Fatigue damage estimation along vessel’s voyages

Chalmers University of Technology

Wengang Mao Igor Rychlik

04/18/23 Smögen Workshop (2008-08) 2

Outline

Background and motivation

Fatigue model in terms of Hs

Application of the fatigue model

Conclusions

04/18/23 Smögen Workshop (2008-08) 3

1.1, Background Vessel construction period Loading period Shipping period 1, Vessel’s fatigue location 2, Loading condition 3, Shipping condition 4, Encountered sea states

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How to estimate vessel’s fatigue damage

1.1, Background

Rain-flow counting method (“correct” fatigue estimation) Narrow bound approximation (NBA) Theoretical method based on NBA

0 2 4 6 8 10 12

x 105

-200

-150

-100

-50

0

50

100

150

200

250

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1.1, Background Vessel’s response process is correlated with its

encountered sea states (5/30 min stationary?)

1900 1950 2000 2050 2100 2150

-80

-60

-40

-20

0

20

40

60

80

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30 minutes’ stationary process check Rain-flow based on the whole voyage signal Rain-flow based on 5 minutes’ signal Rain-flow based on 30 minutes’ signal

1.1, Background

Method/Voyagevoy08010

6voy08012

9voy08021

8voy08060

3

RFC for voyage signal0.009529

40.006236

20.004608

30.000875

4

RFC for 5 min signal0.009340

20.006135

50.004510

60.000810

2

RFC for 30 min signal0.009322

50.006108

20.004498

90.000805

4

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1.1, Background Theoretical fatigue estimation Hydrodynamic RAO’s depends on heading angles

and velocity

),|(),|(),|(),|( 0302010 UwHAUwHAUwHAUwH eteheve

Ai means stress caused by each applied load

Hv – transfer function for vertical bending moment

Hh – transfer function for horizontal bending moment

Ht – transfer function for torsional bending moment

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1.1, Background

Linear wave model Directional wave

spectrum

j

jjjj xktwAw )sin()(

)/cos21/(),(),( 0 gwUwSwS e

Encountered sea states:

Vessel’s response under encountered sea states

2

0

200 ),(|),|(|),,,|( dwSUwHTHUwS eezse

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0

22 zf

04 sh

NBA for expected fatigue damage

)2/1(2)/()( 2/ mhtftDE mmsz

nb

0

2

0 02

02 )()(),|(cos)/(

dwdfwSUwHgUww

n

n

Response zero-crossing frequency

Significant response height

1.1, Background

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Measurement signal process X(t)

zf

)0(0 XV )0(2 XV

)0(44 0 XVhs

Process zero-crossing frequency

1.1, Background

Method based on the measured signal can be taken as the right fatigue criteria

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Comparing among different methods

1.1, Background

Method/Voyage

voy080106

voy080129

voy080218

voy080603

Rain-flow method

0.0080056

0.0056574

0.0044576

0.0007757

NBA estimation

0.0090466

0.0066458

0.0051481

0.0009237

Theoretical method

0.014281 0.018452 0.0079314 0.0014033

Note: Rain-flow and NBA method based on measured signal, Standard method based on theoretical simulation.

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1.2, Motivation—fatigue model of Hs

Drawbacks of the two typical methods 1, Measured signal is seldom available 2, Theoretical RAO’s need more precision 3, RAO’s (FEM & Hydrodynamic software

simulation)

Main motivation 1, Compare different influence factors 2, Simply fatigue model (precise) only in terms

of Hs 3, Check model’s validity

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2, Fatigue model in terms of Hs

Response hs is very correlated with wave Hs, Significant response height:

1 2 3 4 5 6 7 8 90

10

20

30

40

50

60

70

80

90

100

Hs of the P-M wave model

Sig

nific

ant

response h

eig

ht

hs

Encountered significant wave height Hs vs response hs

HDG=0 (short crested sea)

HDG=45 (short crested sea)HDG=0 (long crested sea)

HDG=45 (long crested sea)

ss HCh

1, Relation between response and wave

sh sH

fixed wave Tz

Severe sea states cause heavy stress response!!!

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2, Fatigue model in terms of Hs

Constant C f rom Sesam by di ff erent Tz(PM short crested model )

0. 000

5. 000

10. 000

15. 000

20. 000

25. 000

30. 000

HDG=0 HDG=22. 5 HDG=45 HDG=90 HDG=180

Shi ppi ng headi ng angl es

Cons

tant

coe

ffici

ent

Tz=4sTz=5sTz=6sTz=7sTz=8sTz=9sTz=10sTz=11sTz=12s

Mean C and Wei ghted C f rom Sesam by short P-Mcrested sea

0. 0005. 000

10. 00015. 00020. 00025. 00030. 000

Shi ppi ng headi ng angl es

Cons

tant

coe

ffici

ent

Mean CWei ghted C

Fixed wave Hs, its associate Tz from 4s to 12s has distribution f(t)

Weighted arithmetic average C:

Mean C:

n

iii tfCC

1

)(

n

inCiC

1

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2, Fatigue model in terms of Hs

Significant response height hs observed vs from model

Voyage name voy080106 voy080129 voy080218 voy080603

Constant C 18.4177 17.1639 20.1642 17.3098

1, Constant C works quite well for

the

model in left figure.

