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Paper No. Year- Hageman 1
Structural Fatigue Loading Predictions and Comparisons with Test
Data for a New Class of US Coast Guard Cutters
Remco Hageman1, Ingo Drummen1, Karl Stambaugh2, Thierry Dupau3, Nicolas Herel4, Quentin
Derbanne5, Marcus Schiere
1, Yung Shin
6, Peter Kim
6
1. MARIN
2. USCG Surface Forces Logistics Center
3. DCNS, Formerly DGA Hydrodynamics
4. DGA Hydrodynamics
5. Bureau Veritas
6. American Bureau of Shipping
This paper presents an overview of the fatigue assessments conducted for the US Coast Guard’s fatigue life
assessment project. A typical fatigue assessment is associated with several assumptions and simplifications
introducing uncertainties. The measurements conducted within the project included full and model scale tests.
Considerable numerical analyses have taken place as well. Furthermore, the measurements and numerical analyses
allow to assess the effect of several of these assumptions on the fatigue life prediction. For example, different
methods of calculating the hull girder bending have been compared with measurements.
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 design procedure; monitoring;
uncertainties assessment; fatigue life prediction
INTRODUCTION The United States Coast Guard (USCG) initiated a project to
assess fatigue design approaches for its new National Security
Cutters (NSC), which became known as the Fatigue Life
Assessment Project (FLAP). A condensed overview of this
project and its results are provided by Stambaugh et al. (2014).
Predicting the fatigue lifetime of a ship hull structure involves
the prediction of hull loading in a seaway, and comparison of
the loading 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, Defense R&D Canada, DGA
Hydrodynamics, Lloyd’s Register, Ingalls Shipbuilding and
Office of Naval Research participated in the VALID Joint
Industry Project. 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.
The FLAP goals were achieved through a model test program
supported by dedicated full scale trials (Drummen et al., 2014).
Measurements taken during the 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 USCGC
BERTHOLF. A photograph of the USCGC BERTHOLF is
shown in Figure 1. Main characteristics of the Cutter are shown
in Table 1.
This paper presents a comparison between fatigue loading
predictions and measured data from full scale measurements of
structural response to a measured wave environment. The
fatigue assessment procedure will be described in detail to show
which assumptions and models are important in the procedure.
The main part of this paper will show the effect of several
assumptions on fatigue life prediction using data obtained from
simulations, model tests, full scale trials and monitoring.
Figure 1: USCGC BERTHOLF instrumented as part of FLAP
Paper No. Year- Hageman 2
Table 1: Main particulars of USCGC BERTHOLF at the time of
the dedicated trials
Length Overall 418.60 ft 127.59 m
Length Between Perpendiculars 390.00 ft 118.87 m
Beam, Waterline 48.89 ft 14.9 m
Beam, Maximum 54.00 ft 16.46 m
Design Draft 14.40 ft 4.39 m
Block Coefficient 0.492 0.492
Displacement (fully appended) 4430 LT 4500 ton
FATIGUE DESIGN APPROACH
To assess the safety and potential operational restrictions of a
ship’s structure, designers analyze the limit state functions of
that vessel. Most commonly used limit states include the
Accidental Limit State (ALS), Ultimate Limit State (ULS),
Fatigue Limit State (FLS) and Service Limit State (SLS). The
ALS deals with the ships capacity during and after an accident,
such as fire or collision. The SLS deals with the assessment of
conditions under which the vessel can still perform its main
duties even though some functionality may be impaired. The
ULS considers failure mechanisms such as plate buckling and
yielding of the material. The FLS addresses long-term structural
damage from exposure to irregular loads of varying magnitudes.
This paper considers the assessment and uncertainties of loads
for the FLS. The fatigue failure mode is well established and
commonly addressed using the spectral fatigue assessment
procedure (ABS, 2012).
At the microscopic level, any structure contains minor defects or
cracks. At the tips of these cracks, localized stress concentration
will occur. Due to repetitive loading of the structure, these
microscopic cracks will gradually grow. The crack will
eventually attain a size at which an unstable fracture may occur.
A “fatigue failure” refers to structural failure due to gradual
growth of defects.
