Ice-load estimation for a ship hull based on continuous response monitoring

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1 Ice-load estimation for a ship hull based on continuous response monitoring B Leira 1 *, L Børsheim 1,2, Ø Espeland 1,2, and J Amdahl 1 1 Department of Marine Technology, NTNU, Trondheim, Norway 2 Presently employed by Det Norske Veritas, Norway The manuscript was received on 12 December 2008 and was accepted after revision for publication on 7 April DOI: / JEME Abstract: The expected growth of maritime and offshore activities in arctic areas has led to an increased interest in understanding the risks associated with operating in ice-infested waters. Transportation systems such as large tankers, gas carriers, and bulk carriers that are able to operate throughout the year are of particular interest. One of the key factors for this scenario to occur is the ability to design vessel hulls that possess sufficient strength to be able to resist the pressures generated by the ice fields without any critical damage taking place. This paper is concerned with the estimation of ice loads acting on the hull of the coastguard vessel KV Svalbard, based on strains that were measured during the winters of 2007 and A finite element model of the bow structure is utilized in order to correlate the loading with the measured strains. The influences of ice thickness and vessel speed on the measured strain levels are also investigated. Methods for extrapolation of the hull response into the future for predictive purposes are also addressed. Keywords: ice load, ship hull, strain measurements 1 INTRODUCTION The increased shipping activity in polar waters driven by the oil and gas industry means that transportation systems such as large tankers, gas carriers, and bulk carriers need to be prepared for allyear arctic operations. There are two main options for the operation of such vessels in ice-infested waters: support by an ice-breaker, or cargo ships that can manoeuvre without support from another vessel. It is believed that the utilization of large icebreaking cargo ships has advantages compared to more conventional systems based on the use of an ice-breaker to clear shipping channels. For both types of systems, the loading on a particular ship hull strongly depends on route selection and vessel speed. Lack of information about the actual ice condition and the corresponding inability to estimate or predict the loads acting on the hull have been identified as the critical factors when operating *Corresponding author: Department of Marine Technology, NTNU, Otto Nilsensv. 10, Trondheim, Norway. Bernt.Leira@ntnu.no in arctic waters. This implies that there is a challenging interaction between the adequacy of the rules applied for hull design and the schemes implemented for operation of ships in arctic regions. In particular, the possibility of monitoring the stresses which are induced in the hull by the external ice loading becomes highly relevant. Models for ice-induced loads on the shell structures of ships have a long history. For statistical analysis of ice loads on ship hulls, see references [1 8]. However, accurate models for the computation of prevailing loads on a specific hull is still an identified challenge, and is the background for the ice load monitoring (ILM) project managed by Det Norske Veritas an behalf of its partners. The overall aim of the ILM project is to increase knowledge about the actual ice conditions a vessel will meet, and their effect on the stresses induced within the hull structure. Relevant information obtained from the monitoring system should be communicated to the bridge in order to provide decision support for the navigators. A specific secondary goal for the ILM project is to use instrumentation to assess a credible ice force JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

2 530 B Leira, L Børsheim, Ø Espeland, and J Amdahl distribution on the hull. For an assumed load distribution the hull utilization can be estimated using a finite element analysis approach. This approach reduces the number of sensors involved compared to approaches where utilization is estimated directly from strain sensors. A reduced number of sensors will result in cheaper instrumentation, or may alternatively allow monitoring of larger hull areas. A prototype of the monitoring system has already been tested on the Norwegian coastguard vessel KV Svalbard, resulting in large quantities of collected data on the ice conditions experienced. The vessel is 103 m long with a displacement of 6500 tons. The beam is 19.1 m and the draught is 6.5 m. The vessel operates as a coastguard vessel in the Barents Sea and in the vicinity of the Svalbard islands. These measurements were performed during the winters of 2007 and Some of the results obtained from these measurements are summarized in the present paper. Further details are given in references [9 11]. A brief description of the monitoring system is first given in the following section. 