Full and Model Scale testing of a New Class of US Coast Guard Cutter

Transcription

1 Full and Model Scale testing of a New Class of US Coast Guard Cutter Ingo 1, Marcus Schiere 1, Reint Dallinga 2, and Karl Stambaugh 3 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 Length Between Perpendiculars Beam, Maximum Design Draft m m m 4.39 m Block Coefficient Displacement (fully appended) 4500 ton

2 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. top of house 02 level AP : Bulkheads 01 level main deck 2 nd deck main deck : Instrumented sections 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. 5.0E E E E E E E E E E+07 MY 0.0E section location (m) Speed 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 height 1. 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 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. 0 kt 5 kt 15 kt 18 kt 21 kt 28 kt 0 kt 5 kt 15 kt 18 kt 21 kt 28 kt

3 A decrease in average vertical bending moment is also seen in the model test results presented in Figure 14. 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. 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

4 Horizontal displacement [-] Vertical displacement [-] Vertical displacement [-] 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 Three node vertical mode 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 Two node vertical mode x [m] 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 x [m] 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 two node horizontal three node vertical Two node horizontal mode 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 x [m] 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. 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

5 probability consumed fatigue budget [%] 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. heading and speed. This spectral fatigue approach is outlined in more detail in Hageman et al. (2014) and ABS (2012) GWS Measured up to Measured up to Measured up to Measured up to Measured up to design 30 year target significant wave height [m] 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. 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 (1) design operations measured operations up to 2011 measured operations up to 2012 forecasted measured fatigue year 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.

6 consumed fatigue budget [%] The resulting Palmgren-Miner equation is given as: In Eq. 3 is the fatigue damage and the stress range at the i th stress cycle. Stress cycles were Rainflow counted using WAFO 2. 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. SN unfiltered SN filtered SN unfiltered (CM) FDS A (25MPa) FDS B (25MPa) FDS C (40MPa) FDS D (40MPa) design 30 year target F47S1 year 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). (3) 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

7 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, : contribution of longitudinal displacements in the bending and avoiding structural damping due to friction. (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 (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 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,

8 90deg, 105deg, 120deg and 180deg 3. 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 (H s ), peak period (T p ), 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 H s [m] T p [s] U [kn] Heading [ ] * * * * * * * * * 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

9 FSL01 FSL02 FSL03 FSL04 FSL05 FSL06 FSL07 FSL08 FSL09 FSL10 FSL11 FSL12 FSL13 FSL14 FSL15 FSL16 FSL17 FSL18 FSL19a FSL19b FSL31 fatigue damage [-] fatigue damage [-] 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 Damage ratio : Estimated / Direct 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 et al. (2008) x x 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 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. 0.8

10 Whipping factor [-] fatigue damage [-] fatigue damage [-] whipping factor [-] Figure 18: Contribution of each sea state to the long term mean WFHF damage per hour and test and its 95% confidence interval 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 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) Wave steepness [-] model tests Veres-Winsir Veres-Winsir model test trendline Veres-Winsir trendline 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. 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., 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 (6)

11 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. 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. 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 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 B C D E F 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. Figure 23: Whipping factor obtained from model tests and the derived formulation. The abscissa shows test numbers.

12 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. 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 REFERENCES American Bureau of Shipping. Guidance Notes on Spectralbased 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), 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 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): Hageman, R,, 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 Nihei K, Muragishi O, Kobayashi T, Ohgaki K, Umeda A, Remaining life estimation by fatigue damage sensor, Bridge 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,, 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