or LBB• Repair (grinding, welding,..steel…)

16

See Overview by Moan, in J. Structures and Infrastructure engineering, Vol.1, No.1 March 2005, pp. 33-62


In-service Experiences

Fatigue behaviourFatigue depends on local geometry- Cracks start to grow at ”hot spot”

points, with high stress concentration- Initial crack depth of 0.1 mm - driven by cyclic tensile stresses

Cracks can be detected and repaired.- Mean detectable crack depth:

NDE: 1-2 mm Close visual inspection: 10-20 mm

Fracture or ductile tearing under given extreme stress

Total loss if the structure lacks residualstrength after a member failure

Tubularjoints

Time

Stre

ss, σ

S

Fatigue failure:- through thickness

crack- member failure- visible crack


Experiences with cracks in fixed offshore platforms (See Vårdal, Moan et al, 1997...)

Data basis- 30 North Sea platforms, with a service time of 5 to 25 years- 3411 inspections on jackets- 690 observations of cracks

The predicted frequency of crack occurrence was foundto be 3 times larger than the observed frequency

On the other hand:- Cracks which are not predicted, do occur. Hence, 13 % of observed fatigue cracks occurred in jointswith characteristic fatigue life exceeding 800 years; due to - abnormal fabrication defects (initial crack size ≥ 0.1 mm !)

- inadequate inspection


In-service experiences: Comparison of fatigue lifepredicted by old and new method


In-service experiences:

Corrosion• affects ultimate and

fatigue strength- plate thinning effect- crack growth rate

• no or damaged coatingor cathodic protection

• corrosion rate for general corrosion:0.1 – 1.0 mm/year;

Splash zone:• Corrosive environment / difficult access


• Fatigue loading- Weibull distribution of stress ranges

(with shape and scale parameters B and A)

• Fatigue resistance- SN approach- Fracture mechanics model:

a - crack depthN - number of cyclesc, m - material parameters

• Deterministic vs. probabilistic approach- Reliability model

Time

Stre

ss, σ

S

Stress,σ

fx(x)fx(x)

xcx

Prob. density

Fatigue life models


Fatigue failure expressed by SN – formulation

Load effect (stress range), S

– Fs(s) = 1 – exp(-(s/A)B)

– Total number of cycles in period, N0

Resistance, SN formulation (simplified)

N = KS-m

K, m: material, local geometry dependent

Cumulative damage:

where sref = A(lnNref)1/m

often Nref = N0(108 in 20 years – e.g. or wave loads)

( ) Γ ⎛ ⎞= = = + =⎜ ⎟⎝ ⎠

∑ m m mi 0 0 0eq

i

n N N NmD E S A 1 SN K K B K


Fatigue reliability baed on SN formulationConsider

failure probability in a given (service time) period:

Assumem, B, No deterministicso, k and Δ lognormal distribution

( ) ( )m

i o om B

i o

n N s mD BN K ln N= = Γ +∑ 1

[ ]fP P D= ≥ Δ

( )( )

( )o

f

m Bo

mo o

s K

P

K ln NmN s B

V m V V

X X

where the notation is the modal value of Δ

= Φ −β

Δ

Γ +β =

+ +

i

2 2 2

1


1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 5 10 15 20Time

Failu

re p

roba

bilit

y

Cumulative failure probability

•Probability of failure in interval t +Δt, given it has survived up to t•Suitable for time-dependent problems•i.e. implicitly accounts for degradation of structure!

