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Drummen
Full and Model Scale testing of a New Class of US Coast Guard Cutter
Ingo Drummen1, Marcus Schiere1, Reint Dallinga2, and Karl Stambaugh3 1. MARIN, Hydro-Structural Services
2. MARIN, Ships Department
3. USCG, Surface Forces Logistics Center
This paper presents the setup and results of the full and model scale tests conducted for the US Coast Guard’s fatigue
life assessment project. Results are presented to improve the understanding of the loading side of the fatigue lifetime
calculation and forecasting fatigue damage for the NSC (WMSL) Class.
The views expressed herein are those of the authors and are not to be construed as official or reflecting the views of
the Commandant or of the U.S. Coast Guard.
KEY WORDS: Fatigue; full scale tests; model tests, hull
girder flexibility.
INTRODUCTION
The United States Coast Guard (USCG) initiated a project to
assess fatigue design approaches for its new National Security
Cutters (NSC). It became known as the Fatigue Life Assessment
Project (FLAP). An overview of this project is provided by
Stambaugh et al. (2014). Predicting the fatigue budget
consumption of a ship hull structure involves the prediction of
hull loading in a seaway, and comparison of this with the
structural capacity. Particularly the former is an effort requiring
information from a multitude of disciplines. Therefore, MARIN
was contracted to support FLAP and reached out to involve
other subject matter experts and stakeholders. American Bureau
of Shipping, BAE Systems, Bureau Veritas, Damen Shipyards,
Defense R&D Canada, DGA hydrodynamics, Lloyd’s Register,
Ingalls Shipbuilding and Office of Naval Research participated
in the Valid joint industry project (JIP). The broader goals of the
project are to forecast structural maintenance needs of USCG
Cutters, further improve the understanding of wave loading
leading to fatigue damage, and increase the confidence level in
predicting wave loading leading to fatigue damage on a naval
frigate type hull form and structure. These goals were, among
others, achieved through a model test program supported by
dedicated full scale trials. Measurements taken during these
trials have provided data for correlation with model experiments
and numerical simulations. In order to evaluate fatigue life
prediction methodologies and also forecast structural
maintenance needs, a long term monitoring campaign was
performed on the NSC USCGC BERTHOLF.
This paper presents the setup and the results of the dedicated
trials, the monitoring campaign and the model scale tests
conducted for the USCG’s fatigue life assessment project. The
results presented improve the understanding of the loading side
of the fatigue lifetime and forecasting fatigue damage for the
NSC (WMSL) Class.
TRIALS AND MONITORING
Ship and instrumentation As mentioned in the introduction, the NSC USCGC
BERTHOLF (WMSL 750) was subject to an extensive
dedicated trial and monitoring campaign to assess its structural
performance. Figure 1 shows a picture of the ship. The ship’s
main particulars are listed in Table 1.
Figure 1: NSC USCGC BERTHOLF
Table 1: Main particulars of NSC USCGC BERTHOLF
Quantity Value
Length Overall 127.59 m
Length Between Perpendiculars 118.87 m
Beam, Maximum 16.46 m
Design Draft 4.39 m
Block Coefficient 0.492
Displacement (fully appended) 4500 ton
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During the second half of 2007 and the first half of 2008 the
ship was instrumented with
• 24 long base strain gauges (LBSG),
• 73 unidirectional strain gauges,
• 26 accelerometers,
• 28 fatigue damage sensors, and
• a wave radar.
The vertical and horizontal bending moments were inferred
from strains measured directly on the ship. These quantities
were derived from long base strain gauge measurements. The
location of the LBSGs in the ship is presented in Figure 2.
Figure 2: Overview of the locations (indicated with the red dots)
of the LBSGs installed on NSC USCGC BERTHOLF.
A conversion matrix was used to convert between the measured
global strains and the bending moments,. For the derivation of
this matrix, it is assumed that the total ship deformation is a
superposition of the first few global flexural vibration modes.
These modes are presented in the next section. The first step in
the procedure is to determine the contribution of each flexural
mode to the global strains at the LBSG locations. The second
step is to combine this with the vertical bending moment in each
mode according to the finite element model of the ship
(Hageman et al., 2014). Figure 3 shows the outcome of a
validation study of the conversion matrix. Long term extreme
vertical bending moments were calculated with transfer
functions obtained directly from the hydrodynamic code
Hydrostar. This was compared with an estimate of the vertical
moment derived from the conversion matrix and strains
obtained from the coupling between Hydrostar and a general 3D
finite element structural code through Homer (e.g. Hageman et
al., 2014 or Tuitman and Malenica, 2009). As can be seen from
the figure, good agreement was found. Similar correlation was
derived for the conversion to the horizontal bending moments.
Note that this agreement is based on a pure theoretical
comparison. The overall accuracy of the measured bending
moments is addressed in the next section.
Local unidirectional strain gauges and dedicated fatigue damage
sensors (Nihei et al., 2010) were used to quantify the fatigue
budget consumption. The purpose of the accelerometers was to
determine the modal parameters of the first few global flexural
vibration modes and to determine the rigid body motions.
Figure 3: Comparison of long term extreme vertical bending
moments calculated with transfer functions obtained directly
from the hydrodynamic code Hydrostar (continuous lines) and
estimated from the conversion matrix and strains obtained from
the coupling between Hydrostar and a general 3D finite element
structural code through Homer (dotted lines).
