Date Author Address
March 2007
Tuitman, IT. and W. Trouwborst Deift University of Technology
Ship Hydromechanics Laboratory
Mekelweg 2, 26282 CD De!ft
TU'Delft
Deift University of Technology
Page /of 1/1
Derivation of slamming loads using the optimal state estimation method
by
iT. Tuitman and W. Trouwborst
Report No. 1521-P 2007 Proceedings of MARSTRUCT 2007, Thert International
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PROCEEDINGS OF MARSTRUCT 2007, THE 1ST INTERNATIONAL CONFERENCE ON MARINE STRUCTURES, GLASGOW, UNITED KINGDOM, 12-14 MARCH 2007
Advancements in Marine Structures
Editors
C. Guedes Soares
Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal
P.K. Das
Universities of Glasgow and Strathclyde, Glasgow, Unfted Kingdom
Taylor & Francis
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Advancements in Marine Structures - Guedes Soares & Das (eds) 2007 Taylor & Francis Group, London, ISBN 978-0-415-43725-7
Table of Contents
Preface IX
Methods and tools for loads and load effects
Uricertainty of average wave steepness prediction from global wave databases 3
E.M Bitner-Gregersen & C. Guedes Soares
Wave induced global loads for a damaged vessel 11
L. Folsø, E. Rizzuto & E. Pino
Effect of ship length on the vertical bending moments induced by abnormal waves 23
N Fonseca, C. Guedes Soares & R. Pascoal
On extreme ship response in severe short-term sea state 33
T Fukasawa, H. Kawabe & T Moan
The 2D numerical modelling of slamming on a wedge and bow shape using the
finite volume method 41
A. loan & L. Domnisoru
Extreme value predictions and critical wave episodes for marine structures by FORM 51
.1 Juncher Jensen
Extreme response estimation for marine structures based on design contours and
response surface methods 61
B.J Leira
Ship weather routing based on seakeeping performance 71
MB. Pacheco & C. Guedes SOares
Time domain simulation of ship global loads due to progressive flooding 79
TA. Santos & C. Guedes Soares
Investigation of the variation of loads experienced by a damaged ship in waves 89
TWR Smith, K.R. Drake & S. Rusling
Derivation of slamming loads using the Optimal State Estimation Method 99
iT Tuijinan & W Trouwborst
Effective breakwaters for high speed container vessels 107 KS. Varyani & XE ?ham
Methods and tools for strength assessment
The racking analysis in the early stages of the structural design 117 VAmatulli, M Biot & L. Schffrer
Broadband excitation induced by propellers and ships comfort evaluation 127
F Besnier N Buannic, L. Jian, A. .Blanchet & S. Branchereau
VI
Numerical analysis of eigen vibration modes for an orthotropic ship structural panel 135
I. Chirica & L. Domnisoru
Non-linear hydroelastic response analysis in head waves, for a large bulk carrier ship hull 147
L. Domnisoru & A. loan
Round Robin study on structural hot-spot and effective notch stress analysis 159
W Fri cke, A. BolIem, I. Ozirica, Y Garbato F Jancart, A. Kahi, H. Remes, CM. Rizzo,
H. von Selle, A. Urban & L. Wei
Fatigue strength assessment of floating production storage and unloading vessels 169
V Garbatov, S. Tomasevic & C. Guedes Soares
Effects of changes in curvature on the natural characteristics of curved structures 177
B. Hu, fT Xing, R.A. Shenoi & J Smith
Hydroelastic analysis of cantilever plate in tune domain 187
F Kara & D. Vassalos
Residual strength and survivability of ships under combined vertical and horizontal bending 197
l.A. Khan & RK. Das
Collapse strength of longitudinal plate assemblies with dimple imperfections 207
R.M Luls, C. Guedes Soares & RI. Nikolov
First - principles collision analysis for design 217 G. Mermiris, D. Vassalos & D. Konovessis
On the influence of boundary conditions on the vibrations of ship propulsion systems 225
L. Murawski
Development of a numerical simulation method for fatigue crack propagation in structures
under variable amplitude loading 233
T Okawa & V Sumi
A method for progressive structural crashworthiness analysis under collisions and grounding 241
JK. Paik & JK Seo
Methods for ultimate limit state assessment of marine structures: A benchmark study 249
f K. Paik, JK. Seo, Bi Kim, VS. Suh & B.S. fang
Bending response of laser-welded web-core sandwich plates 263
