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Ocean Engineering 65 (2013) 49–61
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Ocean Engineering
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n CorrE-m
papa@d1 Te
journal homepage: www.elsevier.com/locate/oceaneng
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, UKb National Technical University of Athens, School of Naval Architecture and Marine Engineering, Ship Design Laboratory, Greece
a r t i c l e i n f o
Article history:Received 19 July 2012Accepted 24 February 2013Available online 21 April 2013
Keywords:Damaged stabilityRisk-based designNaval shipsTime domain simulation
18/$ - see front matter & 2013 Elsevier Ltd. Ax.doi.org/10.1016/j.oceaneng.2013.02.014
esponding author. Tel.: þ44 1415483875; faxail addresses: [email protected] (A. Papanikolaou).l.: þ30 2107721409; fax: þ30 2107721408.
a b s t r a c t
The present paper introduces a risk-based design concept to naval ship design. It extends an earlierproposed basic design concept by the authors for the evaluation of the survivability of surfacecombatants by semi-empirical naval ship stability criteria, by introducing modern assessment methodsfor ship's behaviour after flooding, namely by implementing numerical simulation tools for assessing therisk after flooding. The introduced method was applied to the assessment of the damage stability of ageneric frigate operating in specified seaway conditions and typical results of this study are presentedand discussed.
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Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492. Risk-based design approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513. Naval ship code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514. Survivability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515. Vulnerability estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546. Determining pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547. Survival index Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7.1. Probabilistic damage stability quasi-static approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567.2. Probabilistic dynamic flooding/capsizing approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577.3. Flooding simulation by the pressure-correction method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
8. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
1. Introduction
The International Maritime Organization (IMO) and themerchant maritime industry have made significant advances inthe upgrade of the safety standards of merchant ships over thepast decade by adopting pro-active safety measures for futurerules and regulations in the frame of a holistic approach to ship'ssafety. Instead of waiting for the next major catastrophic accident,IMO and major classification societies (IACS) decided to move from
ll rights reserved.
. þ44 1415522879.c.uk (E.Boulougouris),
prescriptive concepts to probabilistic assessment methods andgoal-based standards (GBS). The acceptance of the new harmo-nized probabilistic damage stability framework of SOLAS 2009 forthe assessment of the damage stability of both passenger and drycargo ships (though, more than three decades after the firstintroduction of the probabilistic concept in SOLAS 74…), showsthat the maritime industry, national and international regulatorybodies are now convinced that this is the only way forward. Inparallel, risk and reliability analysis and assessment methods havebecome important design tools in naval architecture facilitatingthe accomplishment of the safety objectives cost effectively(Papanikolaou, 2009a).
The use of advanced computational tools permits nowadays thequantification of the risk level of a particular design and its
Fig. 1. SDL-NTUA ship design optimization procedure (Boulougouris and Papanikolaou, 2006).
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6150
exhaustive comparison with alternatives. In this framework risk isno longer a constraint but a measure of safety performance anddesign objective which can be used in an optimization procedure(see Fig. 1). Therefore ship designs can be optimized for minimumrisk, while performing with best efficiency and economy. This ledto the new scientific and engineering disciplines of risk-baseddesign (RBD) and holistic Multi-Objective Optimization(Papanikolaou, 2009b).
At the same time, the complexity of naval ship design hassubstantially increased in view of the enhancement of relatedstakeholder disciplines (see Fig. 2).
Additionally, the main progress in naval ship design appears tobe concentrating on improvements of outfitting and the perfor-mance in peace times, rather than addressing naval ship's risks inemergency/flooding conditions. Surface combatants are stilldesigned and operated based on traditional naval stability stan-dards, which have a common origin in the experiences gainedduring World War II or even before. Even though these standardshave served their purpose for many decades, they appear nowa-days outdated; there are serious concerns about their limitationsand questions regarding their applicability to modern naval shipdesigns. The shortfalls include (Perrault et al., 2010):
Fig. 2. Naval Ship Design stakeholders disciplines (see Neu et al., 2000).
� The level of safety assured by compliance with such standardsis unknown.�
Today's naval ship hullforms are quite different from those usedfor 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 fullycapture the dynamic behaviour of modern naval ship operatingin extreme seaways both in the intact and damaged condition.The above suggests that both designers and the operators ofnaval ships do not have in general a clear understanding of thesurvivability performance and operational limits of their ships.Moreover, ships that are designed right now and will be operatingduring the first half of the 21st century do not dispose a rationalyardstick for measuring and setting targets for improving theirdamaged survivability performance.
An effective response to this gap is risk-based design andoperation, in which design and operational criteria are related torationally determined risk levels, which are considered acceptableby society (merchant ships) or by a defence agency (naval ships).Risk-based approaches are inherently connected to probabilisticassessment methods (Papanikolaou, 2009a).
The authors have presented in the past a methodology for theprobabilistic damage stability assessment of naval combatants andits application to the optimization of naval ship design(Boulougouris and Papanikolaou, 2003, 2004). Several researchershave also proposed similar methodologies regarding the intact(Perrault et al., 2010) and damage stability of naval ships (Harmsenand Krikke, 2000). Significant effort has been also devoted to the
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 51
assessment of survivability of warships in damaged conditionusing time domain simulation tools (de Kat and Peters, 2002;Andrewartha et al., 2008).