Reliability model (cont…)

Hazard rate, hR(t)

Implied reliabilityCase

Δallow

able

Service lifePf

Annualhazardrate h(t)

1 1 10–1 10–2

2 0.33 10–2 2*10–3

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 5 10 15 20Time

Failu

re p

roba

bilit

y

Annual hazard rate


( )( )1 ( )R

f th tF t

=−

F(t) – distribution of time to failuref(t) – probability density function

If F(t) is the fatigue Pf accumulated up to tand f(t) the “instantaneous” Pf evaluated at t,

Then hR(t) = Annual hazard rate or annual failure probability for fatigue


Reliability level as a function of uncertainty level

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1 2 3 4 5 6 7 8 9 10

Fatigue design factor

Failu

re p

roba

bilit

y


Cumulative, stdv(lnA)=0.15Cumulative, stdv(lnA)=0.3

Annual failure probability

Annual, stdv(lnA)=0.15Annual, stdv(lnA)=0.3

Fs(s) = 1 – exp(-(s/A)B)

.... 0.1 1.01/

= ≤

= −=

∑ iallowable

i

allowable

nD DN

FDF D


Fracture mechanics model

Basic model

Fatigue failure event:

g(x) = acr – a(C, m, lnA, B) ≤ 0C, m - material parameterslnA, B - load effect (stress) parametersNO, Δ - deterministic

Reliability calculation by FORM/SORM or Monte Carlo Simulation

[ ]fg( ) 0

p P g( ) 0 f (x)dx ( )≤

= ≤ = = Φ −β∫∫x

x


Reliability model (cont…)

Prob

abili

ty d

ensi

ty, f

A(a)

Plate thickness a(t) – crack depth

Time in-service

Calculated probability ofthrough thickness crack(without updating)

aupd(ti)

a0

ti

a(ti)

Predicted mean crack size

Prob

abili

ty d

ensi

ty, f

A(a)

Plate thickness a(t) – crack depth

Time in-service

Calculated probability ofthrough thickness crack(without updating)

aupd(ti)

a0

ti

a(ti)

Predicted mean crack size

[ ]( ) 0fP P M t= ≤

Fatigue failure probability, Pf

( ) ( )fM t a a t= −

Often used

β – reliability index

Φ – standard normal distribution

( )fP β= Φ −

Predicted crack size

Final crack size (plate thickness)

11 2 2 1 20( ) (1 )2

m m m m mma t a C S Y Nπ− −⎡ ⎤= + −⎣ ⎦

For special case: Y(a)=constant


Inspection quality (POD curves)• Non-destructive examination• Magnetic Particle Inspection• Eddy Current (EC)• Visual inspection (within 0.5m

distance), depending upon accessto crack site

• (Fujimoto et al., 1996, 1997) based on trading vessels)

ACFM in air

Depth (mm)(length based on

a/2c=0.2)Method Tubular joint in

sea waterButt

weld in air

ACFM (Alternate Current Field Measurement)

0.70(3.5)

0.21(1.05)

Magnetic Particle Insp.

0.89(4.45)

Not reported

Eddie Current 2.08(10.4)

0.32(1.6)

In-service MPI & EC (Moan et al, 1997)

1.95(9.75)


Failure probabilityPf (t) = P[ac – a(t) ≤ 0 ]

ac = critical crack size

Updating of failure probability based onInspection ( Madsen, Moan, Skjong,Sørensen, ….): :

Example: no crack is detected:

Pf,up (t) = P[ac – a(t) ≤ 0 | aD – a(t) ≥ 0]= P[F |IE] = P[F ∩ IE]/ P[IE]

ac = critical crack sizeaD = detectable crack size

where FAD (a) = POD(a)• Known outcomes in-service vs uncertain outcomes at the design stage

• Updating late in the service life has largerinfluence

Reliability based inspection planning w.r.t. fatigue

Mean detectable crack depth of1.5 mm

Pf

CeSOS NTNU

17


Target level, pfsysT for global failure and pfT (βT) for fatigue reliability of a specific joint

P [Fi] P [FSYS(U)|Fi] = pfsysT

Fatiguefailureprobabilityin theservice life

Conditional annual ultimate failure probability

TargetLevel for global failure of the structure;Depending on the potential of- Fatalities- Pollution- Property loss

