efficient prediction of extreme ship responses

MARINTEK

Efficient prediction of extreme ship responses

by

MingKang WuCentre for Ships and Ocean Structures, NTNU

Norwegian Marine Technology Research Institute

MARINTEK

Outline

Predictions of long-term and short-term extreme ship responses (nonlinear VBMs and VSFs)

Time-domain nonlinear simulation Sensitivity study Statistical uncertainty

MARINTEK

Prediction of long-term extreme ship responses

Probability of exceedance

Separation of wave heading and sea state Equal probability of different wave headings Scatter diagram

( ) ( ) ( ) ( , )z s

long term e short term e s zT H

P R r P R r P P H T

MARINTEK

Prediction of long-term extreme ship responses

Minimum steering speed is about 5 knots Head seas is the most critical wave heading as far as VBMs and

VSFs are concerned Only a few sea states are relevant to the extreme ship responses

Part of the IACS scatter diagram (Total number of occurrences is 100,000)

Hs (m)

Tz (s)

9.5 10.5 11.5 12.5 13.5 14.5

8.5 255.9 350.6 296.9 174.6 77.6 27.7

9.5 101.9 159.9 152.2 99.2 48.3 18.7

10.5 37.9 67.5 71.7 51.5 27.3 11.4

11.5 13.3 26.6 31.4 24.7 14.2 6.4

12.5 4.4 9.9 12.8 11.0 6.8 3.3

13.5 1.4 3.5 5.0 4.6 3.1 1.6

MARINTEK

Prediction of short-term extreme ship responses

Probability of exceedance per unit time for extreme linear rigid-body responses

Probability of exceedance per unit time for extreme nonlinear flexible-body responses (hydroelastic responses)

2

22( ) r

eP R r n e

( )( )cr

eP R r ne

( 1) ( )( )( )

( )

cc m r

e

r eP R r n

m

MARINTEK

Evaluation of distribution parameters

Method of moments Assumes equal importance of all peak values Distribution function for an overall fit to all peaks may fail to

accurately describe the high peaks

Weighted curve fitting Force the distribution function closer to the simulated one in the

high-value region No theoretical method for selecting the best weighing function Larger weight in the high-value region can produce better

distribution tail but will also increase the statistical uncertainty due to the randomness of individual time-domain simulations of limited period

MARINTEK

Peak Over Threshold (POT)

Conditional distribution function of the peaks over sufficiently high threshold asymptotically approaches generalized Pareto distribution (Pickands, 1975)

Probability of exceedance

1/1 (1 / ) , 0( )

1 exp( / ), 0

ccx cG x

x c

1

( )( ) 1 , 0 and

c

e

c r tP R r k c r t

MARINTEK

Time-domain nonlinear simulation

Computer program WINSIR (Wave-INduced ShIp Responses).

Potential flow theory. Total response=linear response + nonlinear modification. Linear response.

3D approach 2.5D approach (high-speed strip theory) 2D approach (conventional strip theory)

Nonlinear modification. Nonlinear Froude-Krylov and restoring forces Slamming force Viscous roll damping

MARINTEK


Calculation of slamming force Wagner Von Karman + correction for pile-up water Von Karman (momentum slamming)

MARINTEK


Calculation of load effects Conventional approach for rigid ship hull

Modal superposition for flexible ship hull

Hybrid method (mode acceleration)

1 11 2

( ) ( ) ( ) ( )d qi i i i

i i

r t c p t c p t c p t

Hydrodynamic force

Inertia force

1 1 1 1 12 1

1 1 1

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

[ ( ) ( )] ( )

d q d q qi i i i

i i

d q rb

r t c p t c p t c p t p t c p t

c p t p t r t

MARINTEK


Example

Main particulars of the SL-7 containership and the LNG ship

ParameterSL-7 LNG

Length between perpendiculars (m) 270 324

Breadth (m) 32.2 50.0

Draught amidships (m) 9.95 11.7

Displacement (tonnes) 50500 148350

Block coefficient 0.585 0.753

Centre of gravity aft of amidships (m) 9.80 1.37

Centre of gravity above base line (m) 13.7 16.3

Radius of gyration in pitch (m) 65.5 80.8

Moment of inertia amidships (m4) 350 1200

MARINTEK


Example

MARINTEK


Example

2.0x109

1.5

1.0

0.5

0.0

RA

O o

f V

BM

am

idsh

ips

[N]

1.41.21.00.80.60.4

Incident circular wave frequency [rad/sec]

Direct calculation, rigid hull Modal superposition, flexible hull, 1 mode Modal superposition, flexible hull, 2 modes Modal superposition, flexible hull, 3 modes

Head seas

MARINTEK


Example

2.0x109

1.5

1.0

0.5

0.0

RA

O o

f V

BM

am

idsh

ips

[N]

1.41.21.00.80.60.4


Direct calculation, rigid hull Hybrid method, flexible hull, 1 mode

Head seas

MARINTEK


Example

600x106

500

400

300

200

100

0RA

O o

f V

BM

at

205m

for

war

d of

AP

[N

]

1.41.21.00.80.60.4

Incident circular wave requency [rad/sec]


