efficient prediction of extreme ship responses
DESCRIPTION
Efficient prediction of extreme ship responses. by MingKang Wu Centre for Ships and Ocean Structures, NTNU Norwegian Marine Technology Research Institute. Outline. Predictions of long-term and short-term extreme ship responses (nonlinear VBMs and VSFs) Time-domain nonlinear simulation - PowerPoint PPT PresentationTRANSCRIPT
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Efficient prediction of extreme ship responses
by
MingKang WuCentre for Ships and Ocean Structures, NTNU
Norwegian Marine Technology Research Institute
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Outline
Predictions of long-term and short-term extreme ship responses (nonlinear VBMs and VSFs)
Time-domain nonlinear simulation Sensitivity study Statistical uncertainty
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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
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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
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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
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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
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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
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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
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Time-domain nonlinear simulation
Calculation of slamming force Wagner Von Karman + correction for pile-up water Von Karman (momentum slamming)
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Time-domain nonlinear simulation
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
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Time-domain nonlinear simulation
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
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Time-domain nonlinear simulation
Example
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Time-domain nonlinear simulation
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
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Time-domain nonlinear simulation
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 Hybrid method, flexible hull, 1 mode
Head seas
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Time-domain nonlinear simulation
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]
Direct calculation, rigid hull Modal superposition, flexible hull, 1 mode Modal superposition, flexible hull, 2 modes Modal superposition, flexible hull, 3 modes
Head seas
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Time-domain nonlinear simulation
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 frequency [rad/sec]
Direct calculation, rigid hull Hybrid method, flexible hull, 1 mode
Head seas
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Time-domain nonlinear simulation
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
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
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Time-domain nonlinear simulation
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
Incident circular wave frequency [rad/sec]
Direct calculation, rigid hull Hybrid method, flexible hull, 1 mode
Head seas
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Time-domain nonlinear simulation
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
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Time-domain nonlinear simulation
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]
Direct calculation, rigid hull Hybrid method, flexible hull, 1 mode
Head seas
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Time-domain nonlinear simulation
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 calculation, rigid hull Modal superposition, flexible hull, 1 mode Modal superposition, flexible hull, 3 modes
Head seas
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Time-domain nonlinear simulation
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
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Time-domain nonlinear simulation
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]
Direct calculation, rigid hull Modal superposition, flexible hull, 1 mode Modal superposition, flexible hull, 3 modes
Head seas
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Time-domain nonlinear simulation
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]
Direct calculation, rigid hull Hybrid method, flexible hull, 1 mode
Head seas
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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
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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
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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
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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
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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
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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.
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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
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