In order to monitor the wave conditions, wave radar was
installed on the ship. The wave directional information of the
wave radar is generally of good quality. This is not necessarily
true for the energy content of the signal. In order to improve this
estimate, a data fusion approach (Thornhill, 2010) was used. For
this approach, the 3D wave spectrum is multiplied by a
computed pitch response amplitude operator (RAO) squared.
The outcome of this multiplication is used to derive the root
mean square value of the pitch. This is compared with the root
mean square value of the measured pitch. The ratio of the
measured and calculated value is used to update the measured
wave height1. The accuracy of this estimate thus fully depends
on the accuracy of the measured pitch motion, and the computed
pitch RAO. Confidence in the estimated wave heights was
gained by comparing estimated heights with the ones measured
by NOAA wave buoys when the ship was close to one of these
buoys. Good correlation was found for the investigated cases.
Trials Dedicated trials with the NSC USCGC BERTHOLF were
carried out in August 2009. This was done in the Pacific Ocean
West of Seattle, Washington and San Diego, California. Tests
were conducted in waves and in calm water. Figure 4 shows the
mean vertical bending moment derived amidships as a function
of speed in calm water. Included are also results from the same
tests performed during the model experiments described in a
subsequent section. Good agreement is found between the
steady vertical bending moments obtained from both sources.
This finding, among other considerations, provides confidence
in the accuracy of the measured bending moments. Also, the
bending moments derived from measurements taken while
shifting ballast water and fuel agreed well with estimates from
the loading computer.
1 In practice this is also done for heave. The final significant
wave height is derived from a combination of both.
AP 88 82 76 70 64 52 44 36 28 22 16 10
main deck
25+36+47+58+70+ : Instrumented sections
: Bulkheads
81+ 9-
01 level
main deck2nd deck
02 leveltop of house
0.0E+00
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1.5E+08
2.0E+08
2.5E+08
3.0E+08
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0 20 40 60 80 100 120
section location (m)
0 kt
5 kt
15 kt
18 kt
21 kt
28 kt
0 kt
5 kt
15 kt
18 kt
21 kt
28 kt
Speed
MY
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Figure 4: Comparison of mean vertical bending moment
measured amidships in calm water as a function of the forward
speed as obtained from model tests (red and green lines) and the
trials (blue circles).
The tests in waves were the primary focus of the dedicated
trials. In total, 80 tests were carried out in waves. The test
conditions included different relative wave headings, varying
ship speeds, and waves with a significant height between 1m
and 3m. This makes the wave conditions encountered very
suitable for correlation with linear analytical calculations, and to
support the analysis of uncertainties in the spectral fatigue
analysis process. All tests were carried out as legs of in total 11
different octagons. The duration of each leg was based on 250
encountered wave cycles. The maximum duration of a single leg
in an octagon was set to 45 minutes. This was relevant for
waves coming from the aft direction combined with ship speeds
of 15kn and 20kn because the encounter frequency becomes
very low.
During the trials, wave radar measurements were supported by a
wave buoy. For most of the tests, the sea state consisted of a
wind sea and a cross swell component. In low sea states,
statistics of the peaks and troughs of stresses are about equal,
they approximately follow the Rayleigh distribution. In higher
sea states, this is no longer true, and an asymmetry develops
between peaks and troughs. Figure 5 and Figure 6 respectively
show exceedance probabilities of the vertical bending moment
measured during trial Runs 61 and 77. In both cases, the speed
was 15kn. For the former run, the significant wave height was
1.7m, for the latter 2.8m. The increased hog/sag asymmetry,
when increasing the wave height from 1.7m to 2.8m, is clearly
visible. It can also be seen that, for Run 61, the distributions of
the hogging and sagging vertical bending moments agree well
with the Rayleigh distribution. Note that the asymmetry in
Figure 6 has little influence on the range between the sagging
and hogging moments, the range is slightly decreased.
Therefore, its effect on fatigue damage is expected to be small.
A decrease in average vertical bending moment is also seen in
the model test results presented in Figure 14.
Figure 5: Exceedance probability of the vertical bending
moment amidships for a speed of 15kn and 1.7m significant
wave height (Trial Run 61). Red and black represent hogging,
blue and green sagging and the dotted line the Rayleigh
distribution. The black and blue lines present bending moments
that include the effect of whipping events present in the
response. For the green and the red line, this effect was excluded
by applying appropriate filtering.
Figure 6: Exceedance probability of the vertical bending
moment amidships for a speed of 15kn and 2.8m significant
wave height (Trial Run 77). Red and black lines represent
hogging, blue and green sagging, and the dotted line the
Rayleigh distribution. The black and blue lines present bending
moments that include the effect of whipping events present. For
the green and the red line, this effect was excluded by applying
appropriate filtering.
In seas higher than the ones encountered during Runs 61 and 77,
slamming might occur. The resulting whipping vibration of a
slam will influence the fatigue budget consumption as both the
hogging and sagging moments will be enlarged, thereby
affecting the range. This influence was investigated using data
from the model tests and is discussed in a subsequent section. In
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order to quantify the whipping effect both numerically and
experimentally, it is important to have knowledge about the
shapes and frequencies of the first few global flexural vibration
modes of the ship.