Head seas

MARINTEK


Example

600x106

500

400

300

200

100

0RA

O o

f V

BM

at

205m

for

war

d of

AP

[N

]

1.41.21.00.80.60.4



Head seas

MARINTEK


Example

20x106

15

10

5

0

RA

O o

f V

SF

at

205m

for

war

d of

AP

[N/m

]

1.41.21.00.80.60.4



Head seas

MARINTEK


Example

-8x109

-6

-4

-2

0

2

4

6

8

VB

M a

mid

shps

[N

m]

27.55x103 27.5327.5227.5127.5027.49

Time [sec]

Direct calculation, rigid hull Modal superposition, flexible hull, 1 mode Modal superposition, flexible hull, 3 modes

Head seas

MARINTEK


Example

-8x109

-6

-4

-2

0

2

4

6

8

VB

M a

mid

ship

s [N

m]

27.55x103 27.5327.5227.5127.5027.49

Time [sec]


Head seas

MARINTEK


Example

-4x109

-2

0

2

4

VB

M a

t 20

5 m

for

war

d of

AP

[N

m]

27.55x103 27.5327.5227.5127.5027.49

Time [sec]


Head seas

MARINTEK


Example

-4x109

-2

0

2

4

VB

M a

t 20

5 m

for

war

d of

AP

[N

m]

27.55x103 27.5327.5227.5127.5027.49

Time [sec]

Direct calculaton, rigid hull Hybrid method, flexible hull, 1 mode

Head seas

MARINTEK


Example

-100x106

-50

0

50

100

VS

F a

t 20

5 m

for

war

d of

AP

[N

]

27.55x103 27.5327.5227.5127.5027.49

Time [sec]


Head seas

MARINTEK

Sensitivity study

Sensitivity of short-term extreme load effects to changes in Stiffness distribution

Modal damping ratio (0.005, 0.01, 0.015)

Stiffness level

1.5

1.0

0.5

0.0

I yy/

I yy

amid

ship

s

1.00.80.60.40.20.0

x/Lpp

Distribution 1 Distribution 2 Distribution 3

MARINTEK

Sensitivity study

Influence of stiffness distribution

Influence of stiffness distribution on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; damping ratio=0.01; P3hrs(Re>r)=0.01; U=5knots; Hs=7.5m, Tz=10.5s

Stiffness

distribution

Sagging Hogging

VBMf/VBMr

Amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

1 1.177 1.116 1.098 1.134 1.130 1.097

2 1.178 1.114 1.097 1.137 1.128 1.101

3 1.175 1.114 1.100 1.134 1.127 1.104

MARINTEK

Sensitivity study

Influence of stiffness distribution

Influence of stiffness distribution on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; damping ratio=0.01; P3hrs(Re>r)=0.01; U=10knots; Hs=7.5m, Tz=10.5s

Stiffness

distribution

Sagging Hogging

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

1 1.335 1.364 1.187 1.190 1.360 1.130

2 1.333 1.360 1.187 1.193 1.360 1.137

3 1.332 1.360 1.189 1.197 1.367 1.136

MARINTEK

Sensitivity study

Influence of modal damping

Influence of modal damping on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; Stiffness distribution 2;P3hrs(Re>r)=0.01; U=5knots; Hs=7.5m, Tz=10.5s

Damping

ratio

Sagging Hogging

VBMf/VBMr

Amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

0.005 1.183 1.093 1.099 1.157 1.158 1.122

0.01 1.178 1.114 1.097 1.137 1.128 1.101

0.015 1.168 1.105 1.095 1.118 1.106 1.087

MARINTEK

Sensitivity study

Influence of modal damping

Influence of modal damping on the short-term extreme vertical load effects in the SL-7 containership modelled as a flexible body. Stiffness level 2; Stiffness distribution 2;P3hrs(Re>r)=0.01; U=10knots; Hs=7.5m, Tz=10.5s

Damping

ratio

Sagging Hogging

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

VBMf/VBMr

amidships

VBMf/VBMr

at 0.25Lpp

VSFf/VSFr

at 0.25Lpp

0.005 1.346 1.357 1.191 1.240 1.484 1.164

0.01 1.333 1.360 1.187 1.193 1.360 1.137

0.015 1.316 1.355 1.184 1.162 1.277 1.110

MARINTEK

Sensitivity study

Variations in the longitudinal stiffness distribution do not produce any noticeable difference in the extreme vertical hydroelastic load effects. Using the simplest constant longitudinal stiffness distribution over the whole ship length is totally acceptable.

50% decrease or increase in the modal damping ratio cause less than 2% changes in the extreme sagging hydroelastic load effects but slightly larger changes in the extreme hogging hydroelastic load effects. Those changes are not considered to be significant in practice. Therefore, using 0.01 as the modal damping ratio can be justified.

MARINTEK

Statistical uncertainty (on-going research work)

Selection of the threshold in the POT method and its impact on the prediction of the short-term extreme load effects

Scattering of the predicted short-term extreme load effects due to the time-domain simulations of limited period

MARINTEK

efficient prediction of extreme ship responses

Documents