J Romanoff& P Varsta
Studies on the behaviour of bottom structures during grounding 273
M.S. Samuelides, J Amdahl & R. Dow
Global strength analysis in head waves, for a tanker with longitudinal uniform structure 283
L. Stoicescu & L. Domnisoru
A numerical approach for fatigue crack propagation in ship structures underwave
loading - A review of the development of CP-System 295
YSumi&TOkawa
The natural vibration characteristics of a water-shell tank interaction system 305
fTXing, YRXiong&M Tan
Natural dynamic characteristics of an integrated liquid - LNG tank - water interaction system 313
VII
Analysis of sharp corners in structural details 323
L. Xu & N Baritrop
Formulation for ultimate shear strength of ship structure 331
S. Zhang & P Kumar
Experimental analysis of structures
Comparison of experimental and numerical impact loads on ship-like sections 339
A. Joan, S. Brizzolara, M. Vwiani, N Couly, R. Donner 0. Her,nundstad, T Kukkanen, S. Malenica & P Temarel
A plea for large-scale testing 351
B. Boon
Numerical study of the absorbed energy in clamped steel beams with different lengths
under transverse impact 357
D.M Dimas & C. Guedes Soares
Measuring damping properties of viscoelastic materials for marine applications 367
A. Ferrari & E. Rizzuto
Experimental evaluation of the behaviour of a mild steel box girder under bending moment 377
JM. Gordo & C. Guedes Soares
An experimental and numerical study on GFRP box girder under pure bending 385
C. Guedes Soares, NZ C'hen, FM Santos & C. Santos
Structural loads and response analysis for a Canadian frigate 391
D.C. Stredulins/cy, N G. Pegg & C.P Gardiner
A benchmark study on ductile failure criteria for shell elements in multiaxial stress state 401
K Tabri, H. Alsos, J Broekhujsen & S. Ehiers
Materials and fabrication of structures
Buckling strength of square composite plates with geometrical imperfections - Preliminary results 413
Berggreen, C. Jensen & B. Hayman
Vibration characteristics of smart sandwich beams embedded with magnetorheological
elastomer cores 421
WJ Choi, YR Xiong & R.A. Shenol
Improving the strength of adhesive butt joints for pultruded composites 429
S.A. Hashim, 0. Fozzard & EK. Das
A review of the causes of production defects in marine composite structures and their influence on performance
Hayman, C. Berggreen & N. G. Tsouvalis
Methods and tools for structural design and optimization
Benchmark on ship structural optinusation 453
N. Besnard, M. Codda, A. Ungaro, C. Toderan, A. Kianac & F Pécot
A concept of 0mm-optimization for ship structural design 473
A. Kianac & J Jelovica
Least cost optimization of a large passenger vessel 483
T Richir N Losseau, E. Pircalabu, C. Toderan & P Rigo
Structural optimization in fatigue-life assessment concerning a DDG of Ammiragli Class of
the Italian Navy 489
G. Vacca, Mi Galliussi & S. Simone
Decision support problem formulation for structural concept design of ship structures 499
V Zanic, P Prebegn & S. Kitarovic
Structural reliability, safety and environmental protection
Holistic analysis of ship's sustainability 513
0. Cabezas-Basurko, E. Mesbahi & S.R. Moloney
Inland water going ship risk assessment 523
G.VEgorov
Impact of the new common structural rules on the reliability of a bulk carrier 529
A. W Hussein, A.R Teixeira & C. Guedes Soares
Practical reliability assessment method of ship's hull girder in longitudinal bending 539
KIjima,YFujii&TYao
Structural system reliability using FEM and reliability processors 547
MShahid&RK.Das
Structural reliability levels in Ice Class rules 557
X Wang,HSun&R.Basu
Factors affecting the non-destructive inspection of marine structures 565 A. Zayed, l Garbatov & C. Guedes Soares
Author index 577
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Advancements in Marine Structures - Guedes Soares & Das (eds)
2007 Taylor& Francis Group, London, ISBN 978-0-415-43725-7
Conference Chairmen
Prof. Carlos Guedes Soares, 1ST, Technical University of Lisbon, Portugal
Prof. Purnendu K. Das, Universities of Glasgow & Strathclyde, UK
Technical Programme Committee
Prof. N. Baritrop, University of Glasgow & Strathclyde, UK Dr. N. Besnard, Principia Marine, France
Dr. M. Codda, CETENA, Italy
