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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

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section location (m)

0 kt

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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

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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

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Measured up to 11-2010

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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

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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.

REFERENCES

American Bureau of Shipping. Guidance Notes on Spectral-

based Fatigue Analysis for Vessels, 2012

Brodtkorb PA, Johannesson P, Lindgren G, Rychlik I,Rydén J,

Sjö E, “WAFO - a Matlab toolbox for analysis of random

waves and loads”, Proc Int Offshore and Polar Eng Conf,

Seattle, Washington (2000)

Drummen, I, “Experimental and numerical investigation of

nonlinear wave induced load effects in containerships

considering hydroelasticity”, Ph.D. Thesis, Department of

Marine Technology, Norwegian University of Science and

Technology, Trondheim, Norway, 2008

Drummen I, Storhaug G, Moan T, “Experimental and numerical

investigation of fatigue damage due to wave-induced

vibrations in a containership in head seas”, Journal of Marine

Science and Technology 2008;13(4):428–45.

Hageman, R, Drummen, I, Stambaugh K, “Structural Fatigue

Loading Predictions and Comparisons with Test Data for a

New Class of US Coast Guard Cutters”, to be presented at the

Ship Structure Committee Ship Structures Symposium held

in Linthicum Heights, Maryland, May 18–20, 2014

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Engineering 163, Issue BE 1, March 2010

Rogers, L, Stambaugh, K, “Application of acoustic emission

technology for health monitoring of ship structures”, Ship

Structure Committee, Baltimore, Maryland,2014

Stambaugh, K, Drummen, I, Cleary, C, Sheinberg, R, Kaminski,

ML, “Structural Fatigue Life Assessment and Sustainment

Implications for a new class of US Coast Guard Cutters”, to

be presented at the Ship Structure Committee Ship Structures

Symposium held in Linthicum Heights, Maryland, May 18–

20, 2014

Thornhill, E., “Real Time Local Sea State Measurement Using

Wave Radar and Ship Motions”, SNAME Transactions, 2010

Tuitman JT, Malenica Ŝ, “Fully coupled seakeeping, slamming

and whipping calculations”, Journal of Engineering for

Maritime Environment 2009, Vol 223, No M3