A fatigue model for evaluating the damage of container vessels during

various sea states

Igor Rychlik, Jonas Ringsberg, Gaute Storhaug

Wengang MaoWengang MaoEmail: wengang@chalmers.se

Dept. of Mathematical Sciences, Chalmers University of TechnolDept. of Mathematical Sciences, Chalmers University of Technologyogy

UTMIS Network, Eskilstuna, Sweden2009/01/28 ~ 2009/01/29

2/16

OutlinesOutlines

Fatigue of Marine structures

Shipping routing tool

Fatigue model in terms of Hs

Validation of proposed model

Conclusions and further work

References

3/16

FatigueFatigue of Marine structuresof Marine structures

Vibration period of ≈ 2 seconds

Ship operating during storm (big Hs) induced structure vibration

Fatigue cracks observed in ship after 5 years serviceTanker operated in the storm

4/16

Fatigue Issues Today & FutureFatigue Issues Today & Future

Future fatigue challenge due to maritime conditions:• globalization - increase of transports, changes of ship routes,

larger vessels will be launched!• climate changes - more severe storms?• melt of polar ice - the north-west passage for transporting

goods between EU/US and Asia?

One of the biggest container vessel 350 m long

5/16

Ship Routing Tool (Fatigue inside?)Ship Routing Tool (Fatigue inside?)

Commercial routing tool used in the shipping market (with updated weather information 6-24 hours)

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0 2000 4000 6000 8000 10000 12000 14000 16000-150

-100

-50

0

50

100

150

Record No. of measurement in 10 minutes

Res

pons

e st

ress

[MP

a]

Rain-flow counting method

Time series of stress

1, Rainflow fatigue analysis

Fatigue model of HsFatigue model of Hs

2, Narrow-band approximation (NBA)

Hs – significant wave height Tz – crossing period of wavesU – ship speedβ – heading angle

-100 -50 0 50 100 150-4

-3

-2

-1

0

1

2

3

4

Qua

ntile

s of

sta

ndar

d no

rmal

0.01%

0.1%

0.5%1%2%5%10%

30%

50%

70%

90%95%98%99%99.5%

99.9%

99.99%

Measured stress [MPa]

7/16

Narrow band approximation

NBA for expected fatigue damage[ ] αα /47.0)2/1(2)/()( 32/

szmm

sznb htfmhtftDE =+Γ≈ −

Response should be available!

zero upcrossing response frequencyzfsignificant response heightsh

1. Ship time series response X(t) from measurement

zf

[ ])0(44 0 XVhs == λ

zero upcrossing frequency of X(0)

8/160

22λλ

π ⋅⋅=zf04 λ⋅=sh

Narrow band approximation

∫ ⋅= πσσ ααββ 2

02 ),(|),|(|),,,|( dwSUwHTHUwS eezse

∫ ∫ += ∞0

20

22 )()(),|(cos)/(π ααββλσ

dwdfwSUwHgUwwn

n

2. Ship response spectrum S(ω) from software simulation

2.1 Ship response spectrum

2.2 Response spectral moments

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Fatigue model of HsFatigue model of Hs

∫ ⎥⎦

⎤⎢⎣

⎡−⋅= ∞ −0

454

232 )

2(1exp4),|(4 dwwT

wTHUwHh z

z

ss ππ

πβσ

1. Significant response height

Constant Ci :

Polar diagram of C depends on heading angle and ship speed

∑==

n

iii tfCC

1)(

Tz has fixed distribution f(ti) from long-term wave statistics:

a) Fatigue estimation in one sea state (20-30 minutes)

b) Fatigue estimation of long period (1 voyage)

c) Constant Ci depends on HDG and ship speed

)(/)(),,( iHihTzUC s=β

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Fatigue model of HsFatigue model of Hs

2. Zero upcrossing response frequency

sz HT ⋅= 75.3281.9cos21

zzz T

UT

f βπ+=

3. Further simplification

0

22λλ

π ⋅⋅=zf (Gaussian process)

Zero upcrossing of 4 typical response

(Gaussian process, proposed model, and measurement)

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅≈∑=

i

siis

iivoy g

HUHTCdD 2

20

5.23

75.32

75.347.0 πα

Ship speed assumed to be service speed U0, HDG 0 to make acceptable conservative

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Validation of the fatigue modelValidation of the fatigue model

80oW 60oW 40oW 20oW 0o

12oN

24oN

36oN

48oN

60oN

2800 TEU Vessel in North Atlantic

Strain gauge (time series of stress)

Onboard Radar (wave measurement)

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0 2 4 6 8 1 0 1 2

x 1 0 5

- 2 0 0

- 1 5 0

- 1 0 0

- 5 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

Measured data

05

1015

2025

3035

40

05

1015

2025

3035

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1. Time series stress (signal) of the whole voyage (left) & one typical sea state (right)

2. Sea states (directional wave spectra) of whole voyage (left) & one sea state (right)

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Validation of the model

7 voyages from Canada to Europe

Fatigue damage distribution along different voyages Damage of different voyages by RFC (x-axis) vs proposed model (y-axis)

0 1 2 3 4 5 6 7 8 9

x 10-3

0

1

2

3

4

5

6

7

8

x 10-3

Fatigue damage estimated by Rain-flow method

Fatig

ue d

amag

e es

timat

ed b

y th

e pr

opos

ed m

odel

Fatigue estimated by preliminary modelFatigue estimated by improved model

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

1.2

1.4x 10-4

No. of different sea states

Fatig

ue d

amag

e ac

cum

ulat

ion

Fatigue damage estimated by rain-flow methodFatigue damage estimated by proposed modelFatigue damage estimated by DNV softwareseparator marker for different voyages

7 from Canada to EU & 7 from EU to Canada

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Further investigation

• Springing– Resonance– Oscillating loads along the hull

• Whipping– Transient response– Wave impacts in bow and stern

1. Non-Gaussian properties, such as:

How much influence of these non-Gaussian response?

2. Other types of vessels?

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Conclusions and Future work

The fatigue estimation model proposed here works well ( comparing with the rain-flow estimation)

For the fatigue estimation location of above vessel, the constant C is 20 for head sea, and 14 for following sea

There are some uncertainties of fz in the model…

Include uncertainties for reliability analysis…

Whipping influence …(further work)

Routing tool design….

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References

1. Mao, W., Ringsberg, J., Rychlik, I. and Storhaug, G., 2008, “A fatigue model applicable for evaluation of the fatigue damage accumulated in container vessels during various sea states ”, Submitted.

2. Mao, W., Ringsberg, J., Rychlik, I. and Storhaug, G., 2008, “Estimation of Fatigue Damage Accumulation in Ships during Variable Sea State Conditions”, Submitted.

3. Mao, W., Rychlik, I. and Storhaug, G., 2008, “Safety index of fatigue failure for ship structural details”, Submitted.

4. Rychlik, I., 2000, “On Some Reliability Applications of Rice's Formula for the Intensity of Level Crossings”, Extremes, 3:4, 331-348.

5. Rychlik, I., 1993, “On the "Narrow-band" Approximation for Expected Fatigue Damage”.

6. Rychlik, I., 1987, “A New Definition of the Rainflow Cycle Counting Method”. 7. WAFO-group, 2000, “WAFO - a Matlab Toolbox for Analysis of Random Waves

and Loads - A Tutorial”.8. Bendat, J.S., 1964, “Probability Functions for Random Responses: Prediction of

Peaks”.9. Lewis, E.V., 1989, Principles of Naval Architecture: Volume III - Motions in

Waves and Controllability, Society of Naval Architects and Marine Engineers.