Prof. R.S. Dow, University of Newcastle upon Tyne, UK
Prof. W Fricke, TUHH, Germany Dr. S. Gielen, TNO, Netherlands
Prof. J.M. Gordo, 1ST, Technical University of Lisbon, Portugal
Prof P.F. Hansen, DTU, Denmark Dr. B. Hayman, DN\ç Norway
Prof A. Incecik, University of Newcastle upon Tyne, UK Prof T. Jasirzebski, TUS, Poland
Prof J.J. Jensen, DTU, Denmark
Dr. J. McGregor, Bureau Veritas, France
Prof T Moan, NTNU, Norway Prof V. Papazoglou, NTUA, Greece
Prof R.A Shenoi, University of Southampton, UK Prof P. Temarel, University of Southampton, UK
Prof A. Ulfvarson, Chalmers University of Tech., Sweden
Prof P. Varsta, Helsinki University of Technology, Finland
Advisory Committee
Dr. R.I. Basu, ABS, USA Prof. WC. Cui, CSSRC, China
Dr. M. Dogliani, RENA, Italy
Prof S. Estefen, COPPE, Brazil Dr. P. Hess, NSWC, USA
Dr. M.L. Kaminski, MARlIN, The Netherlands Prof. J.K. Paik, Pusan National University,. Korea
Dr. N.G. Pegg, DND, Canada Dr. R. Porcari, CETENA, Italy
Dr. B.C. Simonsen, DN Norway
Prof Y Sumi, Yokohama National University, Japan
Dr. P.M. Videiro, Petrobras, Brazil Dr. S.G. Waestberg, DNV, Norway Prof T. Yao, Osaka University, Japan
Conference Secretariat
Alma Moise, 1ST, Technical University of Lisbon
Maria de Fatima Pina, 1ST, Technical University Of Lisbon
Nicola Pollock, Universities of Glasgow & Strathclyde
V
Advancements in Marine Structures - Guedes Soares & Das (eds) © 2007 Taylor & Francis Group, London, ISBN 978-0-415-43725-7
Derivation of slamming loads using the Optimal State
Estimation Method
IT. Tuitmafl
Delfi UniversitY of Technology, Ship Hydromechanics and Structures, The Netherlands
W. TrouwbOrSt
TNO, Centre for Mechanical and Maritime Structures, The Netherlands
ABSTRACT: This paper shows the use of the Qptimal State Estimation Method (OSE) for estimation of
slamming forces for model experiments. The OSE estimates the external loads using the response of the model
and calculated natural modes. The response is measured with several accelerometers to allow the OSE to estimate
the response of the flexible modes which is needed for an accurate estimation of the external forces. When the calculated natural modes are close to the actual natural modes and with well conditioned measurement signals, the OSE estimates the external force accurately.
1 INTRODUCTION
To measure slamming loads for model experiments -usually pressure gauges, load cells or segments with force transducers are used. Another way to derive the
slainmiEiig load is the Optimal State Estimation Method
(OSE). The OSE method uses the measured response
of the model to predict the slamming loading by
combining numerical and experimental results. For the OSE method the model needs to be equipped with accelerometers only, which normally give no restric-tions to the model except that one should be able to calculate the eigen modes accurately.
The OSE method is developed during the joint
US-NL research program DYCOSS (Dynamic Behavior of
Composite Ship Structures) (Trouwborst & Costanzo
1999). The OSE method has been used for the analyses
of full scale shock trial and slamming measurements. This is the first time the method is used to derive the slammmg impulse for model experiments.
This paper will first present the theoretical back-ground of the OSE method. Some results of the OSE
method for full scale measurementswill be shown.
Finally the use and results of the OSE method for the model slamming experiments will be discussed.
2 OSE METHOD
The theory of the OSE method will
be discussedbriefly based on the discussion that can be found
99
in (Thouwborst & Costanzo 1999). An extensive
discussion can be found in (Molengrafi 1990).
The OSE method uses the modal equations and measurements to make an estimate of the response
and external loading.
2.1 Modal equations
The common dynamic equations are used as starting point:
M+C±+Kx=f
(1)The mass matrix includes the added mass of the fluid. The infinite, frequency independent, added mass can
be used because of the high frequency of natural modes
of ship structures. Using a FE-package the eigen value
problem- is solved:
(wiVI + K)
<p = 0 (2)The results are the eigen frequencies o and eigen
modes .