Figure 7, Figure 8 and Figure 9 show the shapes of the vertical
and horizontal wet global flexural vibration modes. In blue
results obtained from full scale on board measurements are
presented. Shapes from the test model and numerical finite
element (FE) model are also included. The zero for the x-axis
was taken at the longitudinal centre of gravity and points
towards the bow of the ship. Very good agreement is seen
between the shapes from the different sources.
Figure 7: Shape of the vertical two node wet global flexural
vibration mode. In blue results obtained from on board
measurements. In green results are from model tests and in red
are the shapes derived from finite element model.
Figure 8: Shape of the horizontal two node wet global flexural
vibration mode. In blue results obtained from full scale on board
measurements. Results shown in green are from model tests and
in red are the shapes derived from finite element model.
Figure 9: Shape of the vertical three node wet global flexural
vibration mode. Results obtained from full scale on board
measurements are in blue. Results from model tests are in green
and the shapes derived from finite element model are in red.
The natural frequencies corresponding to the shown mode
shapes are presented in Table 2. Also here, good agreement is
found between results obtained from full scale, model scale and
numerical work.
Table 2: Natural frequencies of first three wet global flexural
vibration modes
Mode Ship
[Hz]
Test model
[Hz]
FE model
[Hz]
two node vertical 2.0 2.1 1.9
two node horizontal 2.7 2.8 2.8
three node vertical 3.7 4.2 3.5
The structural damping ratio of the global modes was
determined from tests during which the ship was excited by
firing the gun with an empty shell. This resulted in a very weak,
but measurable, global vibration of the ship. The damping ratio
of the modal vibration is estimated to be between two and three
percent based on these measurements.
Monitoring Since the fall of 2010, the NSC USCGC BERTHOLF was
monitored during five deployments. This amounts to 376 days
of operation. During these deployments, the system measured
continuously and collected data from all sensors. Per month, this
amounts to approximately 600Gb of data.
As mentioned in the previous section, the sea state parameters
were measured using wave radar in combination with a wave
data fusion algorithm. In order to compare encountered wave
conditions with those used for designing the ship, Figure 10
shows the probability distribution of the significant wave height
for data from global wave statistics (GWS) and measurements.
Results from the monitoring campaign are given for an
increasing part of the measurement period. Comparing the GWS
-60.0 -40.0 -20.0 0.0 20.0 40.0 60.0-1.0
-0.5
0.0
0.5
1.0
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x [m]
Vert
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Two node vertical mode
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x [m]
Horizonta
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Two node horizontal mode
-60.0 -40.0 -20.0 0.0 20.0 40.0 60.0-1.5
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Three node vertical mode
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distribution with the measured distributions it is clear that the
ship encountered much more conditions with a significant wave
height below two meters than can be expected based on the
GWS database.
Figure 10: Probability distribution of the significant wave height
as given in GWS and derived from different deployments of the
NSC USCGC BERTHOLF
Figure 11 shows a plot with the forecasted fatigue budget
consumption as a function of time for the most severely loaded
fatigue sensitive detail, fatigue sensitive location one (FSL01).
The red reference line shown in the figure is the target 30 year
fatigue budget line. The full black line represents the forecasted
fatigue budget using design operational conditions in
combination with stresses determined using stress transfer
function from the coupling of the hydrodynamic code Hydrostar
and a general 3D finite element structural code through Homer.
The fatigue damage, , per cell (combination of wave height,
wave period, relative heading and speed) was determined using
the following equation assuming a narrow banded response.
(1)
In this equation, is the time the ship spent in the cell
characterised by the response spectrum . is the zero
crossing period in the cell and and are the SN-parameters.
The damage was based on the ABS/BS5400 E Class SN curve,
where , and MPa was the unit of stress.
No stress concentration factor was used. In equation 1,
represents the zeroth order moment of the response
spectrum, . Here denotes the complete gamma function.
The response spectrum is determined from the wave spectrum,
, and the stress RAO, , as follows.
(2)
A long crested JONSWAP spectrum with a peak enhancement
factor of 3.3 was used. The total fatigue budget consumption
was determined by summing the damages resulting from Eq. 1
for all combinations of wave height, wave period, relative
heading and speed. This spectral fatigue approach is outlined in
more detail in Hageman et al. (2014) and ABS (2012).
Figure 11: Forecasted fatigue budget consumption at FSL01
using different combinations of measurements.
The dotted black line was obtained using the above described
procedure for the full black line. Instead of using the design
conditions; however, the operational and environmental
measured up to 2011 were used. When applying the same
procedure for the conditions measured up to 2012, the dashed
line is found. This indicates a trend in increased fatigue budget
consumption from high latitude deployments. Finally, the green
line was obtained by assuming two of the measured
deployments as typical yearly deployments.
A long term spectral fatigue analysis was performed with a short
crested spectrum using a cosine squared spreading function
resulting in a reduction in fatigue damage of 25%. In order to
assess this effect from the measurement, the energy in the
measured directional spectrum was integrated around the mean
heading. In this way, a long crested spectrum was made. The
fatigue damage was calculated using this long crested spectrum
and compared with the one determined using a short crested
spectrum. This resulted in an increase of the fatigue damage of
about 20% when compared to the damage from the long crested
spectrum.
As mentioned in the introduction, the accumulated fatigue
damage at the fatigue sensitive locations was derived from two
types of sensors: strain gauges and fatigue damage sensors. The
measured strains were post processed using Rainflow counting
to determine the number of closed stress cycles, and the
Palmgren-Miner assumption to calculate the fatigue damage.