2 ICE-LOAD MONITORING SYSTEM 2.1 Fibre optic strain sensors The applied fibre optic strain sensors are based on fibre Bragg gratings and are equipped with individual temperature compensation. Their relatively small size means that they are easily installed on girders and stiffeners in all parts of the hull. Mounting the sensors on girders and stiffeners ensures that the measurements are not contaminated by local vibrations. 2.2 Electromagnetic ice thickness measurements An important difference between the ILM system and other monitoring systems is the ice thickness sensor sketched in Fig. 1. In the prototype of the system, the sensor was mounted on a wooden beam that protruded ahead of the vessel. Ice thickness data were collected with a sampling frequency of 15 Hz. The sensor combines an electromagnetic (EM) conductivity meter with a sonic distance-measurement system. The EM instrument measures the distance between the instrument and the water below the ice, d EM. The sea ice has a negligible electrical conductivity, whereas the water has a high value. A magnetic field will therefore be induced in the water by the EM instrument, whereas the influence from the ice is negligible. The distance to the water surface is calculated from the strength of the induced field. The altimeter measures the distance to the top of the ice sheet, d sonic, and with d instr expressing the vertical difference between the distance-measurement system and EM instrument. The ice thickness Z ice can be obtained as Z ice 5 d EM 2 d sonic 2 d instr. Some properties of the ice thickness sensor are important to note. Ridge keels will not be measured correctly since they consist of a mixture of unconsolidated ice and water. Their depth will thus be underestimated. Calibration tests have previously been performed on ice ridges in the Gulf of Bothnia. Typical trends were estimated ridge thickness values systematically around 60 per cent of the true ones. It is also important to note that the EM device measures the distance to the water surface over an area of about 12 m 2, whereas the sonic device is capable of detecting more local effects. For further information about the ice thickness sensor, see reference [12]. Fig. 1 Measurement of ice thickness: (a) principle of ice thickness measuring device and (b) the EM device mounted on the bow of KV Svalbard Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009

3 Ice-load estimation for a ship hull based on continuous response monitoring Satellite and meteorological information During the voyage, WeatherView 2 from C-MAP Marine Forecast was used. Information about the ice conditions was supplied from the Norwegian Meteorological Institute in addition to satellite images from other suppliers. This information was used for route planning and validation. 2.4 Display on the bridge A screen is located on the bridge to display the estimated stress levels in relation to utilization of the hull structure as well as all the other measured parameters. Both the instant values and the statistical values are available. 2.5 Mounting of strain sensors A total of 66 optic sensors have been mounted onboard KV Svalbard. The strain measuring arrangement is based on spot checks of critical frames mainly in the bow area. The sensors were mounted on a total of nine frames. Figure 2 shows the location of the instrumented frames and how the sensors are mounted on a frame. Measuring the support reactions rather than the local strains in single plates allows the forces acting on a larger part of the hull to be estimated. At the Fig. 2 (a) Location of instrumented frames and (b) mounting of sensors on a frame JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

4 532 B Leira, L Børsheim, Ø Espeland, and J Amdahl same time the local ice pressure can be estimated by application of empirical or assumed pressure area relationships, i.e. p 5 p(a). By assuming a constant pressure across the area, the pressure is then found by solving the equation A6p(A) 5 F (where F is the estimated ice force on each frame). 3 FINITE ELEMENT ANALYSIS 3.1 Introduction In the following, a finite element analysis of the bow area is outlined. The main task of the finite element study was to determine the area in which the mounted sensors can recognize that a load is present. Such studies were mainly performed prior to installation of the measurement system itself. This will also be useful when the loads are to be estimated based on the measured strains. This task is also important in order to be able to limit the area where an acting load can influence the different strain sensors. If a load far away from an instrumented stiffener influences the measurements at the sensor locations, it is difficult to determine which load gives rise to the specifice measurements observed in each case. For the analysis, the computer program ABAQUS.CAE was applied. 