Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France

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1 Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France OMAE PROBABILISTIC SELECTION OF SHIP-SHIP COLLISION SCENARIOS Samy A M Youssef Jeom K Paik Yang Seop Kim The Ship and Offshore Research Institute, Pusan National University, Busan, Korea Min Soo Kim Lloyd s Register Asia Busan, Korea Fai Cheng Lloyd s Register London, UK ABSTRACT Within the framework of quantitative risk assessment and management in the design stage, it is essential to select relevant sets of accidental scenarios, while a huge number of possible scenarios are obvious. The current industry practices are likely based on prescriptive approaches for the most unfavorable accidental scenarios. However, these approaches are often inadequate for obvious reasons because they may result in too large values of design loads in some cases but they may underestimate design loads in other cases. In the present study, an innovative method using probabilistic approaches is suggested to select relevant sets of ship-ship collision accident scenarios which represent all possible ones. Historical database for each of individual collision parameters which is dealt with as a random variable have been collated and are analyzed by statistical methods to characterize the probability density distributions. A sampling technique is then applied to select collision scenarios. Applied examples to a double hull oil tanker are presented to demonstrate the applicability of the developed method. Keywords: Ship collision; probabilistic approach; probability density distributions; collision scenarios. 1 INTRODUCTION Today s keywords in the global maritime industry include health, safety, and the environment. All such key elements are equally important [1]. In this regard, it is of crucial importance to be able to reduce the probability of accidents, assess their consequences and ultimately minimize or prevent potential damage to ships and to the marine environment [2]. The International Tanker Owners Pollution Federation (ITOPF) maintains a database of oil spills from tankers, combined carriers and barges. This contains information on accidental spillages since 1970, except those resulting from acts of war [3]. Figure 1 shows incidents of spills greater than 700 tonnes by cause through four periods of time. It was observed that the percentage of the oil spills which are caused by collision accidents is increased from 27.9, 28.3 to 29.1 % in periods ( ), ( ) and ( ) respectively and is decreased with a very small amount (0.1 %) to be 29.0 % in the period of ( ). It means, in spite of the great development in marine technology and although the majority of oil tankers are safely built, operated and is constructed to reduce the amount of oil spilled in the event of an accident; the oil spills due to collision could not be prevented. There is still a room for more analysis and investigation related to all aspects of collision between ships to be considered. Ship collisions are normally classified into two groups, namely ship-ship collisions and head-on collisions. Ship-ship collision represents a situation in which the bow of a striking ship collides with the side structure of another struck (collided) ship. Head-on collision typically represents a situation in which the bow of a vessel collides with fixed rigid walls such as piers and bridge abutments [4]. In this study, an innovative method using probabilistic approaches is suggested to select relevant sets of ship-ship collision accident scenarios for double hull oil tanker as a struck ship. In literature, a lot of efforts were found to establish ship-ship collision scenario models near to the reality which can be divided in three groups; the first one is statistical collision scenario which is based on statistical data of historical collision accidents and suggested before by Rawson et al.[5], National Research Council (NCR) [6], Brown [7] and Tuovinen [8]. 1 Copyright 2013 by ASME

2 (a) (b) (c) (d) Figure 1. Incidents of spills greater than 700 tonnes by cause [3]. The second one is encounter collision scenario which is based on simulating the marine traffic flow for a certain area and period of time, this type of scenario suggested by Pedersen [9,10] and Montewka et al. [11]. Also Automatic Identification system (AIS) can be used to simulate the marine traffic flow. The third one is blind navigator collision scenario at which there are no maneuvering actions taken to avoid the collision and is used for finding the so-called collision candidates for collision probability evaluation in the models [12] which is suggested by Pedersen [9], Van Drop & Merrick [13] and Goerlandt & Kujala [14]. 2 ANATOMY OF SHIP-SHIP COLLISION ACCIDENTS After performing an extensive analysis of ship-ship collision accidents, the collision scenario can be described by the most effective parameters (see Fig. 2) which are listed below: (a) Striking ship type, (b) Striking ship displacement (Δ 1 ), (c) Struck ship displacement (Δ 2 ), (d) Striking ship speed (V 1 ), (e) Struck ship speed (V 2 ), (f) Striking ship draught (d 1 ), (g) Struck ship draught (d 2 ), (h) Struck ship impact longitudinal location (l 2 ) and (i) Collision angle (θ). Figure 2. Schematic of a ship-ship collision. Collision angle is assumed to be between the initial directions of motion of the two colliding ships at the moment of impact as shown in Fig. 2. Based on this assumption, the collision happening at a relative angle of zero degrees is determined to 2 Copyright 2013 by ASME

