083 Moan Structural Reliability

8/20/2019 083 Moan Structural Reliability

1/22

T.Moan MARE WINT Sept.20131

Structural reliability and risk analysis

of «offshore structures»By Torgeir Moan, CeSOS and Department of Marine Technology, NTNU


List of content Introduction

- Facilities

- Regulatory framework

- Accident/failure experiences

- Safety Management

Structural 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 factors

Fatigue reliability

- Background

- Fatigue life models (based on SN- and Fracture Mechanics)

- Reliability updating approaches


List of content - continued

Fatigue reliability - continued- Inspection scheduling

- Calibration of fatigue design criteria

- Fatigue reliability of gear components

Quantitative r isk 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 sensitiveto IMMR (O&M) costs

(access)

Integrating

knowledge

4Introduction


2/22


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 stabilit y Strength Escapeways/lifeboats

Offshore oil and gas Wind turbines

- National regulatory

bodies;

- Industry: API, NORSOK,

- Classification soc.

- ISO/IMO

- National Regulatory

bodies

- Classification societies ??

- IEC

Introduction


Introduction

Experiences

Oil and gas platforms- significance of the oil and gas industry to the world econmy

- need for technology development for deeper water, challenging

natural and industrial environment,…

- ageing facilities

Wind turbines

CeSOS NTNU

Gathering of experiences – development of procedures/methods/data

Failure - and accident data

Safety 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 fai lure - due to ” natural hazards” ?

Severe damage caused by

hurricane Lilli in the Gulf of

Mexico

Technical-physical causes:Observation: Wave forces exceeded the

structural resistance

Human – organizational factors:

Design

- Inadequate wave conditions or load calculation

or strength formulation or safety factors

Fabrication deficiencies

due to

- inadequate state of art in offshore

engineeringor,

- 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


3/22


0

2

4

6

8

10

12

14

16

18

20

B l o w o u t

C o l i s i o n / c o n t a c t

D r o p p e d o b j e c t

E x p l o s i o n F i r e

G r o u n d i n g

S p i l l / r e l e a s e

S t r u c t u r a l d a m a g e

C a p s i z e / f o u n d e r i n g / l i s t

Mobile

Fixed

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

Accident experiences for mobi le drill ing and

fixed production platforms(Number of accidents per 1000 platform years)

Operational errors

Design or

Fabricationerrors

CeSOS NTNU

7Introduction


In-service experiences with cracks infixed 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 found

to 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 inspection

CeSOS 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 few

components) &

smart maintenance,

but also improved

accessibility

- Larger turbine size?

( > 5 - 20 MW)

Courtesy:

Fraunhofer

- Predict,

monitor and

measure degradation

(Courtesy: Fraunhofer)

Introduction


Risk Control Measures

Cause of failure Safety measure

Inadequate design check to

account for normal variability

−Increase safety factors or use

lower 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 check

R&D

Introduction


4/22


Safety management (ISO 2394, ISO19900, etc)

ULS

FLS: D = Σni/Ni ≤ Dallowable ALS

• Measures to maintain acceptable risk

- Life Cycle Approach

design, 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

n ro uc on


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

model

tests

Introduction


Safety cri teria for design and reassessment(with focus o n 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 joints

due to repetitive loads

Component design check

depending on residual

system strength and

access for inspection

Accidental co llapse ( ALS)

- Ultimate capacity1) of

damaged structure with

“credible” damage

Platethick-

ness

Collapsed

cylinder

Jack-up collapsed

Fatigue

crack

CeSOS NTNU

10Introduction


Accidental Col lapse 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


5/22


Ocean

environment

Analysis for demonstrating compliance with

design criteriaFunctional loads

- dead loads

- -pay loads

Accidental

loads

Piper Alpha

Responseanalysis- dynamic v.s.quasi-static/quasi-dynamic

Sea loads

Designcriteria

Loadeffects

Collapseresistance

SN-curve/fracturemechanics

Ultimate

globalresistance

Extreme

moment (M)andaxialforce (N)

Localstressrangehistory

Extremeglobalforce

Designcheck

ULS:

FLS:

ALS :

Damaged

structure

Analysis of damage

Industrial

and

Operational

Conditions

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, foundations loads and resistances are subjected to uncertainties

- normal variability and uncertainty; gross errors

design is decision under uncertainty :

- rational treatment of uncertainty (range, mean+st.dev. etc)- implying probabilistic methods

especially in connection with new technology, no standards

CeSOS NTNU

ALARP

principle

13Introduction


Estimation of Failure Probability of components A s imple 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

Notional

probaility,

not true, actuarial

[ ] [ ]