Figure 2: Fatigue design procedure
In order to perform a fatigue assessment, several steps need to
be followed. Figure 2 gives a general overview of these
calculation steps. When executing a spectral fatigue analysis,
the hydrodynamic loading and structural response can be
assessed in a joint model. The overall procedure can be executed
entirely in the frequency domain and, as a result, the procedure
becomes very time efficient. In this section, the calculation steps
in Figure 2 and the associated equations will be discussed. The
final result is a procedure to determine the expected fatigue
damage accumulation during the lifetime of the vessel.
Fatigue failure is the result of exposure of the structure to load
cycles. In order to assess fatigue, all load cycles that the
structure will experience during its lifetime have to be
accounted for. The resistance of the structure with respect to
fatigue is modeled by an SN-curve. This is a statistical model
which describes the relationship between load magnitude and
the expected number of load cycles before failure. Methods
based on first principle physics to describe fatigue resistance are
available (Rogers and Stambaugh, 2014). However, these
methods are not as straightforward to implement and require
more extensive calculations than the S-N approach.
The following steps describe how the number of load cycles
during a sea state of limited duration can be found. During this
time the wave energy spectrum is described by a spectral
shape and a spreading function as follows:
(1)
A frequently used spectral shape is the JONSWAP spectrum;
the spreading function is often represented by a cosine function
(DNV, 2010). The wave energy spectrum describes how the
total wave energy is distributed over different frequencies and
different directions. The wave spectrum is typically described
using the significant wave height and a characteristic period.
The entire range of wave conditions comprises the
“environmental conditions” referred to in Figure 2.
When operating in waves, the vessel will experience motions
and hull girder bending. In this analysis, only loads due to hull
girder bending will be considered. A hydrodynamic analysis is
executed to assess the amount of hull girder bending. The vessel
will respond differently to waves with different frequencies due
to the inertial and stiffness properties of the system. The
response amplitude operator (RAO) is a transfer function which
describes the magnitude of the response, in this case vertical
bending moment (VBM), with respect to a unit wave as a
function of the frequency of the incoming wave. Different tools
and techniques are available for calculating the RAO. For this
paper, a number of numerical approaches and an empirical
approach have been used. These will be discussed in the next
section.
The RAO depends on the way the unit is operated. For example,
the vessel will respond differently to head waves than to beam
Paper No. Year- Hageman 3
waves. The speed of the vessel in waves will also affect the
response. The vessel speed and heading are referred to as
operational conditions.
The RAO describes a linear relationship between load and
response. In order to examine nonlinear results, time domain
simulation is required. A fatigue assessment requires the
analysis of a large number of combinations of environmental
and operational conditions. A time domain simulation for all of
these conditions may lead to unacceptable calculation times. For
fatigue analysis, the effect of nonlinearities in the hydrodynamic
loads, such as whipping and asymmetry between hogging and
sagging moments, is limited, since the majority of the fatigue
load is encountered during moderate sea states (Drummen et al.,
2014).
The local stresses at fatigue critical elements originate from the
global hull girder bending. The transfer function describing the
relationship between vertical bending moment and local stresses
can be found using coarse methods, such as using tabulated
factors, or more advanced finite element (FE) analysis. A
detailed FE model of this vessel was created by Bureau Veritas.
This model is used for the analysis of local stresses. Due to local
inertia and stiffness properties, the transfer function between
stresses and vertical bending moment, , will depend on
the frequency of the applied load. This transfer function neglects
any nonlinear material behavior, such as plasticity. Eq. 2 shows
how a stress RAO, which describes the relationship between the
local stress and the incoming waves, can be calculated. The
response spectrum of local stresses can be calculated
following Eq. 3.
(2)
(3)
Wave heights within a short-term period are assumed to be
narrow-banded. As a result, the stress cycles are narrow-banded.
In the case of analyzing long-crested waves, i.e. there is no
wave energy spreading over different directions, this implies
that the stress ranges follow a Rayleigh distribution. However,
Sharpe (1990) shows that, in short-crested waves, the deviation
of the stress range distribution from the Rayleigh distribution is
very small. The Rayleigh distribution is, therefore, also applied
for short-crested waves. The Rayleigh density function is given
by Eq. 4.