3 have an impact point at the stern of the struck ship. At a relative angle of 180 degrees is determined to have an impact point at the stem of the struck ship. 2.1 Striking bow shape The bow shape of the striking ship is important because it determines the volume of structure damaged during the collision [5]. Refined bow models are more realistic, but more difficult for analysis [15]. Lützen [16] suggested a striking bow model in his PhD. thesis as shown in Fig. 3. If the bow shape is unknown and the length, breadth and depth of the striking ship are known, its bow shape can be estimated by the following parameters: (a) Bottom shape parameter (B b ), (b) Deck shape parameter (B d ), (c) Stem angle (φ), (d) Distance between the bulb tip and the foremost part of the bow (R D ), (e) Bulb length (R L ), (f) Vertical radius of the bulb (R V ) and (g) Horizontal radius of the bulb (R H ). Figure 3. Bow shape [16]. 3 COLLATION OF COLLISION ACCIDENTS DATABASE In this study, Authors collected ship-ship collision accidents data within ( ) which has been provided by fourteen accident investigation boards under the responsibility of the national maritime authorities for different countries. All of these accident investigation boards have a similar target, covering all accidents in national waters and all accidents on nationally flagged ships all over the world. It is very important if near-misses (i.e. near-collision) and small accidents are reported in database, to motive a proactive concept rather than the frequent reactive measures that are taken subsequent to accidents. For this reasons, some near misses are recorded in database. A near-collision is a situation in which two ships come close to each other to a certain distance. Unfortunately, ship displacement for both colliding ship was not available in the database. For that reason, some empirical formulae [17] have been used to calculate ship displacement that is depended on ship type and main particulars. 4 STATISTICAL ANALYSIS In this section, the collated ship-ship collision database has been used as a basis to establish the distribution of vessel types in accidents. Also database for each of individual collision parameters which is dealt with as a random variable have been analyzed by statistical methods to characterize the probability density distributions. 4.1 Distribution of vessel types in accidents The historical collision accidents database is analyzed to derive percentage distributions of vessel types in accidents and divided in eleven groups; each one includes a number of more specific types such as: Tankers: include crude and product tankers. Chemical tankers: include chemical and other liquid carriers. Bulk carriers: include dry bulkers and coal carriers. Cargo vessels: include general cargo and refrigerated vessels. Container vessels: include container and refer container vessels. Gas carriers: include LNG and LPG carriers. RO/RO vessels: include car carriers, cargo/ro-ros and RO-ROs. Passengers: include passenger vessels and ferries. Service vessels: include tugs, supply boat and salvage vessels. Fishing vessels: included all types of fishing vessels. Others: include barges, dredgers, factory vessels, heavy lift vessels, pleasure boats and yachts. Figure 4 shows three types of distribution; both colliding vessels, striking vessels, and struck vessels that are involved in accidents. Figure 4. Distribution of vessel types in accidents. 3 Copyright 2013 by ASME

4 4.2 Probability density distributions In this section, probabilistic analysis is applied for each collision parameter based on the historical database to describe the range and variability of each one; and deriving probability density distributions to be used in ship-ship collision scenarios. In this study, the relative displacement (Δ 2 /Δ 1 ), relative speed (V 2 /V 1 ), location of impact through the struck ship length (l 2 /L 2 ), relative draught [(d 2 /D 2 ) / (d 1 /D 1 )] and collision angle (θ) are studied as random variables. Figure 5 shows the general procedures for the proposed probabilistic analysis. Goodness-of-fit technique Historical data for a specified variable Selection of best probability density distribution to represent the historical data Probability plotting of the historical data at a certain confidence interval Calculation of selected distribution parameters for various histogram bin width (interval) Selection of the best histogram bin width (interval) Figure 5. Flow of the proposed method for the probabilistic analysis Probability density distribution of striking ship type The striking ship type plays an important role in ship-ship collision accidents. In this regard, it is great of interest to deal with the striking ship type as a random variable. In this study, the striking ship parameter is presented by dividing the striking ship types involved in database in six groups which are ordered to be seemly formulated by normal distribution to be represented by range of values. Each striking ship group includes a number of more specific types such as: Tankers: include crude and product tankers, chemical tankers and gas carriers. Bulk carriers: include dry bulkers and coal carriers. Cargo vessels: include general cargo and refrigerated vessels. Container vessels: include container, car carriers, container/ro-ros and RO-ROs. Passengers: include passenger vessels and ferries. Others: include service vessels, fishing vessels, barges, dredgers, factory vessels, heavy lift vessels, pleasure boats and yachts. 5 APPLIED EXAMPLE In this section, double hull oil tankers which are involved in the collision accident database as struck ships have been used to demonstrate the applicability of the developed method. The procedure for probabilistic analysis (see Fig. 5) is applied for each of the foregoing collision parameters. Figure 6 shows the probability density distribution (PDF) and cumulative density distribution (CDF) versus each of individual collision parameters. Figure 6 also compares possible representations of the several probability density functions to each parameter. When it is assumed that the data follow a specific distribution, a serious risk is taken. If the assumption is wrong, then the results obtained may be invalid [18]. For that reason, Goodness-of-Fit (GoF) tests are used to measure the compatibility of a historical data with a theoretical probability distribution function. The Kolmogorov-Smirnov test (K-S test) technique [19] is applied for each of individual collision parameters in this study to determine the best probability density function to represent the historical data. Table 3. Goodness of fit test (Kolmogorov-Smirnov) statistics for various probability distribution functions. Distribution function PDFs test statistics for collision parameters Δ 2 /Δ 1 V 2 /V 1 (d 2 /D 2 )/(d 1 /D 1 ) l 2 /L 2 θ Striking ship type 2-Parameter Weibull Parameter Weibull Exponential Normal Lognormal Parameter Gamma Parameter Gamma Logistic Log-Logistic Copyright 2013 by ASME