[ ] ( )f

P P R S 0 P ln R lnS 0

.... P R ' S' 0 '

= − ≤ = − ≤ =

= − ≤ = Φ −β

22

ln

2121ln

21

21ln

S R

S

R

S R

R

S

S

R

V V V V

V

V

≈

⎟

⎠

⎞

⎜

⎝

⎛

⎠

⎞

⎜

⎝

⎛

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

⋅

=

μ

μ

μ

μ

β

where Φ ( ) is the standard normal density function

φ(u)

( ) ( )u

u t dtφ

−∞

Φ = ∫


β Pf Pf β

1

2

2.5

3

3.5

4

4.5

5

5.5

6

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

1.29

2.32

3.09

3.72

4.27

4.75

5.20

5.61

6.00

6.36

Relation between Pf and β

1.2 1.4( ) 10 β β −Φ − ≈= f P A rough approximation:

Estimation of Failure Probability


6/22


General methods to determine PfThe probability of failure , Pf , for

a time-invariant reliability problem, is

( ) ( )

( ) 0

0 ( )

≤

⎡ ⎤= ≤ = = Φ −⎣ ⎦ ∫∫ f g

P P g f d β x

x

x x x

- g(x) is the limit state function, i.e. g(x) = R - S

- X is the set of n random variables

- f x(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 and

resistance in terms of: f x(x)

Notional

probaility,

not true, actuarial



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

Volume: f RS(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 generalized

NOTE:

The probability density function for independent variables is )()( s f r f S R

⋅



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 independentstandard normal variables, u1 and u2. This is done here for the simpleproblem where

Transformation of variables

Transformtion of failure function

1

2

R

R

S

S

RU

S U

μ

σ

μ

σ

− ⎫= ⎪⎪⎬

− ⎪=⎪⎭

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

( )2, R R R N μ σ = ( )2,S S S N μ σ =

'

1 2( ) ( ) R R S S M R S U U σ μ σ μ = − = + − +

1

( ) ( )

( ( ))−

Φ =

= Φ x

x

u F x

x F u

In general transformation of (independent variables)

x into variables u is :



( )d cfr. previous definitionμ − μ

= → βσ + σ

R S

2 2

R S

1 2' '

'

1 2 1 2 1 2 1 2

( 0) ( 0)

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

P P M f u u du du u u du duφ φ β ≤ ≤

⎡ ⎤= ≤ = = = Φ −

⎣ ⎦ ∫∫ ∫∫

Distance d:

Failure p robability

The same answer as before.

The advantage of this method is when multiple variables are needed.

R,S space U-space



7/22


Monte Carlo simulation

Instead 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 f R(r)

and f S(s), respectively.

pf may be determined as follows:

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

[ ]0= ≤

= − f p P M

R S

( )

( )

( )

( )

1 1

2 2

3 3

n n

ˆ ˆ r , s

ˆ ˆ r , s

ˆ ˆ r , s

ˆ ˆ r , s



Samples for a variable X with a distribution function FX(x) or

a density f X(x) may be generated by , where pi is a

sample 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)

{ }iˆ x( )1−=i X iˆ ˆ x F v

iˆ v

= −i i iˆ ˆ ˆ r s

0


8/22


System reliability System failure may imply fatalities

A 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 i

i 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

[ ]= ≤ max f P P R S

( ) )100(8.01 maxmax yearsS year S ⋅≈

)100(8.0

)1( yearsSmax year Smaxμ μ

⋅

μ s yearsmax( )100 50= 40)1max( = year sμ

( ) β ′−Φ= f P ln

22

S R

S

R

V V +≈′

μ β

18.2)100( =′ years β 246.1100: E years P f

89.2)1( =′ year β 393.11: E year P f

7~3

1093.1

21046.1

)1(

)100(

⋅

⋅

=

year P

years P

f

f

What is the probability of

failure in 20 years compared

to the failure prob. in 1 year ?


Structural Reliabili ty 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


9/22


Uncertainties in Load effects (S) and Resistance

(R): Classification of uncertainties according to

their “nature”

Normal Uncertainties or, Variability

─ Fundamental (natural) Variability

Example - 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 (f X(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/PViEstablish 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 with

probabilistic methods simply because they are unknown !

x

xCOV μ

σ =

ValueMean

Dev. Stand.


Uncertainties according to their

physical 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/ISO

Mean 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 wave

height is represented by H.