(4)
in Eq. 4 is the square root of the integral of the response
spectrum found in Eq. 3 multiplied by . defines the
number of cycles before failure at a certain stress range. This
parameter can be determined from the SN-curve, see Eq. 5. In
combination with the Palmgren-Miner rule for fatigue
accumulation, Eq. 6 for the total fatigue is obtained. is the
total fatigue damage accumulation during a single short-term
sea state. In these equations, and are SN-curve parameters.
Depending on the geometry and loads, each structural detail is
assigned a fatigue class. For each fatigue class tabulated, SN-
curve parameters are available.
(5)
(6)
is the number of cycles with a given stress range during
the time with duration T. Eq. 7 shows the relation with the
distribution function in Eq. 4.
(7)
is the mean zero-crossing period, which can be derived from
the response spectrum in Eq. 3. The gamma function is defined
in Eq. 8. By combining Eqs. 4, 6, 7 and 8, a very condensed
expression for the fatigue accumulation during a single sea state
with duration T is found in Eq. 9. This result is very commonly
used in shipbuilding fatigue assessment; see e.g. Nolte and
Hansford (1976).
(8)
(9)
Eq. 9 describes the sustained fatigue during a short-term sea
state with given environmental and operational conditions. To
assess the long-term fatigue, a scatter diagram, which describes
the long-term environmental conditions, and an operational
profile, which describes the long-term mode of operations, are
required. To calculate the long-term fatigue, each possible
combination of environmental and operational conditions needs
to be analyzed. The combined probability of occurrence of these
conditions needs to be taken into account. Eq. 10 provides the
long-term fatigue assessment, represented by , for a vessel
with a design life . In this Eq. and refer to
environmental and operational conditions respectively.
(10)
According to the Palmgren-Miner rule, the fatigue damage
calculated in this way should not exceed one. In fatigue design
of offshore structures, the maximum allowable fatigue damage
is often lower, depending on the accessibility and criticality of
each detail (Kaminski, 2007). In this paper, no such safety
factors will be considered.
UNCERTAINTIES In the previous section, the fatigue analysis procedure was
described. In this process, a number of assumptions and
simplifications have been made. Efforts have been made to
Paper No. Year- Hageman 4
quantify the effect of these uncertainties on the fatigue
assessment.
In order to assess fatigue life damage onboard of the Cutter, the
vessel was heavily instrumented with different types of sensors.
The sensors included a wave radar and multiple strain gauges.
More details on the sensors and the monitoring campaign can be
found in Drummen et al. (2014). The application of a wave
radar system allows an evaluation of design assumption on wave
energy descriptions. This also allowed a comparison between
spectral fatigue approach based on wave measurements and the
time domain fatigue approach based on measured strains. The
primary fatigue load on the vessel is hull girder bending.
Therefore, some analyses focus on the quantification of hull
girder bending accuracy.
The strain gauges were used to measure the load cycles at
different fatigue sensitive structural details. To determine the
load cycles from the strain measurements, the WAFO rainflow
counting algorithm was used (Brodtkorp et al., 2000). Rainflow
counting is usually assumed to be the most accurate way of
determining load cycles through strain measurements. Equation
6 is used to calculate the fatigue using strain measurements. The
number of stress cycles, , is directly obtained from the
rainflow count algorithm. The measurement sensors are
assumed to measure the stresses exactly. Moreover, multi-
axiality of the stresses is usually neglected. In this paper only
fatigue load is analyzed, fatigue resistance is not discussed,
neither is the Palmgren-Miner damage criterion.
Wave modelling The method outlined in Figure 2 assumes the waves to have a
theoretical spectrum shape and are generally long-crested. The
relevant parameters are as indicated under “environmental
conditions” in the top right corner of this figure. When
performing the long-term spectral fatigue analysis outlined in
Figure 2 with a short-crested spectrum based on a cosine
squared spreading function, a reduction in fatigue damage of
20% was found. In order to assess this effect from the
measurements, the measured wave spectrum was integrated
around the mean heading. In this way, a long-crested spectrum
was obtained. By combining this long- crested spectrum with a
stress RAO, the fatigue damage was found. This was compared
with the fatigue obtained when using the measured short-crested
spectrum directly. Doing this resulted in an increase of the
damage of about 20% when going from a short to a long-crested
spectrum.