The eigen modes are normalized with
respect to the mass matrix:
JVIço=1, çoK,çc=w2, fori=1,n
(3)The dynamic equation is transformed to modal
coor-dinates using the transformation matrix T which
contains a subset of eigen modes.
With:
= TMXT.
C,, = TCT
(5)
Kp=TtKT,
.fpTtf
The transformation to modal coordinates allows for a
significant reduction of the number .of degrees of
free-dom. Only the eigen modes below a cut-off frequency and with sufficient energy will be used.
2.2 Measurement equations
A vector with measurements signals Zm Cfl be
introduced:
zm Z8p + Zji + Zaji + ZuU (6)
with p,j and )E3 the modal displacements, velocities
and accelerations according to equation (4). The
math-ces Z, 1, and Z are the participation matrimath-ces for
the mesured displacements, velocities and
acceler-ations as present in Zm. In fact, based on the kept eigen
modes, these matrices transform the modal- quantities p,Ab and j5 to physical displacements, velocities and
accelerations.
Vector u are the measured external forces, if any. The boolean matrix Z selects which measured forces
are used.
2.3 The optimal state estimation method
There will always be differences between the
measure-ments and the mathematical model. To account for
these differences residuals are introduced for all equa-tions. The OSE estimates the response and external loads of the model by minimizing these residuals.
First a residual is introduced for the time-üerivative
equations:
=i,+ii,
v=a+2,
(7)Where , and a are the estimated displacements,
velocities and accelerations respectively, based on the set with modal degrees of freedom.
By replacing the p, and j5 in the model equation
(4) by the estimation variables , and a the residual
is introduced.
(8)
Vector i are unknown external forces which the USE
should estimate. Matrix H is the participation matrix for the external forces.
The last residual 2 is introduced for the measure-ment equation (6):
Zm
Z8.+ ZIJ+Z0â+ Zü+(
(9)100
Equations (7) to (9) form the so-called
identifica-tion model, which is the basis for the optimal state
estimation method. Following (Molengraft 1990), the
identification model can be formulated more
com-pactly using the augmented state estimator and the
augmented input estimator :
x=(s,v)
- ,p=(u,a)
,'t -t t
--St -St t
(10)
Using these estimators, equations (7) to (9) can be
rewritten as: (11)
Ezm =F+F+(
with: A(
0 0)'
'
B(
o I)'2
F
C'\
-
,Z)
F
(H M'\
- Z Z0)'(=)
For an optimal state estimation, and b have to be
determined such that the residuals and are
min-imized. For the minimization of the residuals the
following penalty function is introduced:
J() =
1((t)w(t)
+Ct(t)VC(t))dt+ ((to).qo)tR0((to) - qo) (14)
This function is minimized using the conditions of
equations 11 and 12. Vector q are the initial conditions
at the starting time t0 as defined by the user. The term
((t0) qo) is a residual on the initial conditions at
start-ing time t0. The user supplies the weightstart-ing matrices
W, V and R0 which express the confidence in the time
derivative equations, model equations, measurements and initial conditions.
The approach to minimize function (14) can be
found in reference (Molengraft 1990). The estimated
response and external forces are known after the
optirnisation.
3 PREVIOUS USE OF THE USE METHOD
The OSE method has been used for estimation of the
response and external loading for full scale shock trials
and slamming events.
oy
4 EXPERIMENTS
In,g,Ced md o4000 en e,nJod 4odty
Figure 1. OSE results for rn-frigate.
Figure 1 shows the velocity at a location of a Dutch
M-frigate during a shock trial. This shock trial was analysed using the OSE method. The measurement at the location is not used for the OSE estimation of the response. The velocity signal is reconstructed using
the- estimated response.
The shock load excitated many high order modes
which are not used for the OSE estimate. Also
--there--will. always be differences between the struc-tural model and the actual ship. Therefore the
esti-mated velocity response will differ from the measured velocity
Figure
1 shows that the estimated response is
reasonable close to the measured response at the
location.
Estimation of slamming impulse for a full scale
slamming experiment showed also reasonable results.
In the summer of 2006 experiments were held in the towing tank of the Technical University of Deift. The goal for the experiments was to determine the
slam-ming loads and added mass for flexural modes fora
simplified hull shape. The OSE methodwas chosen to
derive the slamming loads after the experiments.The
experiments where setup such that it would beeasy to
apply the OSE method.