The Palmgren-Miner assumption (Eq. 3) states that the total
fatigue damage is the sum of the partial fatigue damages, in
which the partial fatigue damage is the ratio of the number of
measured cycles with a given stress range and the number of
allowed cycles at that stress range.
0 1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
significant wave height [m]
pro
ba
bili
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GWS
Measured up to 11-2010
Measured up to 07-2011
Measured up to 12-2011
Measured up to 04-2012
Measured up to 10-2012
year
con
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d f
atig
ue
bu
dg
et
[%]
design 30 year target
design operations
measured operations up to 2011
measured operations up to 2012
forecasted measured fatigue
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The resulting Palmgren-Miner equation is given as:
(3)
In Eq. 3 is the fatigue damage and the stress range at the ith
stress cycle. Stress cycles were Rainflow counted using
WAFO2. An important limitation of Eq. 3 is that it gives a linear
damage prediction from initiation to failure, whereas the crack
growth process is nonlinear in reality. This implies that also the
known effect of the sequence of encountered stress cycles is not
taken into account (Rogers et al., 2014).
Figure 12 shows the fatigue budget consumption for FSL01
derived from the measurements as a function of years. The
orange and blue dots present the accumulated fatigue damage
derived from strain gauge measurement. The blue dots (which
are overlapped by the orange ones) give the damage obtained
using the unfiltered signal. For the orange dots, the signal was
low pass filtered at 1.75Hz to exclude structural dynamic
effects. The frequency of the lowest global flexural vibration
mode is 2Hz, see Table 2. Due to a failing strain gauge, the
derived damage has not been increased during the last
deployment resulting in a horizontal orange and blue line. The
red line is again the reference line that represents a cumulative
consumed fatigue budget of 100% after 30 years of operation.
Figure 12: Fatigue budget consumption for FSL01 derived from
measurements. Due to a failing strain gauge, the derived damage
has not been increased during the last deployment resulting in a
horizontal orange and blue line.
Using a conversion matrix, it is possible to estimate the local
strains from LBSG measurements. The purple dots in Figure 12
represent a comparison between the fatigue damage obtained
from this approach. As can be seen from the figure, the damage
derived from the LBSGs agrees very well with the one
2
WAFO is a Matlab toolbox for statistical analysis and
simulation of random waves and load effects, developed at the
Centre for Mathematical Sciences at Lund University in Sweden
(Brodtkorb, 2010).
determined directly from the local strain gauge up to 2012,
when the local strain gauge failed.
The fatigue damage sensor (FDS) is a passive sensing gauge of
a thin film of metal with a machined notch. This gauge is
welded on a steel structure and a fatigue crack grows form the
machined notch depending on the number and magnitude of
stress cycles encountered by the structure. The crack in the FDS
grows at an accelerated rate compared to that of the underlying
structure. The length of the crack may be converted into the
fatigue damage of the underlying structure. The fatigue damage
is determined from measurements of the FDSs are shown as
crosses are in Figure 12. Four FDSs were installed on each of
the seven selected fatigue sensitive locations. Two of these had
a stress threshold level of 25MPa and for the other two this
threshold was set at 40MPa. The different sensors can be
distinguished by color, as can be seen from the legend in the
figure. The FDSs have to be read manually. This was made
during visits to the ship, which explains the discrete character of
these measurements. The FDSs were developed to emulate the
crack growth in the structure using linear assumption of the
damage parameter obtained from the Palmgren-Miner
summation. Results from the strain gauge should, therefore, be
given more weight than those of the fatigue damage sensors.
Figure 12 shows that FDSs C and D have higher damages than
sensors A and B. Sensors C and D are gauges with a 40MPa
threshold and Sensors A and B are gauges with a 25MPa
threshold. From these threshold levels, one expects that the A
and B sensors should give results higher than the C and D
sensors. At first sight, measurements from FDS D seem out of
line with measurements from the other FDSs. However, other
locations also show a clear separation in two distinct differences
between FDSs C and D and FDSs A and B, where the former is
higher than the latter. The reason for the deviation between the
two types of FDSs is currently unclear. However, residual stress
effects are likely to play an important role here because of the
geometry of the structural detail. The fatigue damage sensors
are small, but not small enough not to be affected by stress
gradients and residual stress in way of welded details. The exact
size of the FDS depends on the specific type, but the sensor is
between 5mm and 10mm wide and between 10mm and 20mm
long.
MODEL SCALE TESTS
Experimental setup A self propelled, self steering model of the NSC USCG
BERTHOLF was built to a scale of 1:25 and tested in MARIN’s
Seakeeping and Manoeuvring basin. This basin is 170 m long
and 40 m wide. The depth is 5 m. The wave maker consists of
331 flaps on two sides of the basin that are all individually
driven by an electric engine. This facilitates generation of
regular and long and short crested irregular waves from any
direction relative to the free sailing model.