P [FSYS(U)|Fi] = Φ(-βFSYS|Fi)

Φ(-βT) = P [Fi] = pfsysT / P [FSYS(U)|Fi] =

βTGlobal failure model

of jacket withmember (i) removed


Inspection sceduling for a welded joint based upon no detection of crack during inspection

0 4 8 12 16 20

Inspection at time t=8with no crack detection

No inspection

Rel

iabi

lity

leve

l, β

Time (years) 1st inspection 2nd inspection

Target levelfor a given joint

In-service scheduling of inspectionsto maintain a target reliability level

Extension of method:- consideration of other inspection events;- effect of corrosion etc- many welded joints , i.e. system of joints

; depending on theconsequences of failure

1.2 1.4( ) 10

0.85 0.7 log

ββ

β

−Φ − ≈

≈ −

=f

fPP

CeSOS NTNU

18

βT


Contribution to cumulative fatigue damage of wind loads, wave loads and interaction of wind and wave loads

Tubular

Joints

Characteristic fatigue damage

Raw

data

Weibullmodel

General-ized

gamma model

Leg1-Joint2

0.0881 0.0859 0.0952

Leg1-Joint3

0.2713 0.2714 0.2862

Sur12-Joint1

0.2142 0.2069 0.2213

Leg2-Joint2

0.0876 0.0836 0.0889

Characteristic fatigue damage for different model

Long term fatigue analysis of multi-planar tubular jointsIn an offshore jacket wind turbine

Two-parameter Weibull model:

Fs(s) = 1 – exp(-(s/A)B)


Fatigue reliability results:

Reliability index for welded joints in jacket as a function of time. No inspection and repair. .0.1corrR =

Reliability index for welded joints in jacket as a function of time. ,

years, mm, mm, andmm.

0.1corrR =5ptt =0.11Ra =

0 0.11a = 2.0Da =

Fatigue reliability analysis of multi-planar welded tubular joints considering corrosion and inspection

(Source: W.B.Dong et al., diff.papers)


Reliability - based calibration of FLS requirements

Design criterion :

FDF - depends upon:

• consequence of failure

• inspection quality

Criterion:

( ) ( ) fsysTP FSYS FF i P FF i P⎡ ⎤ ⎡ ⎤⋅ ≤⎣ ⎦⎣ ⎦

FailureConsequence

Noinspection

Inspectionin splashzone

Inspectioninside/topside

Static determ. 10 (10) 5 (3) 3 (2)

Fulfills ALSwith onemember failed

4 (3) 2 (2) 1 (1)

0 2 4 6 8 10 12 14 16 18 20

6

5

4

3

2

1

withinspection

noinspection

Δd = 0.1Δd = 0.2Δd = 0.3

Time after installation t [year]

Rel

iabi

lity

inde

x β

∑ =Δ≤= FDF/1Nn

D di

i


Main purpose:

(1) Check the effects of gearboxon the Torque calculation;

(2) Check the effects of global model on the contact forcecalculation.

Time domain based simulation model of 750 kW land-based wind turbineComparison between coupled and decoupled analysis method:


• Model for crack propagation:

Linear elastic fracture mechanics (LEFM) model is used:

( )_

m

II effda C KdN

= ⋅ Δ

, :C m material parameters, which can be determined by experiments;

:a half crack length;

:N cycle numbers;

_ :II effKΔ effective Mode II (shear) stress intensity factor range ; dependent onHardness ; microstructure; friction; crack closure

- Subsurface initiated pitting.