5 (a) PDF versus relative displacement parameter (b) CDF versus relative displacement parameter (c) PDF versus relative speed parameter (d) CDF versus relative speed parameter (e) PDF versus collision angle parameter (f) CDF versus collision angle parameter Figure 6. Probability density distribution (PDF) and cumulative density distribution (CDF) versus collision parameters. 5 Copyright 2013 by ASME

6 (g) PDF versus impact location parameter (h) CDF versus impact location parameter (i) PDF versus relative draught parameter (j) CDF versus relative draught parameter (k) PDF versus striking ship type parameter (l) CDF versus striking ship type parameter Figure 6. Probability density distribution (PDF) and cumulative density distribution (CDF) versus collision parameters (continued). 6 Copyright 2013 by ASME

7 The K-S test statistic is the large absolute value of the difference between the empirical CDF for a set of observations (i.e., historical data) and the CDF of the candidate distribution under the null hypothesis. These statistics are compared with certain significance level. Table 1 summarized the test statistics of K-S test for each collision parameter versus several types of PDFs. The better the distribution fits the historical data, the smaller the statistic. Probability plot is a graphical technique for assessing whether or not a data set follows a given distribution [20]. Figure 7 shows the probability plots for the location of impact parameter (L 2 /L 2 ) versus several of PDFs at 95 % confidence interval, where each value is plotted versus the percentage of values in the sample that are less than or equal to it, along a fitted distribution line (middle blue line). Two curved blue lines represent the approximate 95% confidence for the percentiles that typically used for most applications. In the statistical modeling of a random variable the effect of the histogram bin width (or interval) is usually significant. The bin width that gives the largest mean value and the smallest coefficient of variation (COV) should be selected [21]. Sturges' formula [22] and Doane's formula [23] are useful for determining the best bin width value for normally distributed data and non-normally distributed data respectively. Figure 8 shows the effect of histogram bin width on the mean and COV values at the studied collision parameters, and indicates the bin width (interval) that gives the largest mean and the lowest COV is selected. D= D= D= (a) Normal distribution - 95% confidence interval (b) 2-parameter Weibull distribution - 95% confidence interval (c) 3-parameter Weibull distribution - 95% confidence interval D= D= D= (d) Lognormal distribution - 95% confidence interval (e) 2-parameter Gamma distribution - 95% confidence interval (f) 3-parameter Gamma distribution - 95% confidence interval D= D= D= (g) Exponential distribution - 95% confidence interval (h) Logistic distribution - 95% confidence interval (i) Log logistic distribution - 95% confidence interval Figure 7. Probability plots for the impact location parameter at 95 % confidence interval. 7 Copyright 2013 by ASME

8 (a) Relative displacement parameter (b) Relative speed parameter (c) Collision angle parameter (d) Impact location parameter (e) Relative draught parameter (f) Striking ship type parameter Figure 8. Effect of histogram bin width (interval) on the mean and COV values for collision parameters. Figure 9 shows the selected PDFs which are the best fit to represent the historical data versus each of the studied individual collision parameters. 5.1 Selection of collision scenarios Although a huge number of possible collision scenarios may be relevant, it is not practical to consider all of them. The Latin Hypercube Sampling (LHS) technique [24] is useful for selecting probable scenarios. Probability P of each of M samples generated by the LHS technique for N variables is obtained as Eq. (1) Copyright 2013 by ASME