3.2 The model The area that was modelled is indicated in Fig. 3. The rear part of the model is limited by the bulkhead at frame 9 in the horizontal direction and by the first and fourth decks in the vertical direction. The model covers the sensors located at frames 1 to 4. The complete finite element model is also shown in Fig. 3. To avoid any interference with the boundary conditions, both the port and starboard sides of the ship hull were modelled. The model was fixed in all translation directions along the rear edge of the model. This assumption is plausible because the model ends at the bulkhead at frame 9. Since the model covers the entire bow area there is no need for a boundary at the bottom of the model. The initial trial finite element calculation was performed on half of the model. The model was then also fixed along the centreline of the ship. The results within the instrumented area were the same as for the two models, but a small difference was detected when the load was applied at the front of the model. This is the reason for making the complete model of both the port and starboard side. Because this is a ship, the global motion could have an influence on the applied loads. However, since ice loads are mostly impulse loads, and will therefore not contribute to a global motion of the ship, this effect is not considered when applying the boundary conditions. 3.3 Location of sensors within the model Figure 4 shows the numbering of the sensors. KV Svalbard was equipped with sensors on both port and starboard sides, but owing to the symmetry in the model, stresses were only extracted on the starboard side. 3.4 Load outside the instrumented area One important aspect to consider when analysing the measured results from KV Svalbard is to what extent a load applied outside the instrumented area will affect the measurements. The instrumented area is defined as the distance between two stringers in the vertical direction, and the distance between two partial bulkheads in the horizontal direction, assuming an instrumented stiffener is located between bulkheads. If a load acting outside this area were to affect the measured results, it would be difficult to separate the different loads acting on the hull. Regarding the calculated stress in the stiffeners, the difference between a load applied outside the Fig. 3 The finite element model of the hull: (a) the complete model and (b) inside the model Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009

5 Ice-load estimation for a ship hull based on continuous response monitoring 533 Fig. 4 Location of sensors instrumented area and a load applied within the instrumented area is large. For reference loads applied two frames away from the sensors, the induced stress was only around 0.5 MPa. When the load was moved one frame closer to the sensor location, the stresses at sensors 1 and 2 increased to approximately 1 MPa. When the load was applied directly on the stiffener, the von Mises stress in sensors 1 and 2 increased to more than 20 MPa. Hence, the effect of a load applied outside the instrumented area on the sensors on a stiffener is negligible. When considering the horizontal stringers only, the difference between a load applied outside the instrumented area and a load applied on the instrumented area is not that evident. A total of 13 load cases and their respective results were considered. In general the trend is the same as discussed above. When the load was outside the instrumented area, the stresses in the stiffeners were small. The stresses in the horizontal stringers were somewhat larger, but as explained above this effect Fig. 5 The von Mises stress distribution on instrumented stringer 5900 above base line for load case 1 can be neglected. Thus, a load applied more than one partial bulkhead away from an instrumented stiffener or stringer will not affect the measurements in the sensors. Figure 5 shows the von Mises stress distribution within the horizontal stringer when it is subjected to load case 1. It can be observed that the stress distribution is not symmetric around the middle stiffener (which corresponds to frame 4). However, when considering, say, load case 4 the stress distribution will be symmetric, and accordingly the measured strains at both sides are equal in magnitude. 4 MEASUREMENTS FROM KV SVALBARD 4.1 General The following contains an analysis and discussion of the measured data from KV Svalbard. The test voyage was carried out in March The raw data files contained the strain measured at each sensor. The data were sampled at a frequency of 600 Hz. For some of the recorded strain series, the raw data were corrected in order to account for temperature effects where this was found to be required. The statistics files were divided into 30 s, 2 min, and 5 min sequences. In the present study, the 30 s statistics files were applied, as this gives the best time resolution. Within each file one could find statistical data for 157 different parameters. The most important parameters used in this study are: JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