Gear contact fatigue analysis of a wind turbine drive train under dynamic conditions

(a) Contact model of two gear flanks and(b) Equivalent model of two cylinders

(Glodez, et al.,1997)

Schematic of crack propagation


Reliability-based gear contact fatigue analysis-a frame work

Reliability as a function of time

Uncertainties:- loading: contact pressure

- Model uncertaintiesin aerodynamic loads, global and local struct.analysis

planet gear


Summary of reliability methods

Simple formulae (“lognormal format”)─ Convenient as reference. Note: used in API Code Calibration

FORM/SORM─ Very efficient─ Approximate and need to be validated

Monte Carlo method─ Basic method yields “exact” solution if the sample n is large

enough (time consuming)─ Improved efficiency by

• Importance sampling (but caution is required)

Combined FORM and MC ─ Estimate approximate solution by FORM─ Improve solution by MC, focused on the most important area


Practical use of Structural Reliability Analysis

Choice of method (simple explicit method based on lognormal variables - FORM/MC)

Estimate uncertainties─ Focus on the most important variables/ uncertainties─ Introduce variable to represent uncertainty of the “mechanics”

model─ Effect of probabilistic model (e.g. pdf)

Calculate reliability─ Check relative importance/ influence of variables and possibly

improve uncertainty measures

Estimation of target level


Case-by-case Structural Reliability Analysis

Reliability-based design

• New types of structures

• New use

Design and inspection planning

• Integrated design and inspection planning

Requalification

• New use

• New information

• Damage/subsidence

• Extension of service life


Guidelines for Structural Reliability Analysis

Content

– Methods

– Uncertainty modelling

– Target levels

Issued guidelines

– Det norske Veritas

– Norwegian Geotechnical Intitute

Criticism

– Important to develop such guidelines by an authorized committee

– The target reliability level should be defined by close calibration to acceptable design/ operation practice and properly defined reliability methodology.


Risk Assessment in Offshore Safety Management

With respect to • Fatalities• Environmental

damage• Property damage

Offshore structures are designed according to approaches which are: - Goal-based; rather than prescriptive- Probabilistic; rather than deterministic- First principles; not purely experiental- Integrated total; not separately (i.e. system consideration)- Balance of safety elements; not hardware only

Critical eventFault tree Event tree

NPD Guidelines for Quantitative Risk Analysis(1981)NPD’s Accidental CollapseLimit State (ALS) (1984)UK Safety Case (1992)

T.Moan MARE WINT Sept.201370RISK ANALYSISRISK ANALYSISRISK ANALYSIS

RISK ESTIMATIONRISK ESTIMATIONRISK ESTIMATION

Risk Analysis PlanningRisk Analysis Planning

System DefinitionSystem Definition

Hazard IdentificationHazard Identification

Risk PictureRisk Picture

Risk Reducing Measures

Risk Reducing Measures

Frequency Analysis

Consequence Analysis

Risk Acceptance

Criteria

Risk Acceptance

Criteria

AcceptableAcceptable

UnacceptableTolerable

Critical eventFault tree Event tree

Risk analysis framework (oil and gas industry)• Empirical data: Accumulated no. of platform years world wide:

fixed platforms: ~ 150 000mobile units: ~ 15 000

• Theoretical analysis (Fault tree/event tree)


Internal hazards:Blade pitch and control system faults

• Blade seize: imbalance loads• Shutdown loads: impulse from aerodynamic braking can lead to pitch vibrations• What about sensor faults?• Does changing the shutdown pitch rate help?• Possible instability for TLPWTs (idling with one blade pitched – Jonkman and

Matha, 2010)

Wilkinson et al., 2011

Pitch system

-200 -150 -100 -50 0 50 100 150 200-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Tow

er T

op B

MY

, kN

m

TLP, EC 5

time - TF, s

BC

Shut down turbine quickly

Fault occurs

Continue operating with faulted blade


External hazards: Accidental Loads

1Explosion loads (pressure, duration - impulse)

scenariosexplosion mechanics probabilistic issues⇒ characteristic loads for design

2 Fire loads (thermal action, duration, size)

3 Ship impact loads(impact energy, -geometry)

4 Dropped objects 5 Accidental ballast6 Unintended pressure7 Abnormal Environmental loads8 Environmental loads on platform

in abnormal floating position


Accidental Collapse Limit State relating to structural strength (NPD,1984, later NORSOK)