⎩⎨⎧

−

−==

GoM

Sea NorthCOV

H

H

20.015.0

15.010.0

μ

σ


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


10/22


Estimate of uncertainty in the global wave load on jackets

– base shear force of the Magnus and Tern jackets:

i) predicted(F

)measured(iF

μ

σ

Model uncertainty =

Mean = 1.06

COV = ≡ 25%

The Magnus platform

CeSOS NTNU

Keulegan-Carpenter number

ISO 19900load analysis procedure

21


Modelling of uncertainty in ult imate strength of beam-column

X A - parameter uncertainty in cross-section area

Xfy - parameter uncertainty in yield strength f YXR- model uncertainty = Rtrue/Rpred:

Mean :

CoV :

Model uncertainty of ECCS method for strength of tubular columns

N N

fy A Rc pred

ynom

y

nom

Rnom ynom

pred y

u

R y

pred y

u

uu

X X X R

f

f

A

A X A f

f

f A X f

f

f A f N R

⋅

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

⋅

⎟

⎠

⎞

⎜

⎝

⎛

=

⎟

⎠

⎞

⎜

⎝

⎛

=

)(

R X1.00+0.10 for 0 2.0μ = λ < λ ≤

⎩

<

≤

=

0.26.0 for 08.0

6.0 for 05.0

λ λ

λ R X

V

Slenderness, λ

u

y pred

f

f

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

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 !)


11/22


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 S f 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 C B Rμ = S S C B S μ =

μ μ R R S S V ); ,V )( (

≥ < R S

;B B 1 1

14

0.85 0.7 log β ≈ − f P


Reliability - based ULS requirements

R — resistance

D, 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 the

systematic and random

uncertainties 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 degradation

failure is achieved by design, inspection and repair

• Design criteria: FLS

ALS

.... 0.1 1.0

= ≤

= −

∑ i allowablei

n D D

N

Brace

wall

Ground

Chordwall

CeSOS NTNU

NDE diver inspection or LBB

• Repair (grinding, welding,..steel…)

16

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


In-service Experiences

Fatigue behaviour

Fatigue 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

Tubular

joints

Time

S t r e s s , σ S

Fatigue failure:

- through thickness

crack

- member failure

- visible crack


12/22


Experiences with cracks infixed 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 found

to 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 joints

with 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 life

predicted by old and new method


In-service experiences:

Corrosion

• affects ultimate and

fatigue strength

- plate thinning effect

- crack growth rate

• no or damaged coating

or 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 depth

N - number of cycles

c, m - material parameters

• Deterministic vs . probabilistic approach

- Reliability model

Time

S t r e s s , σ S

Stress,σ

f x(x)f x(x)

xcx

Prob. density

Fatigue life models


13/22


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 0 eqi

n N N N m D E S A 1 S

N K K B K


Fatigue reliability baed on SN formulationConsider

failure probability in a given (service time) period:

Assume

m, B, No deterministic

so, k and Δ lognormal distribution

( ) ( )

m

i o o

m B

i o

n N s mDB N K ln N

= = Γ +∑ 1

[ ]f P P D= ≥ Δ

( )

( )( )

o

f

m B

o

m

o o

s K

P

K ln Nm N s

B

V m V V

X X

where the notation is the modal value of

Δ

= Φ −β

ΔΓ +

β =+ +

i

2 2 2

1


1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 5 10 15 20Time

F a

i l u r e

p r o b a b i l i t y

Cumulative failure probability

•Probability of failure in interval t +Δt , given ithas survived up to t

•Suitable for time-dependent problems

•i.e. implicitly accounts for degradation of

structure!

Reliability model (cont…)

Hazard rate, h R(t )

Implied reliability

Ca

se

Δ

allow

able

Service

life

P f

Annual

hazard

rate 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

F a

i l u r e


Annual hazard rate


( )( )

1 ( ) R

t h t

F t =

−

F (t ) – distribution of time to failure

f (t ) – probability density function

If F (t ) is the fatigue P f accumulated up to t

and f (t ) the “instantaneous” Pf evaluated at t ,

Then

h R(t ) = Annual hazard rate or annual fai lure probabil ity for fat igueT.Moan MARE WINT Sept.201352

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

Fat igue de sign factor

F a i l u r e



Cumulative, stdv(lnA )=0.15

Cumulative, stdv(lnA )=0.3

Ann ual fa ilure pro bability

Ann ual, std v(lnA )=0.15

Ann ual, std v(lnA )=0.3

Fs(s) = 1 – exp(-(s/A)B)

.... 0.1 1.01/

= ≤

= −=

∑ i allowablei

allowable

n D D

N

FDF D


14/22


Fracture mechanics model

Basic model

Fatigue failure event:

g(x) = acr – a(C, m, lnA, B) ≤ 0

C, m - material parameters

lnA, B - load effect (stress) parameters

NO, Δ - deterministic

Reliability calculation by FORM/SORM or

Monte Carlo Simulation

[ ]f g( ) 0

p P g( ) 0 f (x)dx ( )≤

= ≤ = = Φ −β∫∫x

x


Reliabili ty model (cont…)