In order to account for the global hydroelastic effect in the
experiments, the model was made of six rigid segments
year
con
su
me
d f
atig
ue
bu
dg
et
[%]
F47S1
SN unfiltered
SN filtered
SN unfiltered (CM)
FDS A (25MPa)
FDS B (25MPa)
FDS C (40MPa)
FDS D (40MPa)
design 30 year target
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connected by a flexible backbone. One may say that the global
structural response, , of a ship can be expressed as the
sum of the products of the vessels global flexural mode shapes
for that response, p , and the corresponding natural
coordinates, :
(4)
The natural coordinate is a time dependent measure for the
contribution of a particular mode to the total response. In
equation 4, is the number of global flexural modes taken into
account. The shapes and frequencies of the global modes are
determined from the mass and stiffness distributions. An
accurate representation by the test model of the relevant mode
shapes and their natural frequencies may be said to imply an
accurate representation of the mass and stiffness distribution, at
least from a global response point of view. The natural
coordinate for each mode is determined from its shape, modal
mass, damping and stiffness, and the modal excitation.
Following from the above, it can be concluded that concerns
regarding the accuracy of the flexural response of the test model
can be handled by discussing the accuracy with which the model
can represent the shapes and frequencies of the relevant global
modes. Modeling flexibility thus becomes a matter of modeling
shapes and frequencies of the global flexural modes of the ship.
Different ways of making a model flexible are discussed in
Drummen (2008). One of these is to use a flexible segmented
model. One specific segmented model is again the backbone
model. In this practical approach, the different ship segments are
connected by means of one backbone which provides the
structural stiffness. The backbone of the model was designed
based on information regarding the shapes and natural
frequencies of the two node and three node vertical and
horizontal flexural vibration modes of the NSC USCGC
BERTHOLF. The first three global modes of the ship are shown
in Figure 7, Figure 8 and Figure 9. The natural frequencies are
presented in Table 2.
The cuts in the model were made at the locations of the
instrumentation frames on the ship. These were Frames 25, 36,
47, 58 and 70, see Figure 2. Numbering here is from fore to aft.
On the model, this corresponds approximately with Stations
15.5, 13, 11, 8.5 and 6, respectively. Here numbering is from the
aft to the forward perpendicular. Frame 81 was also
instrumented on the ship. Due to practical difficulties from the
propulsion system, no cut could be made at this location in the
model. Therefore, measurements are not available from this
location. A picture of the segmented backbone model is shown
in Figure 13. The cuts can be recognized by the white stripes on
the model. This is a membrane which was placed over the cuts
to make them watertight. As can be seen from the picture, the
superstructure was cut into four parts.
Careful attention was required to make sure that the connections
in the vertical and transverse directions between the segments
and the backbone acted as simple supports, avoiding a
contribution of longitudinal displacements in the bending and
avoiding structural damping due to friction.
Figure 13: Segmented backbone model of the NSC USCGC
BERTHOLF.
Based on the shapes and frequencies of the flexural modes and
information available on the stiffness of the ship provided by the
USCG, a backbone was made consisting of three parts. The
inner part is a steel pipe with a diameter of 125mm and a
thickness of 7.5mm. The fore and aft parts are also made of steel
and have a diameter of 110mm with a thickness of 2.5mm.
Further fine tuning of the natural frequencies was made by
making cuts into the beam. The location and depth of the cuts
were calculated using software dedicated for this purpose. The
agreement between the shapes and frequencies of the flexural
modes of the ship and its model are presented in Figure 7,
Figure 8, Figure 9, and Table 2. Clearly visible is that an
additional cut in the aft section would have improved the
correlation between the shapes of the modes of the ship and
those of the backbone model, particularly for the three node
vibration mode. The structural damping of the vibration modes
was estimated to be between one and three percent which is in
line with what has been measured on board the ship’s dynamic
response.
On the five free parts of the beam in between the sections, strain
gauges were mounted from which the bending and torsion
moments were derived. The rigid body motions were recorded
with an optical tracking device. The encountered incident waves
were recorded at four locations with acoustic devices, backed up
with resistance type wave probes. In order to determine and
verify the mode shapes and natural frequencies of the model, 24
accelerometers were placed over the length of the model.
More than 300 runs in regular waves were performed in
different headings, speeds and wave heights. In irregular waves,
more than 60 tests were made consisting of several runs.
Conditions here were significant wave heights between 3m and
9m, again with different headings and speeds. Furthermore, six
tests in irregular waves were dedicated for comparison with full
scale trial results. The next section presents the results from
these experiments.
Experimental results The main goal for performing tests in regular waves was to
obtain RAOs for comparison with numerical methods.
Investigated nominal headings were 0deg, 22.5deg, 45deg,
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90deg, 105deg, 120deg and 180deg3. Speeds between 5kn and
28kn and wave heights between 2m and 8m were tested. As an
example, Figure 14 shows the RAO of the vertical bending
moment amidships in head waves for a speed of 15kn. The
normalized amplitude is given on the vertical axis and the wave
frequency on the horizontal one. Noteworthy in the figure is that
the wave amplitude only has a notable effect on the peak
response. This reduces as the wave amplitude increases. This
decreasing response was also seen for other speeds and headings
and is in line with what is presented in Figure 6. As noted there,
the effect of this decreased range on fatigue damage is expected
to be small. The precision error was investigated by repeating
three of the tests six times. For the case presented in Figure 14,
the 95% confidence interval is about 2% of the mean value of
the vertical bending moment RAO.
Figure 14: Vertical bending moments for Cut 3 obtained from
model tests in regular head waves with a height of 2m (+), 4m
(o) and 8m (*). The nominal model speed was 15kn.