For the long-term calculations shown in Figure 2, a JONSWAP
spectrum is used with peak enhancement factor of 3.3 Using the
design environmental and operational parameters and a long-
crested JONSWAP spectrum, the effect of changing this factor
from 1 to 5 was about 15% on the forecasted fatigue damage.
The damage increases with the peak enhancement factor. When
using a Bretschneider spectrum instead of a JONWAP spectrum,
the fatigue damage is slightly reduced. On the other hand, a
small increase is found when using an Ochi spectrum. It was
concluded that the spectral shape is very limited effects on
fatigue damage. Figure 3 shows a typical comparison of
different theoretical spectral shapes.
Figure 3: Example of comparison of spectral shapes for a
significant wave height of 5m and a peak period of 11s
Narrow-banded loads The method outlined in Figure 2 can be accomplished using
either a spectral analysis or a time domain method using
rainflow counting. In order to determine the damage from the
obtained response spectrum, it is generally assumed that this
spectrum is narrow-banded, i.e. the stress range amplitudes
follow a Rayleigh distribution. In order to investigate the
uncertainty of this assumption, the fatigue calculation was done
twice. Once using spectra, and once using time series derived
from these spectra. A stress time series of three hours duration
was used for this calculation. A time step of 0.1s was used. With
this combination, the error was less than 1% compared to more
refined parameters. Part of the reason for this is that a statistical
error is averaged out due to the large amount of data that is used
in the analysis. The resulting time series was rainflow counted.
By comparing the two, results, it was found that the narrow-
banded assumption produces a fatigue damage that is
conservative by approximately 5%.
Analysis tools The following four tools are used to determine the
hydrodynamic loading as shown in Figure 2:
Universal RAO
VERES-frequency domain
PRECAL
Hydrostar
Hull girder bending is the dominant load considered in the
fatigue analysis; therefore, analysis of the performance of these
tools relates directly to the accuracy of the fatigue calculation.
The universal RAO is an RAO of the vertical bending moment
that is normalized using basic ship parameters and based on a
number of model tests and full-scale measurement on frigates.
The method was developed by e.g. Sikora et. al. (2002). This
0 0.5 1 1.5 2 2.50
2
4
6
8
10
12
frequency [rad/s]
spe
ctr
al d
en
sity
JONSWAP =3.3
JONSWAP =1
JONSWAP =5
Bretschneider
Ochi
Paper No. Year- Hageman 5
method enables quick assessment of the ship’s response based
only on main particulars. It is a useful tool for preliminary
design assessment.
VERES-frequency domain is a linear hydroelastic 2D or 2.5D
strip theory code, see e.g. Drummen (2008). Strip theory
methods assume that the excitation and reaction forces
experienced by the individual sections, which are computed for
zero speed, are completely independent. This neglect of the
downstream interaction also has consequences for the predicted
bending moments; therefore, their accuracy degrades towards
the stern. Linear 3D diffraction theory programs, like PRECAL
and Hydrostar, solve the diffraction problems explicitly.
Because of this increasing accuracy, it yields a complete
prediction of the relative wave elevation. The main problem
with both codes is the use of zero-speed Greens functions in the
evaluation of the dispersion of the reflected and radiated waves.
This neglects the typical V-shaped downstream wave generation
and the resulting influence on hull loading. Consequences are
again visible in the local relative wave elevation and related
added resistance. The predicted internal loads are better than the
strip theory prediction but again, the prediction in the stern area
is not very good.
Although not used in this project, a Rankine source code like
FATIMA (Bunnik, 1999) uses the actual steady flow as a
reference in the linearization. As a consequence, it accounts for
the speed induced changes in hull immersion and its effect on
the restoring terms. Because it accounts for the actual dispersion
of the reflected and radiated waves, it predicts the relatively
high relative wave elevation in the diverging flow at the bow
and the relatively low level in the converging flow at the stern
quite good. As a consequence, the predicted added resistance
and internal loads improve as well.
Although vertical plane hull loading is predicted well by the
panel codes, a complete prediction requires modelling of the
rudder reactions on the ship motions and the related forces. In
addition, they need to account for the roll damping resulting
from sources other than waves (hull lift, bilge keel, skeg, eddy
damping) in the prediction of resonant roll and the manoeuvring
reaction forces (the momentum lift and cross-flow drag terms
used in empirical manoeuvring models) for the cases with very
low wave encounter frequencies. Comparisons between
prediction of VBM, model tests and full-scale measurements
indicate these factors are relatively small impact relative to other
factors identified.