P r o b a b i l i t y

d e n s i t y ,

f A ( a )

Plate thickness a(t ) – crack depth

Time in-service

Calculated probability of through thickness crack(without updating)

aupd (t i)

a0t i

a(t i)

P r e d i c

t e d m e a

n c r a c

k s i z e

P r o b a b i l i t y

d e n s i t y ,

f A ( a )

Plate thickness a(t ) – crack depth

Time in-service

Calculated probability of through thickness crack(without updating)

aupd (t i)

a0t i

a(t i)

P r e d i c

t e d m e a

n c r a c

k s i z e

[ ]( ) 0 f P P M t = ≤

Fatigue failure probability, P f

( ) ( ) f t a a t = −

Often used

β – reliability index

Φ – standard normal distribution

( ) f P β = Φ −

Predicted

crack size

Final crack size

(plate thickness)1

1 2 2 1 2

0( ) (1 )2m m m m mma t a C S Y N π

− −⎡ ⎤= + −⎣ ⎦

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 access

to 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 water

Butt

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 Current2.08

(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 on

Inspection ( 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 size

aD = detectable crack size

where F AD (a) = POD(a)

• Known outcomes in-service

vs uncertain outcomes at the design stage• Updating late in the service life has larger

influence

Reliability based inspection planning w.r.t. fatigue

Mean detectable

crack depth of 1.5 mm

Pf

CeSOS NTNU

17


15/22


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

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

Fatiguefailureprobabilityin theservice life

Conditionalannualultimatefailureprobability

Target

Level forglobal failure ofthe structure;Depending onthe 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 with

member (i) removedT.Moan MARE WINT Sept.201358

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

Noinspection

R e l i a b i l i t y l e v e l , β

Time (years)

1st inspection 2nd inspection

Target levelfor a given joint

In-service scheduling of inspections

to 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 the

consequences of failure

1 .2 1 .4( ) 10

0.85 0.7 log

β

β

−Φ − ≈

≈ −

= f f P

P

CeSOS NTNU

18

βT


Contribution to cumulative fatigue damage ofwind loads, wave loads and interaction of windand wave loads

Tubular

Joints

Characteristic fatigue damage

Raw

data

Weibull

model

General-

ized

gamma

model

Leg1-

Joint20.0881 0.0859 0.0952

Leg1-

Joint30.2713 0.2714 0.2862

Sur12-

Joint10.2142 0.2069 0.2213

Leg2-

Joint20.0876 0.0836 0.0889

Characteristic fatigue damage

for different model

Long term fatigue analysis of multi-planar tubular joints

In 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. .0.1corr R =

Reliability index for welded joints in

jacket as a function of time. ,

years, mm, mm, and

mm.

0.1corr

R =5 pt t =0.11

Ra =

00.11a = 2.0

Da =

Fatigue reliability analysis of multi-planar welded

tubular joints considering corrosion and inspection

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


16/22


Reliability - based calibration of FLS requirements

Design criterion :

FDF - depends upon:

• consequence of failure

• inspection quality

Criterion:

( ) ( ) fsysT P 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

with

inspection

no

inspection

Δd = 0.1

Δd = 0.2

Δd = 0.3

Time after installation t [year]

R e l i a b i l i t y i n d

e x β

∑ =Δ≤= FDF/1 N

nD d

i

i


Main purpose:

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

(2) Check the effects of globalmodel on the contact forcecalculation.

Time domain based simulation model of 750 kW

land-based wind turbine Comparison between coupled and decoupled analysis method:


• Model for crack propagation:

Linear elastic fracture mechanics (LEFM) model

is used:

( ) _ m

II eff da C K dN

= ⋅ Δ

, :C m material parameters, which can be

determined by experiments;

:a half crack length;

: N cycle numbers;

_ : II eff K Δ effective Mode II (shear) stressintensity factor range ; dependent on

Hardness ; 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


17/22


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 largeenough (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 possiblyimprove 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


18/22


Risk Assessment in Offshore Safety

ManagementWith 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 Collapse

Limit 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

RiskReducingMeasures

RiskReducingMeasures

Frequency

Analysis

Consequence

Analysis

Risk Acceptance

Criteria

Risk Acceptance

Criteria

Acceptable Acceptable

Unacceptable

Tolerable

Critical

eventFault tree Event tree

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

fixed p latforms: ~ 150 000

mobi le 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 andMatha, 2010)