9 (a) Relative displacement parameter (b) Relative speed parameter (c) Collision angle parameter (d) Impact location parameter (e) Relative draught parameter (f) Striking ship type parameter Figure 9. Selected probability density distribution of collision parameters. 9 Copyright 2013 by ASME

10 When sampling a function of N variables (i.e., collision parameters) using LHS technique, the range of each variable is divided into M equally probable strata (intervals) as shown in Fig. 10. One sample is chosen from each stratum (e.g., assuming uniform probability over the stratum). M-th column in the N-th dimension of the hypercube corresponds to the value from M-th stratum of the N-th random variable. Sample points are then placed to satisfy the Latin hypercube requirements see Fig. 10. Figure 10. Illustration of Latin hypercube sampling technique for case with two variables and eight samples. This forces the number of divisions M to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables), which is one of the main advantages. In this study, fifty scenarios are randomly selected using the LHS technique. The selected PDF for each of the studied collision parameters is divided into fifty ranges, with the interval of each range determined to ensure that the area below the curve between the probability density versus collision parameter is equal. For double hull oil tankers, fifty scenarios were randomly selected using the LHS technique which as indicated in Table 2. Figure 11 shows PDFs of the selected fifty scenarios for each collision parameter. In table 2, each of the collision parameters is randomly selected within a specified range based on the gathered historical data to cover all possible collision scenarios. If the struck tanker particulars are known, the striking ship displacement, speed and draughts at time of accident will be known for fifty collision cases using table 2. For the striking ship type parameter, LHS technique produced randomly fifty different values, each one represent a certain type of ship as discussed in section CONCLUDING REMARKS This paper presents an innovative method using probabilistic approaches to select relevant sets of ship-ship collision accident scenarios which represent all possible ones. Table 2. Striking ship-struck tanker collision scenarios. Scenario Striking ship type Δ 2 /Δ 1 V 2 /V 1 (d 2 /D 2 )/(d 1 /D 1 ) l 2 /L 2 θ 1 Passenger Cargo ship Cargo ship Cargo ship Cargo ship Cargo ship Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Bulk carrier Container Container Container Container Container Container Container Container Container Container Container Container Container Container Container Container Tanker Tanker Tanker Tanker Tanker Tanker Tanker Tanker Tanker Tanker Tanker Other Other Other Other Copyright 2013 by ASME

11 (a) Relative displacement parameter (b) Relative speed parameter (c) Collision angle parameter (d) Impact location parameter (e) Relative draught parameter (f) Striking ship type parameter Figure 11. Probability density distributions of the selected fifty scenarios of collision parameter. 11 Copyright 2013 by ASME

12 Historical database for each of individual collision parameters has been collated from different sources including some available near misses to encourage a proactive concept in safety management. Each collision parameter which was dealt as a random variable has been analyzed by statistical methods to characterize the probability density distributions. It is concluded that the histogram bin width (interval) can affect on the mean and COV values for each parameters, so the best histogram bin width that gives the maximum mean and minimum COV value should be selected. A sampling technique is applied to select reasonable collision scenarios which can cover the most possible events. To demonstrate the applicability of the developed method, an applied example to collision accidents of struck double hull oil tankers. Further studies are being carried out to apply the produced fifty ship-ship collision scenarios on a real double hull oil tanker (as a struck ship) using Finite element techniques. NOMENCLATURE B b B d CDF COV D D 1 D 2 d 1 d 2 GoF = Bottom shape parameter = Deck shape parameter = Cumulative density function = Coefficient of variation = Ship depth = Striking ship depth = Struck ship depth = Striking ship draught at time of accident = Struck ship draught at time of accident = Goodness of fit (d 2 /D 2 )/(d 1 /D 1 ) = Relative draught parameter K-S = Kolmogorov-Smirnov L 2 = Struck ship length LHS = Latin hypercube sampling l 2 = Distance measuring from the foremost point of the struck ship to the impact point l 2 /L 2 = Impact location along the struck ship length M = Number of samples N = Number of variables P = Probability PDF = Probability density function R D = Distance between the bulb tip and the foremost part of the striking ship bow R L R V R H = Bulb length = Vertical radius of the bulb = Horizontal radius S.D. V 1 V 2 V 2 /V 1 Δ 1 Δ 2 Δ 2 /Δ 1 θ φ = Standard deviation = Striking ship speed at time of accident = Struck ship speed at time of accident = Relative speed parameter = Striking ship displacement = Struck ship displacement = Relative displacement parameter = Collision angle = Stem angle of striking bow ACKNOWLEDGMENTS This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant no.: K E ). The study was undertaken at The Lloyd s Register Educational Trust (The LRET) Research Centre of Excellence (The Ship and Offshore Research Institute) at Pusan National University, Korea. The Lloyd s Register Foundation supports the advancement of engineering-related education, and funds research and development that enhances safety of life at sea, on land in the air. REFERENCES [1] Paik, J., K., Park, J., H., and Samuelides, E., 2009, "Collision Accidental Limit States Performance of Double-Hull Oil Tanker Structures: Pre-CSR versus CSR Designs", Journal of Marine Technology, 46(4), pp [2] Paik, J., K., Amdahl, J., Barltrop, N., Donner, E., R., Gu, Y., Ito, H., Ludolphy, H., Pedersen, P., T., Rohr, U., and Wang, G., 2003, "Collision and grounding", Final report of ISSC 1, International Ship and Offshore Structures Congress, San Diego. [3] International tanker owner s pollution federation, 2012, "Effects of oil spills", [4] Paik, J., K., Chung, J., Y., Thayamballi, A., K., Pedersen, P., T., and Wang, G., 1999, "On Rational Design of Double Hull Tanker Structures against Collision", SNAME Annual Meeting, Baltimore. [5] Rawson, C., Crake, K., and Brown, A., 1998, "Assessing the Environmental Performance of Tankers in Accidental Grounding and Collision ", SNAME Transactions, 106, pp [6] National Research Council (NRC), 2001, "Environmental Performance of Tanker Designs in Collision and Grounding", Special Report 259, The National Academies Press. 12 Copyright 2013 by ASME