6 534 B Leira, L Børsheim, Ø Espeland, and J Amdahl (a) (b) (c) (d) shear stress at each cross-section; vessel speed; vessel heading; ice thickness. Other parameters such as sea water temperature, thrust power, and ship motion are also available in the files. For the different parameters the following statistical values were stored: (a) (b) (c) (d) (e) (f) (g) (h) (i) number of values used to calculate statistical parameters; mean value; standard deviation; skewness; kurtosis; minimum up-crossing count; maximum up-crossing count; mean up-crossing count; max peak peak value. March 2007, between 14:00 and 19:00. Figure 6 shows an example of the ice conditions during that particular period. To get a good graphical presentation of the results, the selected period has been split into periods of an hour. 4.2 Ice thickness measurements In addition to considering the time sequence from 18:00 to 19:00 on 25 March 2007, a selection of other measurement sequences was made in order to obtain more comprehensive statistical information. These sequences are summarized in Table 1. Ice thickness data presented by Kujala [8] argue for a log-normal distribution for ice thickness in level ice conditions. Results obtained from the measurements from KV Svalbard are shown in Fig. 7. The data are mean values over 30 s intervals between 23 March 2007 and 28 March 2007 read from statistical files stored by the monitoring system. The measurements provide a comprehensive database of statistical information. Some of the main observations are discussed below. Based on further study of the data, it was also decided to look at more detailed time series for a particular time segment. The particular record was obtained on 25 Fig. 6 Ice conditions at 17:00 on 25 March 2007 Fig. 7 Histograms of ice thickness based on 30 s statistics for (a) 24 March 2007 to 28 March 2007 and (b) between 19:00 and 21:00 on 26 March 2007 Date Table 1 Interval Selected measurement sequences for the purpose of statistical analysis Mean ice thickness (m) Standard deviation of the thickness (m) Mean speed (knots) :10 05: :30 17: :00 21: :00 19: :35 20: :30 21: Standard deviation of the speed (knots) Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009

7 Ice-load estimation for a ship hull based on continuous response monitoring 535 Negative values below 20.5 m and above 10 m were considered to be meaningless and therefore were disregarded. In total they add up to less than 1 per cent of the data. Small negative values may be due to inaccurate measurements or calibration errors, and values above 250 cm are therefore included. The largest group is found below the 2 m thickness, and probably corresponds to pack ice without ridges. The mean thickness is around 40 cm, which closely agrees with observations during the voyage. The other group is located around 3 m, and may represent ridges. (However, this group is also observed in the 5 min statistics, which is not expected unless the ice thickness sensor is at rest above a ridge.) A third group of data is found between 6 and 10 m thickness values. This is considered as high, but it is unclear whether or not they are real. A ridge encountered during the test voyage was measured to be 8 m thick by the ice thickness sensor, but the true ridge thickness was not measured and is hence unknown [13]. The selection of recording periods for statistical analyses are not grouped in relation to ridging. Instead, they were chosen based on uniform vessel speed, which is not expected in ridged areas. Results for a subset of the thickness measurements are shown in Fig. 7(b) for the period between 19:00 and 21:00 on 26 March The mean thickness is 0.9 m, with a standard deviation of 0.6 m. It should be noted that the negative values clearly deviate from the rest of the samples, which may invalidate the assumption of a calibration error. A log-normal distribution was fitted to the positive data in compliance with the findings of Kujala [8] for level ice observations. The resulting fitted distribution is somewhat skewed to the left as compared to the observation histograms. ice load, there does not seem to be any reasonable correlation. However, if the peak loads for this particular time sequence are compared, then the correlation is more clear. This is shown for frame 2 in Fig. 8(a). A sudden increase in the ice thickness results in a high load peak. However, it is seen that an increase in the ice thickness does not always result in an increase in the load. This can be partly explained by the fact that there is a spatial distance between (all of) the hull frames and the area where the ice thickness is measured (i.e. ahead of the bow). Clearly, the loads acting on the different frames will not occur at the same point in time. To be able to incorporate all the peaks in all frames, Fig. 8(b) shows the maximum peak load for all frames (from frame 1 to frame 6). This gives a more distinct connection between the 4.3 Consideration of response time histories In the following, the relationships between the ice load acting on the hull and the ice thickness and vessel speed are considered. In previous studies, the ice thickness and vessel speed were found to have a strong influence on the forces acting on the hull; see for example references [8, 14]. The ice loads acting on each frame were estimated based on shear strains and resulting shear forces for the respective frames Ice load versus ice thickness The simultaneous variation of the ice load and ice thickness is first considered. Regarding the mean value of the response of a specific frame versus the Fig. 8 Variation of peak load and ice thickness between 18:00 and 19:00 for (a) frame 2 only and (b) all frames JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

