Ocean Engineering 65 (2013) Contents lists available at SciVerse ScienceDirect. Ocean Engineering

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1 Ocean Engineering 65 (2013) Contents lists available at SciVerse ScienceDirect Ocean Engineering journal homepage: Review Risk-based design of naval combatants Evangelos Boulougouris a,n, Apostolos Papanikolaou b,1 a University of Strathclyde, Department of Naval Architecture and Marine Engineering, UK b National Technical University of Athens, School of Naval Architecture and Marine Engineering, Ship Design Laboratory, Greece article info Article history: Received 19 July 2012 Accepted 24 February 2013 Available online 21 April 2013 Keywords: Damaged stability Risk-based design Naval ships Time domain simulation abstract The present paper introduces a risk-based design concept to naval ship design. It extends an earlier proposed basic design concept by the authors for the evaluation of the survivability of surface combatants by semi-empirical naval ship stability criteria, by introducing modern assessment methods for ship's behaviour after flooding, namely by implementing numerical simulation tools for assessing the risk after flooding. The introduced method was applied to the assessment of the damage stability of a generic frigate operating in specified seaway conditions and typical results of this study are presented and discussed. & 2013 Elsevier Ltd. All rights reserved. Contents 1. Introduction Risk-based design approach Naval ship code Survivability Vulnerability estimation Determining p i Survival index S i Probabilistic damage stability quasi-static approach Probabilistic dynamic flooding/capsizing approach Flooding simulation by the pressure-correction method Case study Conclusions References Introduction The International Maritime Organization (IMO) and the merchant maritime industry have made significant advances in the upgrade of the safety standards of merchant ships over the past decade by adopting pro-active safety measures for future rules and regulations in the frame of a holistic approach to ship's safety. Instead of waiting for the next major catastrophic accident, IMO and major classification societies (IACS) decided to move from n Corresponding author. Tel.: þ ; fax. þ addresses: evangelos.boulougouris@strath.ac.uk (E.Boulougouris), papa@deslab.ntua.gr (A. Papanikolaou). 1 Tel.: þ ; fax: þ prescriptive concepts to probabilistic assessment methods and goal-based standards (GBS). The acceptance of the new harmonized probabilistic damage stability framework of SOLAS 2009 for the assessment of the damage stability of both passenger and dry cargo ships (though, more than three decades after the first introduction of the probabilistic concept in SOLAS 74 ), shows that the maritime industry, national and international regulatory bodies are now convinced that this is the only way forward. In parallel, risk and reliability analysis and assessment methods have become important design tools in naval architecture facilitating the accomplishment of the safety objectives cost effectively (Papanikolaou, 2009a). The use of advanced computational tools permits nowadays the quantification of the risk level of a particular design and its /$ - see front matter & 2013 Elsevier Ltd. All rights reserved.

2 50 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) Fig. 1. SDL-NTUA ship design optimization procedure (Boulougouris and Papanikolaou, 2006). exhaustive comparison with alternatives. In this framework risk is no longer a constraint but a measure of safety performance and design objective which can be used in an optimization procedure (see Fig. 1). Therefore ship designs can be optimized for minimum risk, while performing with best efficiency and economy. This led to the new scientific and engineering disciplines of risk-based design (RBD) and holistic Multi-Objective Optimization (Papanikolaou, 2009b). At the same time, the complexity of naval ship design has substantially increased in view of the enhancement of related stakeholder disciplines (see Fig. 2). Additionally, the main progress in naval ship design appears to be concentrating on improvements of outfitting and the performance in peace times, rather than addressing naval ship's risks in emergency/flooding conditions. Surface combatants are still designed and operated based on traditional naval stability standards, which have a common origin in the experiences gained during World War II or even before. Even though these standards have served their purpose for many decades, they appear nowadays outdated; there are serious concerns about their limitations and questions regarding their applicability to modern naval ship designs. The shortfalls include (Perrault et al., 2010): The level of safety assured by compliance with such standards is unknown. Today's naval ship hullforms are quite different from those used for the development of these semi-empirical criteria. It is questionable whether current dynamic stability criteria, using only the properties of the righting arm curve, can fully capture the dynamic behaviour of modern naval ship operating in extreme seaways both in the intact and damaged condition. The above suggests that both designers and the operators of naval ships do not have in general a clear understanding of the survivability performance and operational limits of their ships. Moreover, ships that are designed right now and will be operating during the first half of the 21st century do not dispose a rational yardstick for measuring and setting targets for improving their