As mentioned in the previous section, more than 60 tests were
performed in irregular waves. Table 3 presents an overview of
the significant wave height (Hs), peak period (Tp), speed (U) and
heading. The values in the table are nominal values. For each
sea state, about 30 minutes of full scale data was gathered.
Except for the runs denoted by an asterisk, all runs were
performed in long crested waves.
For each of the tests, the stress at FSL01 was determined using a
matrix converting the measured horizontal and vertical bending
moments to the stress in this fatigue sensitive location. In order
to quantify the uncertainty related to this conversion, the long
term fatigue damage was calculated using the stress transfer
function obtained directly from Hydrostar and Homer and from
a combination of the horizontal and vertical bending moments
from Hydrostar and the above described conversion matrix.
3 Throughout this paper a relative wave heading of zero degrees
corresponds with head waves. 180 degrees corresponds with
following waves.
Table 3: Overview of tests in irregular waves. A heading of zero
degrees corresponds with head waves. 180 degrees corresponds
with following waves.
Test Hs
[m]
Tp
[s]
U
[kn]
Heading
[°]
426 3.5 9.84 5 0
427 6.5 11.16 5 0
428 3.5 8.53 15 0
425 3.5 9.84 15 0
429 3.5 11.16 15 0
430 4.5 9.84 15 0
432 4.5 11.16 15 0
433 6.5 9.84 15 0
434 6.5 11.16 15 0
435 6.5 12.47 15 0
437 8.5 11.16 15 0
438 3.5 9.84 20 0
439 4.5 9.84 20 0
440 6.5 11.16 20 0
451* 3.5 9.84 15 0
452* 6.5 11.16 15 0
486* 3.5 9.84 20 0
487* 6.5 11.16 20 0
410 3.5 9.84 15 45
411 6.5 11.16 15 45
412 3.5 9.84 20 45
413 6.5 11.16 20 45
488 3.5 9.84 5 45
489 6.5 11.16 5 45
490* 3.5 9.84 20 45
491* 6.5 11.16 20 45
480 3.5 9.84 15 135
481 6.5 11.16 15 135
456 3.5 9.84 15 180
457 6.5 11.16 15 180
458 3.5 9.84 20 180
459 6.5 11.16 20 180
482 3.5 9.84 5 180
483 6.5 11.16 5 180
484* 3.5 9.84 15 180
485* 6.5 11.16 15 180
* tests in short crested waves
Figure 15 shows the ratio of these two for the different fatigue
sensitive locations on the ship. For FSL01, the conversion
matrix approach results in fatigue damage that is about 30% too
low. In terms of stress, this is approximately 10% lower. The
maximum value of this ratio is one. This can be explained by the
Drummen
fact that the conversion matrix approach starts from measured
global strains. The only local strains included in the conversion
are those that relate the finite element model to the measured
global modes. Inherently, local strains are thus either missing or
properly included, but not overestimated.
The underestimation of the damage rationpresented in Figure 15
does not seem in line with the very good correspondence shown
in Figure 12 between the measured local strain and the one
derived from the global strain measurements in combination
with a conversion matrix. One thing which plays a role here is
the fact that the long term fatigue analysis is based on a large
number of wave conditions. Results from the monitoring
campaign are for a more limited set of conditions. Furthermore,
converting the LBSG measurements to local strains and
comparing this to measured local strains includes measurement
uncertainties as well as uncertainties related to the conversion
matrix. It seems likely now that the former cancel the latter.
Figure 15: Ratio between the long term fatigue budget
consumption calculated using the stress transfer function
obtained directly from Hydrostar and Homer and from a
combination of the horizontal and vertical bending moments
from Hydrostar and a conversion matrix.
The fatigue damage derived for FSL01 from each model test is
given in Table 3 and was obtained from a Rainflow count of the
stress signal and a subsequent summation using the Miner-
Palmgren linear cumulative damage rule. The resulting fatigue
damage is presented in Figure 16 and Figure 17. Two results are
presented. The total fatigue damage (WFHF) and the wave
frequent (WF) fatigue damage. The total damage denotes the
damage due to the total stress history. Similarly, the wave
frequency damage denotes the fatigue damage due to the wave
frequency stresses. The latter was found by band-pass filtering
the stress signal to include only energy at frequencies in the
wave frequency range. On the horizontal axes of Figure 16 and
Figure 17 the test numbers are given. Presented in the figures
for each test is the mean fatigue damage per hour as well as the
95% confidence interval. This analysis was done by splitting the
total time series into parts of 50 wave encounters. It represents
the statistical uncertainty due to the finite test duration.
Figure 16: Total mean damage per hour and its 95% confidence
interval.
From the figures, it can be seen that the fatigue accumulation
per hour is highest for Tests 433 and 437. This is well in line
with what could be expected from the tests conditions. It is
interesting to see that the trends for the WFHF and the WF
damages are very similar. This implies that decisions about the
importance of sea states for fatigue damage can be taken by only
looking at the WF damage. Similar observations for a 300m
long containership were made by Drummen et al. (2008).
Figure 17: Wave frequency mean damage per hour and its 95%
confidence interval.
The contribution of each sea state to the long term fatigue
damage was obtained by combining the results shown in Figure
16 and Figure 17 with the design operational profile. The GWS
North Pacific scatter diagram was used. It was assumed that the
ship will operate continuously for 20 years. For the relative
comparison that is being made here, this service life is, however,
not important. Results are shown in Figure 18 and Figure 19.