Table 1. Hydrostatics
Length over all 3.8m Length waterline 3.32 m
Length parallel section 3.0 m
Beam 0.75 m Draught 0.08 m Depth 0.20 m Volume of displacement 0.130m3 Displacement mass 130 kg Area of waterplane 2.38 m2
Figure 3. Model constrains.
4.1 Design
The hydrostatics of the modelare presented in table 1.
The cross sections can be found in figure 2. Figure 3
shows the applied constraints. Thesway, roll and yaw
motions are suppressed and springs control the surge
motion. Figure 4 isa photograph of the actual model.
The natural modes have to be calculated using a
FE package. In order to obtain accurate results the
material propei.ties should be well known. Therefore Figure 4. Used model.
101
I
0
-0 4 -0.3
-0.2 -0.1 0 0.1 0.2 0.3 0 4Figure 2. Cross sections.
0.4
0.3 I
0.2 -t
0.1 4
aluminium is used instead the normal material for
building models.
The OSEmethod predicts the response of the model
by estimation of the participation of the natural modes. The better the OSE can make a distinction between the
different natural modes the more accurate the estima-tion will be. Local modes will give only response at a few, or in the worst case none, accelerometers which
make the estimation of the participation of these modes
difficult. For an accurate estimation of the response
and the external forces most of the energy of the
response should be in the response of the global natural
modes.
The model is designed such that the global natural
frequencies are as low as possible and the local natural frequencies are as high as possible to obtain a response
that is dominated by the global modes. This resulted in-a large model for the towing tank with little
free-board. The complete model was build from plates with
a thickness of 5 mm to obtain high frequencies for the local modes.
4.2 Measurements
Twenty accelerometers with a range of 20 g are
mounted on the model. Four are oriented horizontally, fourteen are oriented vertical and two are placed on the bottom plate u the bow which has a small angle.
Frequencies up to 300 Hz will be of interest for
application of the USE method because most
impor-tant natural modes have a frequency up to this
fre-quency. The signals are sampled with a sample rate of
10 kHz to record responses .up to 300 Hz accurately.
For determination of the natural frequencies a
modal hammer is used which measures the applied
force.
The wave elevation in front of the model and the rigid body motions are also measured.
4.3 Experiments
in the first part of the experiments the natural
fre-quencies of the model were measured for both dry and wet, with and without forward velocity. These mea-surements are used to check and correct the FE results and the added mass calculation.
The second part of the experiments bonsisted of
slamming in regular waves. Slamming in a peak wave of a wave train was the third part of the experiments.
The last part of the experiments was excitated
using a large hammer (10 kg) to simulate a slamming event. The force applied with the hammer was
mea-sured. in this way the results of the USE method
can be checked. The impulse of the hammer was
tuned by rubber between the hammer and model to
obtain a response that was comparable to the measured
slamming response.
102
Figure 5. FE model.
5 PREPARATION FOR USE
Before the USE method can be applied the natural
modes should be calculated. The offset and drift of the
acceleration signals should also be removed.
5.1 Natural modes
The natural modes are calculated using the FE package TRIDENT. The used FE mesh is shown in figure 5. The
small mesh size is chosen to make the meshing of the small eometrica1 details possible.
The small blocks are the supports on which the accelerometers where mounted. These blocks are
added to the mesh to obtain the eigen vectors as accu-rate as possible for the locations of the accelerometers.
Boundary elements are placed on all wetted ele-ments for calculation of the added mass in still water.
Hydrostatic springs are added to obtain heave and pitch
modes, but there will be a small error in these modes
because only the infinite added mass is used in the FE
calculation.
The density of the aluini.nium is scaled abit to obtain
the exact weight as the real model. This accounts for the weight of cables, accelerometers, paint, etc.
The natural modes are measured during the first part of the experiments. The frequency response
function (FRF) between the hammer and the 14
vertical accelerometers are calculated. The results
of the measurements in still water are shown iii
figure 6.
The FRF shows the actual frequency of the natural modes very clearly. The measured frequency of the
first dry longitudinal bending mode is used to scale the
elastic property of the aluminium. This compensates for the differences between the FE model and the real
1.4 1.2 1 0.8 0.6 0.4 0.2 0 Frequency [Hz] wet 20 40 60 80 100 120 140 160 180 200
Figure 6. FRF between hammer and 14 accelerometers.