The structural response, as shown in Figure 2, is assessed using
a finite element (FE) model. The coupling between the
hydrodynamic software Hydrostar and finite element software
Homer provides for an integrated framework of assessing the
structural response due to environmental loads. The following
three finite element models were created by Bureau Veritas for
the Valid project:
Coarse mesh model
First level refined model
Second level refined model
The coarse mesh model consists of about 70000 nodes and
140000 elements, see Figure 4. As part of the first level refined
model, the number of elements in the fatigue prone area
between the 01 level and 02 level decks and from Frame 40 to
Frame 56 was increased by a factor four. The first level refined
model consists of about 120000 nodes and 200000 elements.
The second level refined mesh was refined further in the vicinity
of the several sensors. This model consists of about 190000
nodes and 270000 elements. The refined mesh around the
fatigue sensitive locations is shown in Figure 5.
These models also introduce some uncertainties in the
assessment procedure. Among the main sources are the type of
element used, the dimension of the elements and numerical
procedures used. Also, the conversion of loads from the
hydrodynamic model to the structural model will account for
some uncertainties. These specific uncertainties will not be
addressed in this paper; however, they are included in the
aggregate differences shown in later comparisons.
Figure 4: Coarse mesh finite element model
Figure 5: Second level refined finite element model around the
fatigue sensitive areas
Paper No. Year- Hageman 6
Prediction accuracy factor tables were created to gain insight in
the accuracy of the different hydrodynamic tools under multiple
operational and environmental conditions. The accuracy of
different hydrodynamic tools has been examined by comparing
the calculated vertical bending moment with the measured
bending moment during each sea state. The bending moments
were derived from the strain gauge measurements combined
with a conversion matrix that converts global strains to sectional
load effects.
The conversion matrix was derived from FE calculations. For
the derivation of this matrix, it is assumed that the total ship’s
deformation is a superposition of the first few global flexural
vibration modes. Drummen et al. (2014) present the outcome of
a validation study of this conversion matrix. Long- term extreme
bending moments were calculated with transfer functions
obtained directly from Hydrostar and estimated using the
conversion matrix and strains derived from the coupling
between Hydrostar and Homer. Good agreement was found for
both the horizontal and the vertical bending moments.
For each half-hour sea state, the response spectrum of the hull
girder bending moments is calculated. This is shown in Eq. 11,
where the wave spectrum is measured using the wave radar and
the RAO is obtained from one of the analysis tools. A wave data
fusion analysis was executed to ensure accurate wave height
measurements (Thornhill, 2010). The effect of short- crested
waves and spectral wave shape was eliminated from this
comparison by using the actual measured sea state.
(11)
The response is assumed to be Rayleigh distributed. In that case
the standard deviation of the response can be determined
directly from the response spectrum by , in which is the
integral of the response spectrum. This parameter is referred to
as the calculated standard deviation. Following the definition of
the standard deviation, this parameter can also be determined
from a measured time signal. By comparing the calculated
standard deviation with the measured standard deviation, the
tool accuracy is assessed. The prediction accuracy factor, PAF,
is defined as the ratio between measured and calculated standard
deviation. Eq. 12 defines the regression line between these two
quantities using the PAF parameter. The regression line was
derived from the data using a least square estimator. is the
vector containing the measured standard deviations, while is
the vector of the calculated standard deviations using Eq. 11
(12)
Tool accuracy depends on a number of variables. Typical
dependencies are heading vessel speed, wave height and wave
period. Moreover, calculations are performed for different
sections, both fore ship, midship and aft ship.
Over 6000 sea states of half hour duration, i.e. 125 days in total,
was analyzed in this way. In order to keep results insightful, all
data points are aggregated in the format of a scatter diagram.
The results of all processed conditions with similar peak period
and wave height are combined. A regression analysis is then
executed to determine the overall prediction accuracy of the
tool. A typical example of the PAF table for the tool PRECAL is
shown in Table 2. A value of 1 signifies that the standard
deviation of the bending moment calculated by the tool and the
measured value are equal. A value lower than one means that
the measured bending moment is smaller than the moment
calculated by the tool, i.e. the tool is conservative. A value
higher than 1, shows that the tool provides non conservative
results. Overall, the results in Table 2 show that PRECAL
provides conservative results. This table shows only conditions
of limited wave height. Note that conditions with higher waves
have been encountered and have been processed. However, the
total number of these conditions was considered to be too small
to obtain a reasonable PAF.