From these figures, it can be seen that Tests 425, 432 and 434
contribute most to the fatigue damage. These are head waves
with a peak period of around 10s and 11s and significant wave
height between 3.5m and 6.5m. The forward speed is 15kn. It
may be noticed that compared to Figure 16 and Figure 17,
Figure 18 and Figure 19 show, as expected, little difference
between the total and the wave frequency part of the signal. The
similarity between figures indicates fatigue damage is
dominated by the wave frequency component of hull loading for
this Cutter.
Damage ratio : Estimated / Direct
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
FS
L01
FS
L02
FS
L03
FS
L04
FS
L05
FS
L06
FS
L07
FS
L08
FS
L09
FS
L10
FS
L11
FS
L12
FS
L13
FS
L14
FS
L15
FS
L16
FS
L17
FS
L18
FS
L19a
FS
L19b
FS
L31
0
5
15
18
21
28
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
-3
fatig
ue
dam
ag
e [
-]
426
427
428
425
429
430
432
433
434
435
437
438
439
440
451
452
486
487
410
411
412
413
488
489
490
491
480
481
456
457
458
459
482
483
484
485
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
-3
fatig
ue
dam
ag
e [
-]
426
427
428
425
429
430
432
433
434
435
437
438
439
440
451
452
486
487
410
411
412
413
488
489
490
491
480
481
456
457
458
459
482
483
484
485
Drummen
Figure 18: Contribution of each sea state to the long term mean
WFHF damage per hour and test and its 95% confidence
interval.
Figure 19: Contribution of each sea state to the long term total
mean WF damage per hour and test and its 95% confidence
interval.
The influence of whipping vibrations on the fatigue damage can
be quantified by dividing the total damage by the wave
frequency damage. Results are presented in Figure 20. The
horizontal axis again presents the test numbers. The vertical axis
now presents the whipping factor, which is the ratio of the
WFHF damage and the WF damage. The figure includes the
mean values for the different tests as well as the 95% confidence
interval. As can be seen from the figure, the mean value varies
between 1.0 and 1.2. In order to draw conclusions about the
long term contribution of whipping from the above outlined
results, they should be properly interpolated and extrapolated to
cover the entire range of environmental and operational
conditions. As a first step towards doing this, the dependence of
the whipping factor on the wave steepness was investigated.
Here the wave steepness, , is defined as shown in Eq. 5.
(5)
Figure 20: Whipping factor, i.e. ratio between WFHF damage
and WF damage, per test
For a forward speed of 15kn and head waves, Figure 21 presents
the mean whipping factor as a function of the wave steepness.
Experimental results are given by the blue diamonds. The 95%
confidence interval is plotted around the mean whipping ratio.
Figure 21: Whipping factor as function of wave steepness for
head waves and 15kn forward speed
Results in Figure 21 show that the whipping factor increases
with increasing wave steepness. Fitted through the model test
results is a second order polynomial; this is a solid blue line
which has the following parameters.
(6)
Below a wave steepness of 0.04, no whipping occurs. Good
agreement is found between the fit and the measured data. As
bow emergence (see Figure 22) is an important driver for the
whipping response of the ship, it is interesting to see the clear
dependence of the whipping contribution on the wave steepness.
This should be further investigated. Calculations were also
performed with the nonlinear hydroelastic strip theory code
VERES-Winsir (e.g. Drummen, 2008). VERES-Winsir runs
were executed for a number of wave steepnesses. To achieve
this, the wave period was kept constant and the wave height was
varied. To eliminate the effect of statistical uncertainty, all
simulations were done for 10 hours. These results are given in
0
0.05
0.1
0.15
0.2
0.25
0.3
fatig
ue
da
ma
ge
[-]
426
427
428
425
429
430
432
433
434
435
437
438
439
440
451
452
486
487
410
411
412
413
488
489
490
491
480
481
456
457
458
459
482
483
484
485
0
0.05
0.1
0.15
0.2
0.25
0.3
fatig
ue
da
ma
ge
[-]
426
427
428
425
429
430
432
433
434
435
437
438
439
440
451
452
486
487
410
411
412
413
488
489
490
491
480
481
456
457
458
459
482
483
484
485
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
wh
ippin
g f
acto
r [-
]
426
427
428
425
429
430
432
433
434
435
437
438
439
440
451
452
486
487
410
411
412
413
488
489
490
491
480
481
456
457
458
459
482
483
484
485
0.80
0.90
1.00
1.10
1.20
1.30
1.40
0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100
Wh
ipp
ing
fact
or
[-]
Wave steepness [-]
model tests
Veres-Winsir
Veres-Winsir
model test trendline
Veres-Winsir trendline
Drummen
green. VERES-Winsir results are also given in purple. In this
case the particular wave steepness was obtained by varying the
wave period. As can be seen from the figure, the green and
purple results compare quite well. For the green triangles, a
second order polynomial was fitted through the data. The
whipping factor determined using VERES-Winsir about 50%
lower than the one obtained from model tests. This is at least
partly related to the difference between the linear wave
implemented in the software and the nonlinear wave train
propagating in the basin. Similar fits as shown in Figure 21 for
the wave steepness were made for the effect of heading and
speed. This resulted in the formulation of the whipping factor as
a function of wave steepness, heading and speed.