Table 2. Comparison between measured and calculated
frequencies.
Table 2 shows a comparison between the measured and calculated frequencies. Both the wet as well as the dry calculated natural frequencies are close to the
measured values. This shows that the FE model is con-sistent and that the calculated added mass is close to the real added mass. The calculated mode shapes are used
for the OSE calculation but the measured frequencies are used to obtain better results.
5.2 Measurement signals
The accelerations, velocities and displacement are
esti-mated by the OSE method. The error in the velocities
and displacements can not be estimated if only
acceler-ations are used. During the experiment the rigid body displacement is measured using an optical tracking
system. The signal f this system can not be used
directly because the sample frequency is only 60 Hz and the signal does not include the displacement by
the flexible modes.
A displacement signalcan also be obtained by
dou-ble integration ofan acceleration signal. The calculated displacement is shown in figure 7. Line d(t) is the
dis-placement measured by the optical tracking system and line ff a(t) is the double integration of the accel-eration signal. There is a clear difference between the two signals. The difference is mainly due to the fact
that the initial velocity and displacement are not known
for the doubleintegration, but the changing angle with
103 C 1.5 0.5 -0.5 40 20 30 1 0 -10 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time [s]
Figure 7. Displacements at accelerometer I.
11j
a(t)
a(t)
-0.5 1 1.5 2 2.5 3 3.5
Time [s]
Figure 8. Acceleration at accelerometer 1.
respect to the gravity field and inaccuracies of the
accelerometer will also cause drift.
Before the OSE is used the error in both the accel-eration and displacement signals are minimized using
the displacement signals from the optical tracking
system.
The first step of the correction is the subtraction of the additional measured accelerations due to gravity when the pitch angle is not zero. In the second step a fifth order polynomial fit on the differences between the double integrated acceleration and the measure-ment is done. The first coefficient will be the initial displacement of the point, which can not be known from the acceleration only. The initial velocity is the second coefficient. Third coefficient of the polyno-mial fit is the mean offset of the accelerometer. Only the fourth and fifth coefficient are used to remove real
drift.
The original acceleration signal a(t) and the
cor-rected a(t) are shown in figure 8. Only a small change
ofthe.mean value is visible but the integration as shown
in figure 7 is better.
The double integral of the corrected accelerations at the bow and stern are also supplied as additional
signals to enable the OSE to estimate the error in
displacement and velocity.
lth tors. 45.3 42.6 29.9 28.1
Ith long. 47.0 46.9 24.8 25.3
2ndturs. 111 112 72.8 70.8 2nd long. 126 128 63.1 61.2
dry
6 RESULTS
First a validation case will be shown, thereafter a
com-parison between OSE results and calculations for a
slam event will be shown. For these calculations only the acceleration signals of the 14 vertical
accelerom-eters are used. Two additional displacement signals at the bow and stern are also used. The first ten natural modes which have significant displacements in
verti-cal direction are the subset for the estimation of the
response.
6.1 Validation
For validation purpose the model is hit with a large
hammer to obtain a comparable response as measured at slamming events. The hammer force is measured using an accelerometer,f = m a. This will result in a non-zero force before and after the impact because the hammer still accelerates.
The measured force and the estimated force
obtained with the USE method are shown in figure 9.
An unknown force at the location of the hammer
impact is used for the USE calculation. Theestimated
force by the USE during the actual hit is very close
to the measurement. The OSE estimation shows some oscillations after the hit because the actual damping
of the modes is not known. The USE .uses the external
force to compensate for the differences between the real damping and the user defined damping.
6.2 Slamming event
An experiment in regular waves where large accelera-tions due to slamming were measured is selected for analyses with the OSE method. The forward velocity for this experiment was 1 rn/s with a wave height of 0.18 rn and wave frequency of 0.64 Hz.
Two unknown forces, one at the bow and one at the stern, are added to the USE calculation. The unknown force at the bow is located at the estimated center of the slamming force. In this case at least two forces are
needed because also the hydrodynamic heave force and
0.4 0.45 0.5 0.55 0 6
Time [sJ
104
pitch moment should be estimated by the OSE method
to obtain the correct motions. Using more tmknown force locations would give more insight in the actual
force location, but this was not done to reduce the
number of unknowns and problem size.