• Estimate the damage due to accidental event (damage, D or action, A) at an annual probability of 10-4

- apply risk analysis to establish design accidental loads

• Survival check of the damaged structure as a whole, considering P, F and environmental actions ( E ) at a probability of 10-2

Target annual probability of total loss: 10-5 for each type of hazard

P, F

A

P, F

A

P, FP, F

E

A


Estimating the Accidental Event

Theory based on: - accidental events originate from a small fault and develop in a sequence of

increasingly more serious events, culminating in the final event, - it is often reasonably well known how a system will respond to a certain event.

Damage or accidental load with annual probability of occurrence: P = 10-4

Need homogeneous empirical data of the order 2/p = 20 000 yearsto estimate events by empirical approach Accumulated platform years world wide:- fixed platforms: ~ 180 000- mobile units: ~ 20 000- FPSO: ~ 2 000

Account of all measures to reduce the probability and consequences of the hazards


Ship collisions Types and scenarios

– according to type of ships and their function:

• offshore site related ships (supply vessels, offshore tankers, …)

• floating structures (storage vessels, drilling units, crane barges..)

• external ships (merchant, fishing..)Oseberg BSubmarine U27

but not submarines T.Moan MARE WINT Sept.201376

Risk reduction- ship collision risk

• reduce risk by reducing the prob. (traffic control) and/or theconsequences of collision

• Design for collision events- Min collision: Supply vessel

5000 tons displacementand a speed of 2 m/s; i.e. 11, 14 MJ

(to be increased!)- collision events with trading vessels(with a probability of exceedance of10- 4 ) site specific events identified byrisk analysis

Collisions do occur.


– annual impact frequency for a given platform in a given location

– annual number of vessels with a size (j) in route (i)

– probability that vessel of size (I) in navigation group (k) in route (i) is on collision course

Frequency of Impact by Passing Vessels

∑ ∑∑= ==

⋅=n

1i

4

1kjk,FRijk,CC

5

1jijC PPNP

CP

ijN

ijk,CCP

jk,FRPProbability density of ship position

ij,CCPplatform

Cen

tre

line

– probability that a vessel with a size (j) in navigation group (k) does not succeed in avoiding the platform


Calculation of impact damage

External mechanicsThe fraction of the kinetic energy to be absorbed as deformation energy (structural damage) is determined by means of:

Conservation of momentumConservation of energy

Internal mechanicsEnergy dissipated by vesseland offshore structure

Equal force levelArea under force-def. curvedws dwi

RiRs

Ship FPSO

Es,sEs,i

External mechanics

Internal mechanics

Measure of damage: Indentation depth


Ultimate global collapse analysis of platforms

Non-linear analysis to assessthe resistance of - intact and damaged structures

by accounting for

geometrical imperfection,residual stresseslocal buckling, fracture,rupture in joints

nonlinear geometrical and material effects

Nonlinear FEM-General purpose (ABAQUS….)-Special purpose (USFOS…)

28


Residual global ultimate strength after damage(due to collison, dropped objects, ”fatigue failure”)

Residual strength of damaged North Sea jacket. Linear pile-soil model

Ultimate strengthBroad side loading

Brace 261

Brace 363

Brace 463

Ultimate strength Fult / FH100

2.73 2.73 2.73

Residual strength Fult(d) / Fult

1.0 0.76 1.0

70 m 56 m

main structure

deck(261)

(363)

(463)

Broad-side and end view.Deck model indicated by dashed line

(261)

(363)

(463)(455)(456)

collision

droppedobject

29


Framework for Risk-based Design against Accidental actions

][]|[]|[)( )(

,

)( ijk

kj

ijkFSYS APADPDFSYSPiP ∑ ⋅⋅=

probability of damaged system failure under relevant F&E actions

probability of damage, D given Ajk

(i) (decreased by designing against large Aj

(i))

probability of accidental action at location (j) and intensity (k)

(i)jkP A⎡ ⎤⎣ ⎦ is determined by risk analysis while the other probabilities

are determined by structural reliability analysis.