13 [7] Brown, A., J., 2002, "Collision Scenarios and Probabilistic Collision Damage", Journal of Marine Structure, 15(4 5), pp [8] Tuovinen, J., 2005, "Statistical Analysis of Ship Collisions" MSc. Thesis, Helsinki University of Technology, Espoo. [9] Pedersen, P., T., 1995, "Collision and Grounding Mechanics", The Danish society of Naval Architects and Marine Engineers, pp [10] Pedersen, P., T., 2010, "Review and Application of Ship Collision and Grounding Analysis Procedures", Journal of Marine Structures, 23(3), pp [11] Montewka, J., Hinz, T., Kujala, P., and Matusiak, J., 2010, "Probability Modeling of Vessel Collision", Reliability Engineering and System Safety, 95(5), pp [12] Goerlandt, F., Ståhlberg, K., and Kujala, P., 2012, "Influence of Impact Scenario Models on Collision Risk Analysis", Journal of Ocean engineering, (47) pp [13] Merrick, J., R., W., van Dorp, J., R., Harrald, J., Mazzuchi, T., Spahn, J., and Grabowski, M., 2003, "A Systems Approach to Managing Oil Transportation Risk in Prince William Sound", Systems Engineering, 3 (3), pp [14] Goerlandt, F., and Kujala, P., 2011, "Traffic Simulation Based Collision Probability Modeling", Reliability Engineering and System Safety, 96 (1), pp [15] Wang G., Spencer J., and Chen, Y., 2002, "Assessment of a ship s Performance in Accidents", Journal of Marine Structures, 15, pp [16] Lützen, M., 2001, "Ship Collision Damage", Ph.D. Thesis, Technical University of Denmark, Lyngby. [17] Sajdak, J., A., W., and Brown, A., J., 2005, "Modeling Longitudinal Damage in Ship Collisions", Technical Report No. SR-1426, Ship Structural Committee, Washington DC. [18] Romeu, J., L., and Grethlein, C., 2000, "A Practical Guide to Statistical Analysis of Material Property Data", Advanced Materials & Processes Technology Information Analysis Center, New York. [19] Chakravarti, I., M., and Laha, R., G., 1967, "Handbook of Methods of Applied Statistics", Volume I, John Wiley and Sons, New York, pp [20] Chambers, J., M., Cleveland, W., S., Kleiner, B., and Tukey P., 1983, "Graphical Methods for Data Analysis", Wadsworth & Brooks, New York. [21] Paik, J., K., Thayamballi, A., N., Park, Y., I., and Hwang, J., S., 2004, "A Time-dependent Corrosion Wastage Model for Seawater Ballast Tank Structures of Ships, Journal of Corrosion Science, 46, pp [22] Sturges, H., A., "The Choice of a Class Interval", Journal of American Statistical Association, pp [23] Doane, D., P., 1976, "Aesthetic Frequency Classifications", American Statistician, 30(4), pp [24] Ye, K., Q., 1998, "Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments", Journal of the American Statistical Association, 93(444), pp Copyright 2013 by ASME