8 536 B Leira, L Børsheim, Ø Espeland, and J Amdahl ice load and the ice thickness than what was observed when only a single frame is considered Ice load versus vessel speed When considering the time variation of the mean value of the ice load versus the vessel speed, a distinct positive correlation is observed. An increase in the speed is found to result in an increase in the load (however, it should be noted that the mean load is quite small and does not induce any significant stresses in the hull). This is as would be intuitively expected. However, as seen in Fig. 9 the peak load instead seems to increase when the speed is decreasing, as shown in the figure. This could be due to the vessel experiencing a higher resistance from the ice sheet, hence leading both to reduced speed (i.e. for small vessels) and a corresponding increase of peak load. This is further supported by considering the corresponding time variation of the vessel speed versus ice thickness. It is observed that, for time segments where peak values of the ice thickness occur, there is typically an associated reduction of the mean vessel speed. This is even more pronounced for the instantaneous speed (as compared to the mean speed). 4.4 Statistics of ice loads based on measured strains One of the overall goals for the ILM system is to communicate information about the prevailing ice conditions to the bridge. The expected force maxima are relevant in this setting, as they give indications on future loads. Short-term predictions are focused upon here with the aim of predicting the next 30 min of operation. Long-term distributions for expected loads during a season of operation or the lifetime of the vessel may also be established, such as described in reference [8]. In reference [14] two different methods are presented for the purpose of establishing short-term extreme distributions of the ice load. These methods are referred to as the peak amplitude approach and the time window approach, respectively. Homogeneous conditions are assumed by both approaches, which is not necessarily valid for pack ice conditions Peak amplitude approach The peak amplitude approach is also referred to as the peak over threshold method, as peaks are defined as observations exceeding a predefined threshold value. The maximum value in a section is taken as the peak amplitude. A distribution model is then fitted to the observed maxima; see Fig. 10(a) for an example of a fitted exponential distribution. A separate distribution is also fitted to the observed number of events during an interval; see Fig. 10(b) for an example. An exponential distribution fits the data quite well for these cases. These models are combined to describe the distribution of interval maxima Time window approach The time window approach differs from the previous method in the way peaks are identified. In this approach, the time history is divided into shorter subintervals, and the maximum for each interval is considered as a peak value. Instead of finding a distribution for the interval maxima, the method describes the relation between the mean maximum value from a set of subintervals. The interval maxima are then predicted by linear extrapolation of the resulting relationship until a subinterval length which is equal to the whole interval. The approach is easy to implement, and shows good results in examples presented in reference [14]. The following advantages of this method have been highlighted. Fig. 9 Time variation of load on frame 2 versus vessel speed between 18:00 and 19:00 1. No threshold value is needed. A threshold value will influence the duration between load peaks, and there are no physical reasons to assume that load peaks have a minimum amplitude. Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009

9 Ice-load estimation for a ship hull based on continuous response monitoring 537 The other variable x T is calculated as the mean of all time window maxima. The maxima inside time window number i, x i, is used to define x T as x T ~ 1 N T X N T x i i~1 A number of values for x T is then calculated from the load time history by varying the time window length T. Determination of suitable distributions for the variables and prediction of future loads is based on linear extrapolation of the distribution on appropriate probability paper, referred to as (T, x T )-plots. The variables are found to follow one of two principal linearized equations, depending on the time window length. For short window periods, x T tends to follow the first equation below, while for longer time windows the relation in the second equation is more common [14] lnðx T Þ~H lnðtþzc x T ~H 0 lnðtþzc 0 Fig The time window approach can generate statistical models from shorter time histories. 