Table 2: PAF table that shows the prediction accuracy of
PRECAL for different combinations of environmental condition
The result in each cell is based on a large amount of data points
associated with different cross sections, vessel speeds and
headings. To gain insight in the quality of the tools under
different conditions, a number of figures were created to
visualize the results of different sections, speeds and heading.
The results of the tool PRECAL in wave conditions of 2 to 2.5
meter significant wave height and peak period of 7 to 8 seconds
are displayed in Figure 6 through Figure 8. Based on these
figures, the following conclusions can be drawn:
In stern quartering waves and following waves, the tool
tends to underpredict the bending moment slightly.
At high speeds and beam waves, the tool tends to over
predict the vertical bending moment in the aft ship
section considerably.
Under the same conditions, i.e. high speed and beam
waves, the vertical bending moment at the sections
slightly more forward are over predicted considerably.
At lower speeds, the bending moment is slightly under
predicted at the midship sections.
Paper No. Year- Hageman 7
Figure 6: Performance of PRECAL for different headings
Figure 7: Performance of PRECAL for different sections
Figure 8: Performance of PRECAL for different speeds
Figures such as Figure 6 through Figure 8 can be used to
identify if similar trends exist for different environmental
conditions and different tools. This information can be used in
tool development and further research. These figures also allow
the magnitude of random uncertainty to be investigated and
compared with the magnitude of systematic deviations. For
example the following can be concluded for the wave conditions
of 2 to 2.5 meter significant wave height and peak period of 7 to
8 seconds:
All tools, especially the universal RAO, underestimates
the vertical bending for the beam sea conditions
encountered.
The universal RAO tends to under predict the vertical
bending in the aft ship sections, but over predict it in
the fore ship sections. At sections closer to midship, the
agreement between measurement and prediction is
good.
For following seas, all tools tend to underestimate the
vertical bending moment. However, VERES performs
considerably better compared to the other tools with an
under prediction of 20%, whereas application of the
Universal RAO results in about 30% and Homer and
PRECAL up to 50% under prediction. For stern
quartering waves, a similar trend was identified.
Homer and PRECAL are based on the same theoretical
approach with differences in numeric implimentation.
However, there are differences between the results of
these tools. The differences are most pronounced in the
extreme fore- and aft ship sections.
As shown above, this approach allows for an in-depth analysis
of tool performance. This provides useful information for
further tool development. However, for design applications, a
quick comparison of tool performance is more useful. This can
be achieved by comparing the PAF tables from different tools.
Table 3 shows the results of different tools for different wave
heights. The associated peak period is between 7 and 8 seconds.
The following conclusions may be drawn from an analysis of
the performance of different tools:
Generally, the analyzed tools tend to be conservative.
VERES is the most conservative tool, followed by
PRECAL.
Although PRECAL and Hydrostar are based on the
same theory, the results differ significantly. Note that
in this analysis, an older version of PRECAL was used.
It is suggested to repeat the analysis at a later stage
using the updated program.
The Universal RAO is a very simple method to
estimate the RAO based on main vessel particulars
only. Given the simplicity of this method, it performs
remarkably well for the frigate hull form.
With increasing wave heights, the PAF value of the
tools increases, i.e. the predicted bending moment
becomes less conservative.
Paper No. Year- Hageman 8
If the trends identified here continue at higher wave
heights, the results produced by all tools may become
considerably non conservative. Therefore, additional
measurements at higher wave heights are
recommended.
Table 3: Comparison of PAF for different tools
Hs [m] Universal
RAO
VERES PRECAL Hydrostar
<1 0.90 0.67 0.76 0.92
1-1.5 0.89 0.65 0.81 0.85
1.5-2 0.96 0.70 0.75 0.91
2-2.5 1.07 0.77 0.96 1.01
The Prediction Accuracy Factor tables allow for a quick
comparison of different tools. Furthermore, using a visual
representation of the data underlying the PAF tables, insight in
the performance of the tools under different operational
conditions and for different locations can be identified. The
systematic analysis performed using the monitoring data can
thus be used to identify trends in the accuracy of the tools.