damaged survivability performance. Fig. 2. Naval Ship Design stakeholders disciplines (see Neu et al., 2000). An effective response to this gap is risk-based design and operation, in which design and operational criteria are related to rationally determined risk levels, which are considered acceptable by society (merchant ships) or by a defence agency (naval ships). Risk-based approaches are inherently connected to probabilistic assessment methods (Papanikolaou, 2009a). The authors have presented in the past a methodology for the probabilistic damage stability assessment of naval combatants and its application to the optimization of naval ship design (Boulougouris and Papanikolaou, 2003, 2004). Several researchers have also proposed similar methodologies regarding the intact (Perrault et al., 2010) and damage stability of naval ships (Harmsen and Krikke, 2000). Significant effort has been also devoted to the

3 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) assessment of survivability of warships in damaged condition using time domain simulation tools (de Kat and Peters, 2002; Andrewartha et al., 2008). The present paper extends the basic design concept proposed earlier by the authors for the assessment of the survivability of surface combatants after damage by introducing modern riskbased assessment methods for ship's behaviour after flooding, namely by implementing numerical simulation tools for assessing the risk after flooding. The introduced method was applied to the assessment of the damaged stability of a generic frigate operating in specified seaway conditions and typical results of this study are presented and discussed. 2. Risk-based design approach Risk is the product of the frequency of an event times the associated consequences. According to Papanikolaou (2009a) the risk-based design approach is an improved alternative to the traditional design process as it integrates safety as additional design objective. Hence, the designer has to sutisfy an additional requirement i.e. that the risk of any feasible design, R design, should be less or equal than the specified acceptable risk, R acceptable, that is R design R acceptable ð1þ Different risk categories, e.g. of system failure, to human life, to environment or to property, should be treated separately. The total risk is calculated by the sum of the partial risks coming from different damage categories such as explosion, fire, collision or grounding. Each partial risk can be computed with the help of risk models like, e.g. event trees or Bayesian networks. Risk models expressed by mathematical formulae were developed for fast design optimization. The acceptable level of risk that the feasible designs have to exceed can be specified in case of warships by the owner (navy) or other approval authority (NATO and/or classification society). There are two options for the specification of the acceptable risk: relative or absolute. In the first case, a reference design is selected which complies with current rules. In the second case, absolute level, e.g. IMO risk acceptance criteria, can be used or referenced. In the present paper the risk of the ship not surviving damage due to hit by a threat weapon will be discussed and a mathematical risk model will be presented for calculating the survivability in case of such damage. The method is applied to a generic warship that meets the existing deterministic criteria. Therefore her attained survivability index could be used as reference for setting the acceptable risk level. Provide adequate stability to avoid capsizing in all foreseeable intact and damaged conditions, in the environment for which the ship is to operate, under the precepts of good seamanship; Permit embarked persons to carry out their duties as safely as reasonably practical; Protect the embarked persons and essential safety functions in the event of foreseeable accidents and emergencies at least until the persons have reached a place of safety or the threat has receded including preventing the malfunction of the lifesaving systems and equipment. The keyword in the first two goals is adequate. In order to specify the sufficiency of the reserve buoyancy and stability, the maximum acceptable level of risk (minimum level of safety) has to be decided and be set as design criterion. 4. Survivability It may be defined as the capability of a (naval) ship and its shipboard systems to avoid and withstand a weapons effects environment without sustaining impairment of their ability to accomplish designated missions (Said, 1995). It contains two aspects: The susceptibility defined as the inability to avoid being damaged in the pursuit of its mission and to its probability of being hit (P H ). The vulnerability defined as the inability to withstand damage mechanisms from one or more hits and the probability of serious damage or loss when hit by threat weapons (P K/H ). Survivability is the opposite of killability, i.e. the probability that the ship will be killed. Killability is the product of susceptility and vulnerability. The idea of ship kill can be defined in many different ways but here we will refer to the one given by Ball and Calvano (1994). In increasing order of severity we may have after a hit: System Kill, when there is damage to one or more components of a system and this results to system failure Mission Area Kill, when a particular ship mission area is lost (e. g. AAW) Mobility Kill, if immobilization or loss of controllability occurs Total Kill, in case the ship is lost entirely because of sinking, capsizal or a fire that forces abandonment. 