[ ]P FSYS | D Is determined by due consideration of relevant action and their correlation with the haazard causing the damage

For each type ofaccidental action


Accidental actions for wind turbinesIEC 61400-1

• “External” ALS actions may need to be considered

Ship collision:• Maximum size of service vessel and limiting operational conditions to

be specified by designer: • • Vessel speed not less than 0.5 m/s • • Kinetic energy based on• – 40% added mass sideway• – 10% added mass bow/stern• • Impact energy < 1 MJ (small) • • Max. force may be assumed 5 MN - includes dynamic amplification

IEC 6400-3


2.3 Standard directives for approval practice

Number 4: The structures shall be designed and configured in sucha way that –in the event of collisionwith a ship, the hull of the ship shallbe damaged as little as possible.

Design Collision Event

•A single-hull Suezmax tanker with 160,000 tdw•The ship is drifting sideways at 2 m/s •Ship displacement ≈ 190,000 tons•Kinetic energy (40% added mass) = 530 MNm


Mass of 5 MW turbine 450 tons•Drop height 60 m •Energy 275 MJ •Nacelle may fall through the tank!

Suezmax tanker collision

Altenative jacket failure modes(Source: J.Amdahl, Tekna seminar, NTNU, January 2012)

Collapse mode is favourable –nacelle drops into sea•Upper weak soillayers beneficial


Concluding remarks

Experiences regarding- failures and accidents and- life cycle safety managementfor oil and gas installations can serve as a basis for structuresin other offshore industries, notably wind turbines, - when the differences betweenthe oil and gas and the other industriesare recognised

In particular- normal uncertainty and variability in structuralperformance as well as possible “gross errors” in fabrication and operation should be properly considered in the decisionprocess

CeSOS NTNU

Thank you!

30


Selected references – which include more complete reference listsDesign codes: ISO 2394 (Reliability of structures); ISO 19900- (Offshore structures)

Emami, M.R., and Moan, T.: “Ductility demand of simplified pile-soil-jacket system under extreme sea waves and earthquakes”, Third European Conf. on Structural Dynamics, Balkema Publ. G. Augusti et al. (eds.) Rotterdam, 1996, pp. 1029 – 1038.

Moan, T. and Amdahl, J.: “Catastrophic Failure Modes of Marine Structures”, in Structural Failure, Wierzbiecki, T. (Ed.), John Wiley & Sons, Inc., New York, 1989.

Moan, T., Vårdal, O.T., Hellevig, N.C. and Skjoldli, K. “Initial Crack Dept. and POD Values inferred from in-service Observations of Cracks in North Sea Jackets”, J. OMAE, Vol. 122, August 2000, pp. 157-162.

Moan, T. and Amdahl, J.: “ Nonlinear Analysis for Ultimate and Accidental Limit State. Design and Requalification of Offshore Platforms” WCCM V. Fifth World Congress on Computational Mechanics (Eds.: H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner) July 7-12, 2002, Vienna, Austria.

Moan, T. “Reliability-based management of inspection, maintenance and repair of offshore structures”. Structure and Infrastructure Engineering. Vol.1, No.1, 2005, pp. 33-62.

Moan, T. Reliability of aged offshore structures. In: "Condition Assessment of Aged Structures", 2008, Ed. Paik, J. K. and Melchers R. E., Woodhead Publishing.

Moan, T. Development of accidental collapse limit state criteria for offshore structures. J. Structural Safety, 2009, Vol. 31, No. 2, pp. 124-135.

Vinnem, J.E.: “Offshore Risk Assessment”, Kluwer Academic Publishers, Doordrecht, 1999.

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