In total 3.5 seconds were analysed. With a sample rate of 10 kHz the USE has to minimize function (14) for 35.000 time steps using 16 measurement signals, 10 unknown modal responses and 2 unknown forces.
The initial velocities and displacements are user
defined variables. At the start of the measurement they are not zero, but for simplicity the initial conditions in
the USE calculation are set to zero. At the first stages of the calculation the USE method will use the exter-nal forces to obtain a velocity and displacement that is close to the measured velocity and displacements. Therefore the force estimation of the first second will be incorrect.
Figure 10 shows the estimated force at the bow of
the model. The question is whether this estimation
is correct. The estimation will not be as accurate as
the estimation of the hammer force because the added
mass will change in the waves and the USE method uses only modes calculated with the added mass of still water. During the slam event the added mass will change and consequently the modal shape and fre-quency. Because the USE method will still use the natural modes for the still water case there will be an
error in the estimation, but for the total estimated slam
impulse this error is expected to be small. First of all
the shape of the natural modes is not influenced much
by the added mass. Besides, the USE analyzes a time
history, in whichthe added mass will change during the
slam event and the average frequency of the structure during the slam event will be close to the still water
condition.
A calculation of the slamming force is done as ver-ificatidn whether the estimated slamming force is in
the expected order. For this estimation the time domain sea keeping program PRETTI (Veer & van Daalen 2006) is used. PRETTI is coupled with CRS-SLAM which is
a boundary element method based on the theory of
(Zhao & 0. Faltinsen 1997).
The calculation of the rigid body motions using pprrI showed significant differences with the
mea-surements. This could be expected. PRETTI uses the linear hydrodynarnic coefficients for the calculation
of the radiated and diffracted forces, which imply very small wave height and steepnesses with hydrodynamic
loading U to the still water line. The model was at
some time instances more than fifty percent out of
the water. Therefore the radiated and diffracted forces
can never be calculated correctly using the still water
hydrodynamic coefficients.
Because the slamming force is very sensitive to the relative velocity the calculated motions are not
used. The measured motions were imposed on the sea
keeping calculation. In this way the calculated relative
velocity for the slamming calculation will be correct. The OSE estimation for the external force does not
include the linear hydrostatic term because hydrostatic
springs are used for the FE model. The linear
hydro-static force is re-calculated and subtracted from the sea
keeping force for the comparison.
The time and amplitude of the calculated and
esti-mated slamming force compare very well in figure 10.
It seems very likely that both the estimate of the OSE
method and the slamming calculation are close to
the actual slamming force. The comparison between the sea keeping force, force between the slam peaks, is. worse. The estimated external force by the OSE method will not be correct because the infinite added mass approach is not valid for sea keeping motions.
An other reason for the differences is that the cal-culated sea keeping forces are not correct because otherwise the calculated motions would have been
more comparable to the measurements.
7 CONCLUSIONS
The OSE method is used to estimate the slamming loads for model experiments. The model usedwas
105
designed to allow for an optimal use of the OSE
method. Both the FE calculations and preparation of the measurement signals were done with care. With this effort the OSE method was able to make a very
good estimate of a hit with a large hammer. The
estimate for a slamming event was comparable to
the, results of calculations using a boundsry element
method. Based on these results it can be concluded
that the OSE method is able to estimate the slamming force based on the response of the model.
At the moment of writing this paper only one ham-mer hit and one slam event was evaluated using the OSE method. Therefore the performance of the OSE method for the other conditions is not yet known.
ACKNOWLEDGEMENT
'The OSE method software was developed by
Dr.ir. R.H.B. Fey, currently working at theEind-hoven University of Technology, Department of
Mechanical Engineering, using the previous work of
Dr.ir. M. Molengraft. The authors like to thank Mr. Fey
for his support in utilizing the OSE method.
REFERENCES
Molengraft, M. 1990. Identification of non-linear
mechan-ical systems. Ph. D. thesis, Eindhoven University of
Technology.
Trouwborst, W. & Costn7o, F. A. 1999. The optimal state estimation method, a tool to integrate full scale shock trial measurement data and numerical models. In 70th
Shock and Vibration Symposium, 15-19 November 1999,
Albuquerque NM USA.
Veer, R. van 't & van Daalen, E. 2006. Pretti vl.3 theory
manual. Technical report, CRS.
Thao, R. & Faltinsen, J. A. 0. 1997. Water entry of arbi-trary two-dimensional sections with and without flow