3. Naval ship code Recognizing the need for establishment of a set of comparable standards to those of IMO, NATO nations worked on the development of the Naval Ship Code (NSC) (Rudgley et al., 2005). The code is developed based on the Goal Based Standards (GBS) concept, having a 5-tier structure and the goals represent the top tiers, against which a ship is verified throughout its life cycle. Chapter III of NCS covers buoyancy, stability and controllability issues. Its tier-1 goals are (INSA, 2012): The buoyancy, freeboard, main sub-division compartment and stability characteristics of the ship shall be designed, constructed and maintained to: Provide an adequate reserve of buoyancy in all foreseeable intact and damaged conditions, in the environment for which the ship is to operate; Ship system condition Normal operating condition Vulnerability Secondary effects degradation Hit Primary effect degradation DC Fig. 3. Visualization of vulnerability and recoverability. Recoverability time

4 52 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) In this paper when referring to ship kill we will limit our scope to the total kill due to sinking or capsizal. Mathematically survivability (P S ) is related to the other two quantities by the following formula (Ball and Calvano, 1994): P S ¼ 1 ðp H P K=H Þ ð2þ The vulnerability is visualized in Fig. 3. The normal operating condition of the ship is disrupted by the hit. The primary weapon effects (i.e. explosion and fragments) degrades instantly the operating level while the secondary effects (i.e. fire, flooding and system and structure failures) degrades it less rapidly but still significantly. Damage control procedures may only partially restore the ship's capability. These constitute the recoverability. By definition recoverability is mainly an operational aspect relying mainly on the sufficient training of the crew although it may still pose several requirements to the designer. Operational aspects affect the susceptibility of a naval ship, but the major influence factor is due to the intrinsic characteristics of the vessel, namely its signatures. Electronic emissions such as radar scans or external communication attempts could reveal the position of the stealthiest vessel and its susceptibility could be even higher than that of a conventional vessel. Likewise, vulnerability is also affected by operational aspects, such as watertight doors left open at the moment of impact of a weapon or poor performance of the fire-fighting parties, but these should be very unlike events onboard a naval ship. Therefore the intrinsic design part of a naval vessel is almost decisive for the probability of survival after a weapon impact. The difference between the susceptibility and vulnerability is that the first can be altered even in later design stages, even during the operational life of the ship (use of Radar Absorb Materials RAM, infrared signature suppression devices and low emission paints), whereas most of the issues that affect vulnerability will almost certainly characterize the ship throughout her life. Therefore a generic naval ship design methodology for enhanced survivability should consider the minimization of the ship's vulnerability in the early concept design phase. The tendency during recent decades in surface naval ship design was to assess and minimize susceptibility through detailed signature reduction measures. Therefore the probability of detection was usually estimated and it was considered as input in scenarios simulations. On the other hand the probability of staying afloat and upright was less frequently taken into account. Most of the simulations assumed a single-hit-kill probability equal to 1.0 for small naval ships, whereas 2hitswereconsideredadequateforthesinkingoflargervessels.Thus the defence analysis was actually never treating the vulnerability a naval ship as a probabilistic property, but as a property with deterministic outcome. For the naval architect it is usually enough to assess the adequacy of its design with respect to vulnerability through the use of traditional damaged stability requirements introduced by the various navies, such as those used by the USN and the UK MoD, depicted in Table 1 (Surko, 1994). Table 1 Current UK & US Damage Stability Criteria for surface combatants. Criteria UK NES 109 U.S.N. DDS-079 LWLo30 m 1-compartment LWLo100 ft 1-compartment Damage length 30 molwlo92 m 2 comp of at least 6 m 100 ftolwlo300 ft 2 comp, at least 6 m 92 molwl max.{15% LWL or 21 m} 300 ftolwl 15% LWL Permeability Watertight void 97% Watertight Void 95% Accommodation 95% Accommodation 95% Machinery 85% Machinery 85 95% Stores etc. 60% Stores etc % Angle of list or loll o201 Listo151 GZ at C (Fig. 5) 60% of GZmax Area A Area A Area A2 Longitudinal GM 40 Buoyancy Longitudinal trim less than that required to cause down-flooding 3 in margin line Fig. 4. Optimization procedure utilizing NAPA macros and modefrontier optimization tool (Boulougouris and Papanikolaou, 2004).

5 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) Several software tools have been developed for the assessment of the survivability of naval ships, e.g. CETENA's S.A.V.I.U.S. (Molini et al., 2002). Based on related experience in passenger ship design and optimization, SDL-NTUA has extended the application of its survivability assessment and design software tools on the NAPA software platform (NAPA, 2011) to naval ship design. Using a given Fig. 5. Survivability estimation flowchart of the ship against a specific threat weapon (Boulougouris, 2003).