Wilkinson et al., 2011

P i t c h s y s t e m

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

-1

-0.5

0

0.5

1

1.5x 10

4

T o w e r

T o p B M Y , k N m

TLP, EC 5

time - TF, s

B

C

Shut downturbine quickly

Faultoccurs

Continueoperating withfaulted blade


External hazards: Accidental Loads

1Explosion loads(pressure, duration - impulse)

scenarios

explosion mechanics

probabilistic issues⇒ characteristic loads for design2 Fire loads

(thermal action, duration, size)

3 Ship impact loads(impact energy, -geometry)

4 Dropped objects

5 Accidental ballast

6 Unintended pressure

7 Abnormal Environmental loads8 Environmental loads on platform

in abnormal floating position

A id t l C l l Li i t St t


19/22


Accidental Col lapse Limit State

relating to structural strength (NPD,1984, later NORSOK)

• Estimate the damage due toaccidental event (damage, D or action, A) at an

annual probability of 10-4

- apply risk analysis to establishdesign 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 empi rical data of the order 2/p = 20 000 years

to estimate events by empirical approach

Accumulated plat form years world wide:

- fixed platforms: ~ 180 000

- mobile units: ~ 20 000

- FPSO: ~ 2 000

Account of all measures to reduce the probabil ity and c ons equences 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 submarinesT.Moan MARE WINT Sept.201376

Risk reduction

- ship collision risk

• reduce risk by

reducing the prob.

(traffic control) and/or the

consequences of collision

• Design for collision events

- Min collision: Supply vessel

5000 tons displacement

and a speed of 2 m/s;

i.e. 11, 14 MJ

(to be increased!)

- collision events with trading vessels

(with a probability of exceedance of

10- 4 ) site specific events identified by

risk analysis

Collisions do occur.

Frequency of Impact by Passing Vessels


20/22


– 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

1k

jk ,FR ijk ,CC

5

1 j

ijC PP NP

CP

ij N

ijk ,CCP

jk ,FR P

Probability density

of ship position

ij,CCP

platform

C e n t r e l i n e

– probability that a vessel with a size (j) in

navigation group (k) does not succeed in

avoiding the platform


Calculation of impact damage

External mechanics

The fraction of the kinetic energy to be

absorbed as deformation energy(structural damage) is determined by

means of:

Conservation of momentum

Conservation of energy

Internal mechanics

Energy dissipated by vessel

and offshore structure

Equal force level

Area under force-def. curvedws dwi

R iRs

Ship FPSO

Es,sEs,i

External mechanics

Internal mechanics

Measure of damage:

Indentation depth


Ultimate global collapse analysis of platforms

Non-linear analysis to assess

the resistance of

- intact and damaged structures

by accounting for

geometrical imperfection,

residual stresses

local 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 st rength

of damaged

North Sea jacket.Linear pile-soil model

Ultimate strength

Broad side loading

Brace261

Brace363

Brace463

Ultimate strengthFult / FH100

2.73 2.73 2.73

Residual strength

Fult(d) / Fult

1.0 0.76 1.0

7 0 m 5 6

m

main structure

deck

(261)

(363)

(463)

Broad-side and end view.

Deck model indicated by dashed line

(261)

(363)

(463)

(455)(456)

collision

dropped

object

29

Framework for Risk based Design against


21/22


Framework for Risk-based Design against

Accidental actions

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

,

)( i

jk

k j

i

jk FSYS A P A D P D FSYS P i P ∑ ⋅⋅=

probability of damagedsystem failure under

relevant F&E actions

probability of damage, D

given A jk(i) (decreased

by designing againstlarge A j

(i))

probability of accidentalaction at location (j)

and intensity (k)

(i)

jk P 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 andtheir correlation with the haazard causing the damage

For each type of

accidental action


Accidental act ions for wind turbines

IEC 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 such

a way that –in the event of collision

with a ship, the hull of the ship shall

be 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

Al tenative jacket

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

Collapse mode is favourable –

nacelle drops into sea

•Upper weak soil

layers beneficial

30


22/22


Concluding remarks

Experiences regarding

- failures and accidents and

- life cycle safety managementfor oil and gas installations can serve as a basis for structures

in other offshore industries, notably wind turbines,

- when the differences between

the oil and gas and the other industriesare recognised

In particular

- normal uncertainty and variability in structural

performance as well as possible “gross errors” in fabricationand operation should be properly considered in the decision

process

CeSOS NTNU

Thank you! T.Moan MARE WINT Sept.201386

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 wavesand 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 andRequalification 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.

083 Moan Structural Reliability

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