Figure 22: Model of NSC USCGC BERTHOLF emerging from
a breaking wave in a head sea state with a significant wave
height of 9m.
Figure 23 compares the whipping factor determined from the
derived formulation with the measured one. For the different
tests, this figure includes as the blue diamond’s the mean
whipping factor from the model tests together with its 95%
confidence interval. The red squares shown in the figure
represent the whipping factor resulting from the derived
formulation. As can be seen, the two results are quite close. On
average, the difference between them is 0.3%. The standard
deviation is 0.01.
Figure 23: Whipping factor obtained from model tests and the
derived formulation. The abscissa shows test numbers.
With a formulation for the whipping factor established, results
from the model tests can be generalized. This was done on the
basis of a long term spectral fatigue calculation using the
transfer function of the stress at FSL01. The calculation was
done twice, once without inclusion of the whipping factor and
once with the whipping factor included. Design environmental
and operational parameters were used. From the comparison of
the two, it may be concluded that the contribution of whipping
to fatigue damage is about 6%.
Table 3 shows that short as well as long crested waves were
tested. A first direct comparison between mean fatigue damages
determined for the same sea state with short and long crested
waves resulted in a ratio varying between 0.7 and 1.7. In order
to make firm statements about this effect based on model tests,
however, a similar exercise as done for the whipping effect
should be carried out. This has not been done so far.
Correlation between full and model scale As part of the model test program, correlation tests were
conducted. For these tests, a number of the wave conditions
measured with the wave buoy during the dedicated trials were
replicated in MARIN’s Seakeeping and Manoeuvring basin in
order to compare the wave loading. Six combinations of
operational and environmental conditions were replicated. These
are shown in Table 4.
Table 4: Sea states investigated as part of the correlation tests, a
heading of zero degrees corresponds with head waves. 180
degrees corresponds to following waves.
Case Speed Hs
sea
Tp
sea
Hs
swell
Tp
swell
Heading
swell
Heading
sea
[kn] [m] [s] [m] [s] [deg] [deg]
A 14.8 2.9 8.7 0.4 13.9 87.0 146.0
B 14.9 1.7 6.6 0.4 13.4 70.2 -11.2
C 14.9 2.6 8.1 - - - 90.3
D 13.6 2.8 9.2 - - - 54.1
E 5.4 2.7 8.5 - - - -12.7
F 15.4 2.3 8.1 0.6 13.4 148.1 -174.9
An example of the correlation between vertical bending moment
over the length of the ship measured during the trials and the
model tests is given in Figure 24. This figure shows good
correlation. Overall, the results were satisfactory. For the
present tests, replication of the sea condition was based only on
spectral parameters. Modeling the spectral shape allows for a
better assessment of the differences between the two
measurements. Two important additional uncertainties in this
comparison are related to the measured wave and the derivation
of the vertical bending moment from the LBSG measurements.
The effect of the statistical uncertainty is included for the model
test results. A similar interval is applicable to the vertical
bending moment measured during the trials.
Drummen
Figure 24: Example of correlation between vertical bending
moments (in terms of significant amplitude) measured during
the trials (black dashed line) and the model tests (purple full
line).
CONCLUSIONS AND RECOMMENDATIONS
The full scale on board measurements provided substantial data
on the actual operational profile adopted and the environment
encountered by the NSC USCGC BERTHOLF as well as on the
fatigue budget consumption. From the collected wave data, it
may be concluded that the ship is operated in less severe
conditions than was assumed during design of modified
structure. Combined with strain monitoring at key locations, this
provided a valuable indicator of the true operational response
profile of the ship for updating fatigue life predictions and
structural maintenance scheduling, with the potential for
improving availability and extending the safe working life of the
hull.
Model tests with the six segmented backbone model have
contributed to better understanding of the hydrodynamic
loading. A comparison between measured wave induced load
effects during the dedicated trials and model tests showed a
good correlation. Based on results from the model tests, it was
concluded that weakly nonlinear effects do not contribute
significantly to fatigue damage. For sea states with a significant
wave height smaller than about 4m, whipping loads have a
limited contribution to the fatigue budget consumption. The hull
girder bending due to linear wave loads in these conditions
dominates the magnitude of fatigue damage. A criterion was
developed to determine the contribution of whipping to the
fatigue damage. This resulted in a long term whipping
contribution to the fatigue damage of 6%. For the current
correlation work between trials and the model tests, the
whipping response was not addressed. As part of a subsequent
correlation effort, also the whipping response should be
addressed.
From investigations into the spectral shape, it was concluded
based on measurements and long term spectral fatigue analysis
that short crestedness reduces the fatigue damage by about 25%.
ACKNOWLEDGEMENTS The authors would like to thank Rubin Sheinberg, Chris Cleary
and Mirek Kaminski for initiating the FLAP and the Valid
project. The authors also acknowledge the significant
contributions of the Valid JIP members including American
Bureau of Shipping, BAE systems, Bureau Veritas, Damen
Shipyards, Defense Research & Development Canada, DGA
France, Huntington Ingalls, Lloyds Register and Office of Naval
Research. The guidance and expert contributions of Theo
Bosman are also acknowledged.
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Marine Technology, Norwegian University of Science and
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ML, “Structural Fatigue Life Assessment and Sustainment
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