6 54 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) hull geometry and room definition, the display, analysis and optimization tools (ES.TE.CO., 2003) are interfaced by developed purpose-specific NAPA-macros creating a handy design environment for the survivability assessment and optimization of naval ships (see Fig. 4). 5. Vulnerability estimation Risk Based Design (RBD) is defined as a formalized methodology that integrates systematically risk assessment in the design process with prevention/reduction of risk embedded as a design objective, alongside conventional design objectives (Vassalos, in Papanikolaou, 2009a). In this respect the probabilistic damage stability framework is a tool for RBD. The authors have presented earlier a generic concept for the design of both merchant and naval ships of enhanced survivability (Papanikolaou and Boulougouris, 1998; Boulougouris and Papanikolaou, 2003; Boulougouris et al., 2004). It is based on the fundamental probabilistic damage stability concept originally introduced by Wendel (1960) and its derivatives (IMO Resolution A.265; IMO MSC.19 (58); IMO MSC.216 (82)) for the assessment of ship's survival capability after damage. It recognizes the following probabilities of events relevant to the ship's damage stability: The probability that a ship compartment or group of compartments i may be flooded (damaged), p i. The probability of survival after flooding the ship compartment or group of compartments i under consideration, s i. The total probability of survival is expressed by the attained subdivision index A which is given by the sum of the products of p i, and s i for each compartment and compartment group, i, along the ship's length: index R. The parameters in the formula determining R are related to ship's size and the number of people/live saving appliances onboard (passenger ships). The required subdivision index of a ship is so selected to correspond to the mean value of the attained subdivision indexes of a sample of ships of assumed comparable risk exposure (similar size and people at risk) with acceptable damage stability/survival characteristics (IMO MSC.216(82)); or to the attained subdivision index of sample ships of acceptable risk, which has been rationally determined following a Cost Benefit Analysis (GOALDS, ). Likewise for a naval ship's damage stability there is a probability of hit by a threat weapon, causing ship's flooding of one or more compartments or group of compartments. The likely damage can be at any position along the ship and its extent depends on both the characteristics of the threat (weapon) and the characteristics of the target (ship). It is easily understood that the probability distribution of the damage of a naval ship relates susceptibility with vulnerability characteristics. The estimation of the survivability for a given design against a specific threat weapon is following the flowchart in Fig. 5. The probability of survival of a particular function of the ship can be extracted from the total attained index, which represents ship's floatability and stability after damage. If j n ¼{j 1,j 2,j 3,,j n } the set of compartments that host all systems of the particular function F, then the damage of any set j that includes j* will impair the ship from function F. Therefore the probability of survival of the particular function is calculated using the following formula: S f ¼ i p i s i p j s j j where j are all damage cases which include the compartment set j*. ð4þ A ¼ p i s i i ð3þ 6. Determining p i The IMO damage stability regulations for dry cargo and passenger ships (IMO MSC.216(82)) require that this attained subdivision index should be greater than a required subdivision During the initial stages of a naval ship's design, when there is a lack of refined estimations for the threat's signature distribution along the ship we may assume that the probability of weapon Impact point Probability Density Distribution Normal Density Longitudinal Distribution Piecewise Linear Density Longitudinal Distribution SOLAS B1 Mine Longitudinal Density Distribution Non dimensional Length Fig. 6. Comparison of alternative longitudinal damage distributions (see Boulougouris and Papanikolaou, 2003).

7 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) impact along the ship follows a basic mathematical distribution, such as the piecewise linear or the normal one. Although the actual distribution could be determined with actual or virtual engagement scenarios, the authors have proposed for air-to-surface missile (ASM) threats a piecewise linear distribution with the maximum probability amidships, whereas for contact mines we may assume a linear distribution (Boulougouris and Papanikolaou, 2003; Harmsen and Krikke, 2000) (see Fig. 6). Thus the impact point probability density function in the missile's case with a piecewise linear distribution is ( 4x x 0:5 Imp ðxþ¼ 4xþ4 x40:5 whereas in the case of a normal distribution it would be ImpðxÞ¼ ffiffiffiffiffi 1 p exp 1 2π s 2s 2 ðx 0:5Þ2 where s the standard deviation. In Fig. 6 both these distributions are compared with the longitudinal distribution assumed in SOLAS A.265 for passenger ships. The damage length probability density distribution is based on the concept of the Damage Function used in the theory of Defence Analysis (Przemieniecki, 1994). The wellknown log-normal distribution shown in Fig. 7 is considered the most appropriate for this case. Therefore the damage length probability density distribution is give by the following formula: " # 1 DamðyÞ¼ pffiffiffiffiffi exp ln2 ðy=αþ 2π βy 2β 2 Fig. 7. Lognormal damage function. ð5þ ð6þ ð7þ where p α ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi L SS L SK, β ¼ 1 p 2 ffiffiffi ln 2 zss L SS L SK, where L SK is the sure kill length which means that d(l SK )¼0.98, L SS is the sure save length which means d(l SS )¼0.02 and z SS is constant equal to For defining the damage extent range, it is a common approach in naval ship design to consider 2 or 3 damaged compartments around the detonation compartment, as shown in Fig. 8, especially in case of absence of blast resistant bulkheads (Erkel and Galle, 2003). More detailed estimates may result from a careful risk assessment based on live firing tests analysis, the analysis of data from actual engagements, empirical formulas linking the damage range with the type and the weight of the warhead or from the use of damage lengths/extents defined in current deterministic damage stability regulations for naval ships. In the later case, which is the one proposed by the authors, a first approximation of the L SS can be taken according to naval codes NES 109 and DDS-079 and it would be 0.15L (see Table 1). The L SK has been assumed equal to 0.02L (Fig. 9). Using on the above the probability of a damage lying between the boundaries x 1 and x 2 of a naval ship's compartment is p i j x 2 x 1 ¼ Z y 0 DamðyÞ Z x2 ðy=2þ x 1 þðy=2þ ImpðxÞdx dy The equations resulting from a substitution of the piecewise linear Imp(x) into Eq. (8) were presented earlier in Boulougouris and Papanikolaou (2004). The vertical extent of damage may also vary depending on the weapon's characteristics. In a surface combatant such as a frigate or a destroyer there are 3 vertical watertight boundaries, namely the tanktop, the damage control deck and the main deck. An airdelivered weapon (e.g. guided missile) is more likely to cause larger damage above waterline, leaving the tanktop deck probably intact, whereas an underwater weapon such as a contact-mine or a torpedo is likely to leave the damage control deck intact. The problem with an underwater explosion is that modern underkeel torpedoes may cause a extensive damage to the hull girder of even cruiser sized ship, often sufficient to cause breaking and sinking of the ship. Such cases are not covered by the proposed methodology as the maintenance of the structural integrity is a prerequisite for the examination of the damaged stability (Fig. 10). For a hit by an air-delivered weapon, a linear distribution for the probability density function of the vertical extent of damage can be used. Its maximum is at the main deck and the minimum at the keel. The opposite is valid for an underwater weapon. In order to take into account both threats a weighting factor can be applied according to an operational analysis of the potential threats. The damage penetration distribution is not an issue for surface ð8þ Fig. 8. Damage extent on naval ship profile.

8 56 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) Fig. 9. Damage extent on naval ship profile. Table 2 Proposed damage stability criteria for naval combatants. s i ¼1 s i ¼P(H s 8 ft) s i ¼0 φ roll ¼251 wind speed¼accord. to DDS A1 1.4 A2 Min Freeboard 3 in.þ0.5 (H s (0.99)-8 ft) Ship meets DDS-079 damaged stability criteria φ roll ¼111 Wind speed¼accord. to DDS A A2 Margin line immerses. combatants, as commonly a longitudinal watertight subdivision that may result to asymmetrical flooding conditions is avoided by design. 7. Survival index S i Fig. 10. Vertical watertight boundaries. The probability of survival of a ship after damage in waves can be estimated using: A probabilistic damage stability quasi-static approach adjusted for the currently valid, semi-empirical deterministic criteria for naval ships (probabilistic quasi-static study approach). A probabilistic damage stability approach in which the assessment of the probable damage scenarios is accomplished by a time domain flooding and/or capsizing simulation code (probabilistic dynamic flooding/capsizing approach) Probabilistic damage stability quasi-static approach A methodology implementing the probabilistic survivability assessment approach to ship design within a formalised optimization scheme was earlier proposed (Boulougouris et al., 2004). It considers the probability of survival damages based on quasi-static survival criteria, like those of the RN and the USN. They take into account data of real damage incidences of WWII and they proved to be quite reliable for some time in the past. The philosophy behind the earlier proposed methodology regarding the transformation of the deterministic naval ship criteria into a probabilistic assessment procedure was following the approach of IMO Resolution A.265 for passenger ships. It is well established that in all relevant damage stability criteria there is an underlying assumption that the sea conditions at the time of damage are moderate. This constraint was herein lifted for naval ship operating conditions with the requirement for a specific survival sea state in case of damage. This would allow the correction of these requirements by consideration of the probability of exceedance of the wave height considered as basis for the current deterministic RN and USN criteria, namely a significant wave height H s of merely 8 ft. This wave height was used in the above criteria for the determination of φ roll, namely the roll amplitude due to wave action. It was also the underlying assumption behind the guidelines for establishing the watertight features/closures to prevent progressive flooding. Thus, any attempt to change the wave amplitude must take into account changes in both φ roll as well as the margin line or equivalent. The introduction of a nominal operating area and related