PARAMETER ANALYSIS A sensitivity study of fatigue design and long-term extreme
bending moment was conducted. This study is conducted to
identify the sensitivity of the fatigue assessment with respect to
a number of input variables. The uncertainty of the initial
assumptions with respect to the measurements is not addressed.
The VBM RAOs was obtained from PRECAL for the midship
section of the ship. For the following list of parameters, a
sensitivity study was executed. The parameters can be grouped
in four families, according to the design process in Figure 2:
The operational profile of the ship, top left of Figure 2,
characterized by:
o Ship speed V
o Voluntary reduction of V as a function of
significant wave height Hs
o Heading
o Sailing factor (percent time at sea per year)
o Sailing areas
The modeling of sea states, top right of Figure 2,
through:
o Shape of wave spectra
o Angular spreading of wave energy
o Used wave atlases
o Rules prescriptions
The analyzed structural detail, structural response in
Figure 2, described by
o Local inertia modulus Z
o Associated SN-curve
o Absence or presence of a pre-stress, referred
as global mean value
The variability of vertical bending moment RAOs with
longitudinal distribution of mass on-board, i.e.
hydrodynamic response in Figure 2.
For each of the previous parameters, a sensitivity analysis of the
extreme stress and the fatigue life was performed according to
the following method. A reference value was adopted, with
which numerous computations, for instance N, were achieved.
These N calculations have been performed varying other
parameters. The same N calculations have been performed with
M other values of the considered parameter.
Figure 9 is an example of the typical graphs that illustrate the
obtained results when studying a particular parameter; in this
case, the ship speed, with a chosen reference value of 15 knots.
The chart on the left part shows the total collection of results (M
x N points), given as ratios to evaluate the sensitivity of extreme
stress and fatigue life to ship speed. On the right part of the
graph, the N points referring to the same ship speed are then
reduced to the mean value and root mean square (one color per
speed).
Figure 9: Sensitivity of extremes and fatigue damage to ship
speed
The results of Figure 9 show that fatigue damage increases with
roughly 80% when increasing the speed from 15 to 25 knots.
Similarly, the fatigue reduces with 80% when the speed is
reduced to 0 knots. The effect is slightly larger when
considering head waves only. When looking at the extreme
values, the effect is much smaller. Only a 10% increase is found
at larger speed and a 30% decrease is found for lower speeds.
However, the variation in the extreme bending moment is
slightly larger.
After performing this type of calculation for each of the 13
parameters identified, we can obtain a synthesis of uncertainties
generated by the long-term analysis.
Figure 10 illustrates the synthesis of this study. It highlights that
the long-term linear fatigue is more sensitive to input data than
long-term linear expected extreme stress. This is logical
considering the non-linear relationship between load and
fatigue.
Paper No. Year- Hageman 9
Fatigue damage depends significantly on a number of
parameters and an accurate prediction of fatigue life requires an
accurate description of especially these parameters:
Heading,
Sailing factor,
Sailing area,
Wave spectrum,
Wave atlases origin,
Inertia modulus,
SN-curve.
Figure 10: Comparison of sensitivities
For the heading, it was found that assuming an equi-directional
distribution for incoming waves provided a reduction in fatigue
damage compared to the conditions in head waves. This is true
for both short- and long-crested waves, although the reduction
for short-crested waves was slightly smaller.
The sailing factor is the amount of time spent at sea. A value of
0.8 was selected as a reference value. Considerable lower
values, down to 0.3, were encountered in practice. This results
in a negative correlation for fatigue damage.
The reference sailing area is the North Atlantic. The result of the
North Pacific, Indian Ocean and Mediterranean Sea were
compared to the reference area. For the North Pacific, where the
vessel is operating, a reduction of 10% in fatigue life was found,
but the extreme wave bending moment increased with
approximately 20%. Similar to this, wave atlases origin
describes the effect of using different scatter diagrams from
different operators.
The wave spectrum describes the relationship between fatigue
life consumption and the JONSWAP peak enhancement factor.
This has already been addressed in the section on wave
modeling.