3. The length of the subintervals is treated as a variable, and no parameters are then chosen by the analyser. Results from different ships, ice conditions, and locations are therefore always comparable. A distribution is established from two variables, T and x T. T is the length of the time windows the load time history is divided into. For a given value of T this corresponds to N T time windows on a time history of length h N T ~ h T Distribution of peak magnitudes and time intervals between peaks, 26 March 2007 between 19:00 and 19:30: (a) histogram of peaks above 25 kn for frame 2 and (b) histogram of time interval between successive peaks It is important to be aware that the extrapolated variable x T describes the mean value of the maxima in several time windows, and not the respective window maxima x i. According to reference [10], the corresponding distribution for x in intervals with mean value x T will be a type-ii extremal value distribution (Gumbel II) if the first relationship above applies for x T. If the second relationship applies for x T, x will follow a Gumbel (Gumbel I) distribution. (The names in brackets are those applied by reference [14].) This second approach typically leads to conservative estimates, and may call for an adjustment of the method to obtain better results. The adjustment will depend on the extent of extrapolation, and possibly ice conditions and speed. The correction proposed in reference [14] is to remove certain large loads based on statistical considerations, but no further comments about how this should be performed are given. The findings from KV Svalbard are more ambiguous with respect to the relationships, as the different frames and time intervals seem to follow different trends. The time window plots indicate that bow section frames 2 and 4 follow the second relationship for time windows longer than 8 s, whereas the curves for frames 6 and 8 (which are closer to the shoulder) follow the other relationship. Figures 11(a) and (b) may serve as examples for JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

10 538 B Leira, L Børsheim, Ø Espeland, and J Amdahl frame 2 and frame 8, respectively. For other investigated intervals the conclusions are different. In the interval with the lowest mean ice thickness and highest speed, between 19:35 and 20:05 on 26 March 2007, all frames were found to fit the first relationship best Comparison of methods Both approaches are able to predict loads in the right order of magnitude for the observed maxima, and may serve as a basis for prediction of future loads. Conservative choices of percentile value or extrapolation curves should be chosen to envelop the observed maxima. Results from the time window approach are somewhat ambiguous with respect to which of the two relationships between T and x T is most accurate. Fairly good fits are obtained for both cases. The first relationship is generally very conservative, but this is the only relation which is able to predict the highest observed value of 345 kn for frame 6. The second relationship was found to be comparable with the mean value of the maxima which were obtained by application of the peak amplitude approach. It should be noted that the 345 kn for frame 6 was well above the 99th percentile in the classical extreme value distribution which was obtained from the peak amplitude approach. (Other high loads were also experienced during the same interval, and it is hence not regarded as a single special event.) From the few cases which were considered, the peak amplitude approach seems most promising. However, further investigations for extended amounts of data are required before any firm conclusions can be drawn Correlation of ice force versus ice thickness and vessel speed Registered force versus ice thickness is shown in Fig. 12(a), and it might indicate a trend of higher force maxima in the area between 0 and 2 m ice thickness. Reports presenting collected data from the ships Nathaniel B. Palmer [15] and Polar Sea [16] show comparable results, and explains the behaviour by means of the random nature of ice loads. The highest observed values of the force may then be expected to occur in areas with the highest number of registered events. (A few loads are Fig. 11 Time window approach for data collected between 19:00 and 19:30, 26 March 2007: (a) frame 2 and (b) frame 8 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009

11 Ice-load estimation for a ship hull based on continuous response monitoring 539 Fig. 12 Scatter plots relating (a) force to ice thickness and (b) force to vessel speed registered with a negative ice thickness, and this is expected to be due to calibration errors or measurement uncertainties.) As mentioned above, there will in addition be some disturbance owing to the influence of the ice thickness on the vessel speed, which will also modify the force acting on the hull. Figure 12(b) leads to similar conclusions for the relation between ice force and vessel speed. The absence of observations for low speeds is partly explained by the selection of intervals for analysis, where higher speeds were focused upon. Considering only the mean value of the highest fraction (e.g. 10 per cent) of the forces for a given vessel speed, a monotonuously