seaway conditions is in line with relevant classification rules and regulations for structural loading; it has been also used in a variety of recent IMO regulations regarding passenger ship safety (High Speed Code-MSC.97(73), SOLAS Res. 14-Stockholm agreement, SOLAS 2009 and Safe Return to Port ). Another important environmental parameter is the wind speed. Given the small probability of exceeding the values given by the U.S. Navy standards for warships (namely, about 33 knots for a 3500 tons frigate), this value could be left unchanged. Alternatively the Kruseman wind wave relationship can be used for determining the mean wind velocity (Palazzi and Kat, 2003): V m ¼ 372 H1:829 s ðm=sþ T 2:66 p where H s the significant wave height and T p the peak period. The above formula gives the same mean wind velocity with that used in DDS-079 for 8 ft significant wave height, for a peak period of approximately 6 s. The following survival criteria, shown in Table 2, could be applied in the frame of a probabilistic approach for the survivability of naval ships (see Fig. 11 for the meaning of the various notions of the righting arm curve). For intermediate stages, interpolant values can be used. Implementing the above criteria for ships operating in North Atlantic P (H s 8 ft) would be 0.56 and for East Mediterranean Sea 0.90 (Athanassoulis and Skarsoulis, 1992). Therefore, a combatant, meeting the U.S. Navy criteria for warships, should have according to the proposed criteria 56% probability of survival in the North Atlantic for a damage length not exceeding the current regulations (Ochi, 1978). This probability will increase to 90% probability of survival in the Mediterranean Sea. Obviously a similar methodology can be introduced for auxiliary naval vessels. The minimum required values for compliance could be estimated after application of the above procedure to sample/existing ships. ð9þ

9 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) Fig. 11. Damage stability criteria Probabilistic dynamic flooding/capsizing approach A fast time domain flooding/capsize simulation programme/ code can be a very useful tool in the calculation of the probability of survival in any damage condition. It could be used repeatedly for a large range of conditions and provides the designer with a more accurate picture of the attained survivability of a design under assessment. Several time domain ship motions flooding/ capsize simulation programs were developed and presented in the past, such as CAPSIM (Papanikolaou et al., 2000; Spanos, 2002), FREDYN (de Kat and Peters, 2002) or PROTEUS (Jiasionowski, 2002), enabling the prediction of survival after damage and flooding with satisfactory accuracy, but at the expense of appreciable computing time. Related work on the assessment of naval ships survival by time domain simulations were presented in several publications (Alman et al., 1999; Harmsen and Krikke, 2000; de Kat and Peters, 2002; Andrewartha et al., 2008). The approach for the determination of the survivability index when using a time domain simulation programme is that given/ assuming adequate buoyancy (including reserve buoyancy), the main risk is the probability of capsize. The latter is assumed to be directly related to the probability of exceeding a critical roll angle: P(φ4φ critical ). Using a time simulation programme (e.g. FREDYN) the critical roll angle is determined, and then the probability of capsize (or exceeding the critical roll angle) may be determined by the following formula (Perrault et al., 2010): Pðϕ4ϕ critical Þ¼ pðvþpðβþpðh s,t p Þpðϕ4ϕ critical jv,β,h s,t p Þ ð10þ where V is the vessel's speed, β is its heading, H s the significant wave height, T p the peak wave period, and their joint probability density is p(h s,t p ). The final term, p(φ4φ critical V,β, H s,t p ) is the conditional probability of exceeding the critical roll angle given a specific combination of speed heading and seaway conditions. It is determined by multiple simulations using a fitted distribution or a distribution-free probability method. The drawback of this approach is the vast number of required calculations and the associated computing time that makes it difficult to implement it in a formalised optimization procedure involving the assessment of hundreds of thousands of designs, as proposed herein. For a typical frigate with 12 compartments, assuming 6 flooding combinations, 5 damage causes, 4 hole sizes, 4 ship speeds, 8 wave headings and 2 scenarios for the consideration of extinguishing water, the necessary number of simulation runs for the evaluation of just one design is 92,160 and the associated computing time on a desktop computer several tens of hours (Harmsen and Krikke, 2000). Limiting the headings to beam seas at zero forward speed, without considering the fire fighting water, the number of runs drops to Obviously, a more detailed analysis can be performed for the identified critical damage cases Flooding simulation by the pressure-correction method In the present study, the NAPA dynamic flooding simulation tool was tested and implemented in the probabilistic assessment framework. The principles of the method were presented in Ruponen (2007). At each time step the conservation of mass is satisfied in each flooded room, both for water and air. The equation of continuity stipulates Z Z ρ Ω t dω ¼ ρvds ð11þ S where ρ is the density of the fluid, v the velocity vector and S the surface that bounds the control volume Ω. The velocities in the openings are calculated using Bernoulli's equation for a streamline from a point in the middle of a flooded room A to a point in the opening B: Z B dp A ρ þ 1 