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

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me

d f

atig

ue

bu

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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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