increasing relationship would result up to a vessel speed of around 5 6 knots. This would also be more meaningful in relation to structural design of the hull. 5 DISCUSSION AND CONCLUSIONS The ILM system on KV Svalbard was presented. A correlation study between the ice load and the ice thickness and vessel speed has been performed. The study is based on 30 s statistical values. Some of the results were somewhat inconclusive, but in general it is possible to state that the maximum peak loads (i.e. the maximum peak for all frames at any time) depend on the ice thickness (for a given, constant value of the ship speed). However, Because KV Svalbard is a small vessel, the speed was reduced considerably when the ice thickness increased. This will disturb the relationship between the ice load and the ice thickness for the highest values. Plots of peak ice loads versus ice thickness and vessel speed were also found to have a significant scatter. The ILM system is able to inform about the instantaneous stress levels experienced by the hull. Furthermore, procedures are available (i.e. the peak amplitude and the time window approaches) to extrapolate these stress levels into the future, provided that parameters related to ice loading are constant (i.e. stationary conditions). For the case of non-stationary conditions, such extrapolation is more challenging and will require a comprehensive calibration. Further studies based on the present measurements are intended to include estimation of total ice resistance based on consideration of energy balance A statistical evaluation of the time between the load peaks as well as the peak amplitudes has been performed. Both these parameters seem to be exponentially distributed, indicating that the peaks of the ice loading can be represented by a Poisson process with exponentially distributed amplitudes. ACKNOWLEDGEMENTS Det Norske Veritas is greatly acknowledged for giving access to the data from the measurements on KV Svalbard and to allow the publication of the results reported in this paper. REFERENCES 1 Enkvist, E. On the ice resistance encountered by ships operating in the continuous mode of ice breaking, report 24, The Swedish Academy of Engineering Science in Finland, Helsinki, Finland, Kheisin, D. I. and Popov, Y. N. (Eds.) Ice navigation qualities of ships, draft translation 417, Cold Regions Research and Engineering Laboratory (CRREL), Hanover, New Hampshire, Korri, P. and Varsta, P. On the ice trial of a dwt tanker on the Gulf of Bothnia, NSTM-79, JEME141 F IMechE 2009 Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment

12 540 B Leira, L Børsheim, Ø Espeland, and J Amdahl Society of Naval Architects in Finland (LARADI), Helsinki, Finland, Vuorio, J., Riska, K., and Varsta, P. Long-term measurements of ice pressure and ice-induced stresses on the icebreaker Sisu in winter 1978, report 28, Winter Navigation Research Board, Helsinki, Finland, Varsta, P. On the mechanics of ice load on ships in level ice in the Baltic Sea. Publication 11, Technical Research Centre of Finland, Espoo, Varsta, P. Determination of ice loads semiempirically, VTT Symposium on Ship Strength and Winter Navigation, Technical Research Centre of Finland, Espoo, Finland, Daley, C. Ice edge contact - a brittle failure process model, 1991 (Acta Polytechnica Scandinavica, Helsinki). 8 Kujala, P. On the statistics of ice load on ship hull in the Baltic, mechanical engineering series no. 116, Acta Polytechnica Scandinavica, Børsheim, L. Ship hull monitoring of ice-induced stresses. Master s Thesis, Department of Marine Technology, NTNU, Trondheim, Espeland, Ø. Ice action and response monitoring of ships. Master s Thesis, Department of Marine Technology, NTNU, Trondheim, Leira, B. J. and Børsheim, L. Measured ice-loading on KV Svalbard. In Proceedings of OMAE 2008, Estoril, Portugal. 12 Mejlænder-Larsen, M. and Nyseth, H. Ice load monitoring. In Design and construction of vessels operating in low temperature environments, 2007 (Royal Institution of Naval Architects, London). 13 Nyseth, H. Strain measurements on board KV Svalbard with respect to ice loading, technical report no , Det Norske Veritas, Høvik, Norway, Lensu, M. and Hanninen, S. Short term monitoring of ice loads experienced by ships. In Proceedings of 17th International Conference on Port and ocean engineering under Artic conditions (POAC 03), June 16 19, Trondheim, Norway. 15 Ship Structure Committee. Ice load impact study on NSF R/V NATHANIEL B. PALMER, technical report 376, Washington, D.C., (see also 16 Ship Structure Committee. Ice loads and ship response to ice, technical report 329, Washington, D.C., (see also APPENDIX Notation h N T T x i x T total length of the measured time series record number of segments that a measured time series record is split into when applying the time window approach length of the time segment ( time window ) largest measured value within a segment of the measured time series mean value of the largest measured values within a collection of N T segments Proc. IMechE Vol. 223 Part M: J. Engineering for the Maritime Environment JEME141 F IMechE 2009