2 ðu2 B u2 A Þþgðh B h A Þ¼0 ð12þ where p is the air pressure, u is the flow velocity and h is the height for a reference level. The velocity at the centre of the room is assumed zero. The flow is considered inviscid and irrotational, but semi-empirical discharge coefficients are used for the pressure losses in flooding openings and pipes. For the latter, the discharge coefficient is calculated according to the MSC.245(83) (IMO, 2007). The flooding simulation uses the pressure-correction method. The ship is considered as an unstructured and staggered grid of volumes (cells). Each room is a single computational cell. The flux through a cell face is possible only with an opening that connects the room with another one or the sea (environment). The water is level in the room, thus sloshing effects are not taken into account. The volume in each room is calculated using the water depth in it and the heel and trim angles Thus, the progress of floodwater is solved implicitly on the basis of the pressures in the rooms and the velocities in the openings (Metsä et al., 2008). The underlying concept is that the equation of continuity and the linearization of the momentum equation (Bernoulli) are used for the correction of

10 58 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) the pressures until the iteration is converged and both are satisfied at the same time. The tool allows also the estimation of the dynamic roll motion of the ship. However, in contrast to the more accurate time domain simulation tools (CAPSIM, FREDYN, PROTEUS), that allow the consideration of 6 degrees of freedom motions in seaways, the NAPA approximate tool is limited to the roll motion caused by flooding only, whereas trim and draught are treated in a quasistatic way. The resulting roll motion is based on given values for the natural roll period and damping and the impact of seaway is taken in an approximate way into account (Metsä et al., 2008). The main drawback, when applying this tool to the estimation of the survivability index, is its quasi-static nature with respect to the ship motions, whereas the currently implemented maximum wave height is limited to half of the ship's draught. Additionally, there is also restriction for the wave period as a function of length. Therefore, only the impact of the intermediate stages of flooding can be systematically explored, taking into account moderate motions of the ship in beam waves with a significant height of DWL/2. The main advantage, on the other side, offered by this tool is its fast execution, allowing the assessment of many damage scenarios within reasonable time. 8. Case study A generic frigate model defined in the NAPA software tool (Napa, 2011) was used to demonstrate the implementation of the methodology. The ship's main particulars are given in Table 3 and the 3D hull model in Fig. 12. The arrangement is typical for this size of naval combatant with 2 passageways, one at each side of the ship, running along the whole damage control deck. The ship has: two main engine rooms (one for the diesel engines and one for the gas turbine), separated by a reduction gear room and two auxiliary machinery rooms (forward the GT room and aft of the DE room). The hull is subdivided in 17 zones by 16 watertight transverse bulkheads. Horizontal watertight boundaries are formed by four decks, namely main deck (1st deck), the bulkhead Table 3 Main particulars. Length, waterline (m) Breadth, waterline (m) DWL (m) 4.90 Depth (m) 9.40 Displ. (end of life) (ton) 5435 deck (2nd deck), the 3rd deck, and the tanktop (4th deck). A total of 495 different damage cases have been defined extending damages up to 6 zones. The ship has a displacement of 4940 t at the full load condition without the future growth margin and the vertical centre of gravity is 6.45 m above baseline resulting to a GM corr of m. The ship fulfils at this condition all the intact and damage stability criteria of DDS-079. The 15%L damage length results to 4-compartment damages for most cases for this ship. The high D/T ratio results to a substantial amount of reserved buoyancy by design. In order to investigate the impact of the metacentric height on survivability, the attained survivability index using the probabilistic damage stability quasi-static approach was calculated for two different values, namely GM of 0.8 and 1.14 m. For the investigation of the influence of the operational area, two different scenarios were used. The first assuming P(H s 8ft)¼0.8 and H s (0.99)¼4 m (East Med.) and a second one with P(H s 8ft)¼ 0.56 and H s (0.99)¼10 m (North Atlantic). A natural roll period of 10 s, typical for combatants of this size was used in the calculations. Various values of damping ratios were used ranging from 0.01 to The formulas for the calculation of the probabilities of damage pi using Eq. (8) were applied to the sample ship and the results for the one compartment damages are given in Table 4. The calculations have shown that for the given arrangement, damage length and longitudinal distribution, 1 compartment cases contribute approximately 0.2 to the attained index, whereas 2, 3 and 4 compartment cases contribute approximately 0.58, 0.18 and 0.03 respectively (see Fig. 13). Therefore the design that fulfils the survivability criteria for all damage cases of flooding of up to 3 compartments will have a probability of survival of at least Table 4 Pi for frigate 1-comp damages. Room NZ x 1 x 2 x 1 u x 2 u J p i Room Room Room Room Room Room Room Room Room Room Room Room Room Room Room Room Room Fig. 12. Frigate 3D hull model. Source: NAPA Fig. 13. Contributions of the various damage cases to the total index.