The conclusion that scatter diagram and operational conditions
have a large effect on fatigue damage was supported by the
onboard monitoring, see Figure 11. This figure shows a fatigue
forecast based on the actual environmental and operational
conditions that were measured onboard and those used in the
design. The red line is the target line. Figure 11 shows that the
actual operational and environmental conditions were mild
compared to design assumptions. This has a major impact on the
current fatigue condition of the vessel. Further details can be
found in the discussions by Stambaugh et al. (2014) and
Drummen et al. (2014).
Figure 11: Fatigue forecast based on design and actual operating
conditions measured on board the USCG Cutter
The capacity of a structure to resist fatigue damage depends on a
number of parameters including the section modulus of the hull
girder and the S-N curve corresponding to the subject structural
detail. In this study the effect of assuming an increase and a
decrease, of 20% in the value of section modulus was examined.
In addition, S-N curves from five different sources were used in
this part of the study. This showed that there are considerable
uncertainties associated with estimating fatigue resistance as
well as with estimating fatigue loading.
CONCLUSIONS The assumptions and approaches used in fatigue load
predictions were examined in this paper. Considerable
uncertainties also exist in the assessment of fatigue resistance.
These have not been analyzed in this paper.
year
con
su
me
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
Paper No. Year- Hageman 10
The following uncertainties on fatigue load have been addressed
in detail throughout this paper:
Uncertainties due to modeling of wave systems,
Uncertainty due to narrow-banded loads,
Uncertainties arising from hydrodynamic tools.
The assumptions on the spectral shape of the waves, the long-
crestedness of the waves and the narrow-banded loads were
examined. In total these assumptions on the wave energy model
accounted for a deviation of 50% between the measured fatigue
and the fatigue obtained from the calculation procedure. In all
cases, the fatigue calculation procedure showed conservative
results. This improves the confidence in the design techniques.
However, this need not be the case for all conditions, or, more
generally, for different structures.
The following tools for predicting hydrodynamic loading were
investigated:
PRECAL
Universal RAO
VERES-frequency domain
Hydrostrar
Tables have been created with Prediction Accuracy Factors
(PAF) for each tool. These tables represent the ability of tools to
capture the magnitude of wave bending moments in real
operating conditions. From the collected and the processed data
of the monitoring campaign, it may be concluded that
predictions of the vertical bending moments from Hydrostar and
PRECAL are well in line with measurements. For the data
collected so far, results of the universal RAO also agree well
with measurements. The results from VERES show that this tool
provides a significant over prediction of the vertical bending
moment.
Analysis of other conditions than those experienced by the
Cutter could reveal conditions for which the tools perform better
or not. This information can be used in further development of
the tools themselves. For example, due to the nature of the
program, the predictions for the aft ship of both Hydrostar and
PRECAL were assumed to be less accurate. It was found that
this is the case for PRECAL, especially at higher speeds. Good
tool accuracy of different tools is, at least partly, related to a
favorable combination of under and over predictions.
A parametric study has shown the importance of different
assumptions on fatigue and extreme response analyses. This
study shows which parameters are the most important to be
described accurately when executing a design study for fatigue
and extreme response. The most important parameters were the
scatter diagram, operational conditions and structural capacity.
Overall, considerable uncertainties were identified. An
assessment of all these uncertainties is required for accurate
fatigue prediction. However, by conducting continuous
measurements the actual state of the vessel can be monitored,
and design uncertainties can be quantified.
Fatigue accumulation from hull girder bending was the main
parameter in the analysis. However, when considering overall
structural integrity, other failure modes need to be accounted
for. Interaction between different failure modes may cause
failure that has not been foreseen. Ideally, the analysis of other
failure modes should be addressed periodically using knowledge
gained through the monitoring campaign. This requires a smart
method of data analysis and processing; otherwise, this is a
labor intensive process.
These conclusions apply to fatigue loading of a frigate type hull
form. The numerical modeling and full scale measurements
provide a detailed insight into the differences between actual
conditions and predictions. As a complete data set, this effort
represents a major step in understanding fatigue loading and
structural response in ship structure useful in early design
evaluations, as well as detailed design assessments.
ACKNOWLEDGEMENTS The authors would like to 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, MARIN and
Office of Naval Research. The guidance and expert
contributions of Theo Bosman are also acknowledged.
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