2, Constant C for these voyages

around 19

3, C from measurement agrees

well with

theoretical value

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2, Fatigue model in terms of Hs

Assume zero-crossing wave period as:

sz HT 5.3

Hs 1.69 1.21 6.85 6.96 7.39 8.14 7.86 7.50 7.24

Tz (model) 6.73 6.37 10.32 10.75 10.66 10.57 11.22 10.81 10.64

Tz (measure)

4.55 3.85 9.16 9.24 9.52 9.98 9.81 9.58 9.42

This model is ok for the large Hs, but not in the small Hs area

2, Response zero crossing frequency

zf

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2, Fatigue model in terms of Hs Ship’s response frequency should be

corresponding to its encountered wave frequency

Encountered wave frequency is also related with shipping velocity and heading angles

Note: Here the frequency should be encountered wave frequency

20

81.9

cos21

zzz

T

U

Tf

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Response zero up-crossing frequency observed vs simplified model with U0=9m/s, HDG=0

2, Fatigue model in terms of Hs

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3, Application of the fatigue model

5 voyages from Europe to Canada

2 voyages from Canada to Europe

4 special voyages (strange relation between encountered sea states and response)

Voyages between Atlantic ocean travelling in different seasons

80oW 60oW 40oW 20oW 0o

12oN

24oN

36oN

48oN

60oN

The whole measurement positions for all the voyages

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Fatigue damage distribution along voy080106 from different estimation approaches

3, Application of the fatigue model

0 500 1000 1500 2000 2500 30000

50

100

150FDR distribution of voyage080106

voyage time of 5 minutes interval

Fat

igue

dam

age

rate

(F

DR

) fo

r ea

ch 5

min

utes

Rain-flow based on signal of 5 min

Narrow bound based on signal of 5min

Rain-flow based on signal of 30 min

Narrow bound based on signal of 30 min

Narrow bound based on wave Hs & signal Fz of 30 min

Narrow bound based on wave Hs of 30 min

FDR by transfer of DNV and measured wave

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3, Application of the fatigue model

Fatigue damage distribution of voyages from different estimation approaches

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Rain-flow based on signal is “real” fatigue damage

5 and 30 minutes’ periods both assumed stationary

3, Application of the fatigue model

　 Rain-flow NBA on signal NBA on HsNBA on Hs

C=19Theoretical

method

voy080106 0.0080056 0.0090466 0.0092165 0.010119 0.014281

voy080129 0.0056574 0.0066458 0.0064218 0.008711 0.018452

voy080218 0.0044576 0.0051481 0.0059341 0.0049645 0.0079314

voy080603 0.00077569 0.00092373 0.0009877 0.0013062 0.0014033

voy080424 0.0027238 0.0034017 0.0038636 0.003574 0.0054558

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2 voyages from Canada to EU

3, Application of the fatigue model

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80FDR distribution of voyage080613

voyage time of 5 minutes interval

Fatig

ue d

amag

e ra

te (F

DR

) for

eac

h 5

min

utes

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80FDR distribution of voyage080411

voyage time of 5 minutes interval

Fat

igue

dam

age

rate

(F

DR

) fo

r ea

ch 5

min

utes

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Constant C and Fatigue damage accumulation

3, Application of the fatigue model

Voyage name voy080613 voy080411

Constant C 19.0415 19.0201

　 Rain-flowNBA on signal

NBA on Hs

Theoretical method

voy080613

0.0014449 0.0015205 0.0017229 0.0023782

voy080411

0.0024546 0.0026607 0.002717 0.0043745

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4 special voyages from Canada to EU

3, Application of the fatigue model

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Constant C and Fatigue damage accumulation

3, Application of the fatigue model

Voyage name voy071018 voy071030 voy071106 voy080117

Constant C 9.3668 13.1514 6.6783 13.9028

　 Rain-flowNBA on signal

NBA on Hs

Theoretical method

voy071018 0.0005967 0.00077517 0.0008542 0.0055091

voy071030 0.0015034 0.001566 0.0012096 0.0038603

voy071106 0.00016725 0.00021562 0.0001931 0.0021606

voy080117 0.0014336 0.0019291 0.0034943 0.0052134

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4, Conclusions1. Our fatigue estimation model works quite well, and its

precision is much better than the theoretical method

2. For the fatigue estimation location of above vessel, the constant C keeps about 19

3. There are a lot of uncertainties in the model (hs, fz)…

4. Comparing to the other parameters, wave Hs is the most important factor of fatigue damage …(further work)

5. Need to check wave spectrum measurement by satellite wave model…

6. Put this model in shipping routing application…