11 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) The results for the particular design considering up to 6-compartment damage cases resulted to an attained index of A¼0.95 for the Mediterranean scenario, using a metacentric height of 0.8 m while for the same loading condition the attained index is reduced to A¼0.89 for the North Atlantic scenario. The ship at her design full loading condition (GM int ¼1.194) has Fig. 14. Subdivision and survivability index for North Atlantic operation with GM 1.2 m. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.) Fig. 15. Floating position for damage including Z4 9.

12 60 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) Fig. 16. Heel's time history for damage in zones Z4 9. Fig. 18. Heel's time history for damage in zones Z4 9 using compartments openings Zone 9. Waves with height of 2.4 m and period equal to ship's natural period (10 s) are assumed exciting the ship. In Fig. 16 the heel time history is shown assuming that the damaged compartments are open to sea. The relevant draught history is presented in Fig. 17. From the results it is apparent that the ship will heel up to 201 before she will stabilize at If the compartments are assumed interconnected through their openings, then the results show much higher max roll angles exceeding 201, as shown in Fig. 18. The designer should examine carefully such results and decide whether the ship should be considered as survivable in such a case, or using additional measures (e.g. counter-flooding) to attempt to minimize the list of the ship Fig. 17. Draught's time history for damage in zones Z4 9. an attained index of A¼0.94 for the North Atlantic scenario. The local survivability indices for this case are shown in Fig. 14. The damage case for which the ship has s i ¼1.0 are shown with green colour, while the orange indicates values below 1.0. The red boxes indicate case where the ship is not going to survive. Using such figures the designer may identify potential weaknesses of the design, compare different designs on the bases of their survivability index and integrate the methodology into a formalised multi-objective optimization procedure (Boulougouris and Papanikolaou, 2004). The survivability of the mobility function can be calculated using Eq.(4), where j are all the main engine room compartments; in this case rooms 7, 8 and 9. This would result in a mobility survivability index of S f ¼0.90 for the North Atlantic scenario at the design full load condition. For those cases where the ship has a survivability index less than 1.0 and especially for those where sop(h s o8 ft) a more refined investigation is necessary using the probabilistic dynamic flooding/capsizing approach. The damages may be defined both by rooms flooded and open to sea, while internal openings are used for the progressive flooding damage holes modelled as openings An example investigation of the impact of the intermediate stages of flooding is shown in Fig. 15. The ship is subject to a 6- compartment asymmetrical damage extending from Zone 4 up to 9. Conclusions The application of a risk-based approach to ship design requires the availability of (Papanikolaou, 2009b): safety-performance prediction tools adequate risk models and an optimization platform The authors have presented in the past the optimization platform of NTUA-SDL (Boulougouris and Papanikolaou, 2004). This paper supplements their previous work introducing a risk model for the probabilistic assessment of battle damages and a safetyperformance prediction method for calculating the probability of survival as well as maintaining vital functions of a naval ship. This introduces the minimization of risk (and therefore the maximization of survivability) as an additional design objective in the design procedure materializing the RBD process. The introduced method has been applied to a generic frigate design operating in specified seaway conditions and typical results of this study were presented and discussed. Probabilistic damage stability quasi-static derived survivability indices were used for the attained survivability index assessment. Additionally, critical cases were examined using flooding simulations that implement the pressure-correction method. The software tool implementing the proposed methodology is part of the design and optimization tools suite developed by SDL-NTUA using the NAPA software platform. Links to other numerical tools for the calculation of the resistance, the wave field around the ship, the seakeeping performance and the signature assessment software (e.g. RCS) are in place. The suite allows the designer to start from initial

13 E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) requirements and develop optimal design solutions with respect to formulated assessment criteria. In the next stage, the present methodology will be further developed to enable the implementation of Monte Carlo type analysis for the assessment of the survivability index of parametrically generated design alternatives. This will lead eventually to formal multi-objective optimizations. Other enhancements are the integration of more refined hydrodynamic software tools, like non-linear time domain simulation tools (such as CAPSIM) for better capturing the dynamic behaviour of the ship in extreme seaways in damaged conditions as the present NAPA time domain tool is limited to moderate sea states only. References Alman, P.R., Minnick, P.V., Sheinberg, R., Thomas, W.L., Dynamic capsize vulnerability: reducing the hidden operational risk. 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