The present paper extends the basic design concept proposedearlier by the authors for the assessment of the survivability ofsurface combatants after damage by introducing modern risk-based assessment methods for ship's behaviour after flooding,namely by implementing numerical simulation tools for assessingthe risk after flooding. The introduced method was applied to theassessment of the damaged stability of a generic frigate operatingin specified seaway conditions and typical results of this study arepresented and discussed.
2. Risk-based design approach
Risk is the product of the frequency of an event times theassociated consequences. According to Papanikolaou (2009a) therisk-based design approach is an improved alternative to thetraditional design process as it integrates safety as additionaldesign objective. Hence, the designer has to sutisfy an additionalrequirement i.e. that the risk of any feasible design, Rdesign, shouldbe less or equal than the specified acceptable risk, Racceptable, that is
Rdesign≤Racceptable ð1Þ
Different risk categories, e.g. of system failure, to human life, toenvironment or to property, should be treated separately. The totalrisk is calculated by the sum of the partial risks coming fromdifferent damage categories such as explosion, fire, collision orgrounding. Each partial risk can be computed with the help of riskmodels like, e.g. event trees or Bayesian networks. Risk modelsexpressed by mathematical formulae were developed for fastdesign optimization. The acceptable level of risk that the feasibledesigns have to exceed can be specified in case of warships by theowner (navy) or other approval authority (NATO and/or classifica-tion society). There are two options for the specification of theacceptable risk: relative or absolute. In the first case, a referencedesign is selected which complies with current rules. In the secondcase, absolute level, e.g. IMO risk acceptance criteria, can be usedor referenced.
In the present paper the risk of the ship not surviving damagedue to hit by a threat weapon will be discussed and a mathema-tical risk model will be presented for calculating the survivabilityin case of such damage. The method is applied to a genericwarship that meets the existing deterministic criteria. Thereforeher attained survivability index could be used as reference forsetting the acceptable risk level.
Ship system condition
Normaloperating condition
Primary effectdegradation
Recoverability
Vulnerability
3. Naval ship code
Recognizing the need for establishment of a set of comparablestandards to those of IMO, NATO nations worked on the develop-ment 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 toptiers, against which a ship is verified throughout its life cycle.Chapter III of NCS covers buoyancy, stability and controllabilityissues. Its tier-1 goals are (INSA, 2012):
Secondaryeffects
� degradation The buoyancy, freeboard, main sub-division compartment andstability characteristics of the ship shall be designed, con-structed and maintained to:
○
timeHit DCFig. 3. Visualization of vulnerability and recoverability.
Provide an adequate reserve of buoyancy in all foreseeableintact and damaged conditions, in the environment for whichthe ship is to operate;
○
Provide adequate stability to avoid capsizing in all foreseeableintact and damaged conditions, in the environment for whichthe ship is to operate, under the precepts of good seamanship;○
Permit embarked persons to carry out their duties as safely asreasonably practical;○
Protect the embarked persons and essential safety functions inthe event of foreseeable accidents and emergencies at leastuntil the persons have reached a place of safety or the threathas receded including preventing the malfunction of the life-saving systems and equipment.The keyword in the first two goals is ‘adequate’. In order tospecify the sufficiency of the reserve buoyancy and stability, themaximum acceptable level of risk (minimum level of safety) has tobe decided and be set as design criterion.
4. Survivability
It may be defined as “the capability of a (naval) ship and itsshipboard systems to avoid and withstand a weapons effectsenvironment without sustaining impairment of their ability toaccomplish designated missions” (Said, 1995). It contains twoaspects:
�
The susceptibility defined as the inability to avoid beingdamaged in the pursuit of its mission and to its probability ofbeing hit (PH). � The vulnerability defined as the inability to withstand damagemechanisms from one or more hits and the probability ofserious damage or loss when hit by threat weapons (PK/H).Survivability is the opposite of killability, i.e. the probabilitythat the ship will be killed. Killability is the product of susceptilityand vulnerability. The idea of ship kill can be defined in manydifferent ways but here we will refer to the one given by Ball andCalvano (1994). In increasing order of severity we may have after ahit:
�
System Kill, when there is damage to one or more componentsof 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.
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6152
In this paper when referring to ship kill we will limit our scopeto the total kill due to sinking or capsizal. Mathematicallysurvivability (PS) is related to the other two quantities by thefollowing formula (Ball and Calvano, 1994):
PS ¼ 1−ðPH � PK=HÞ ð2Þ
The vulnerability is visualized in Fig. 3. The normal operatingcondition of the ship is disrupted by the hit. The primary weaponeffects (i.e. explosion and fragments) degrades instantly theoperating level while the secondary effects (i.e. fire, flooding andsystem and structure failures) degrades it less rapidly but stillsignificantly. Damage control procedures may only partiallyrestore the ship's capability. These constitute the recoverability.By definition recoverability is mainly an operational aspect relyingmainly on the sufficient training of the crew although it may stillpose several requirements to the designer.
Operational aspects affect the susceptibility of a naval ship, butthe major influence factor is due to the intrinsic characteristics ofthe vessel, namely its signatures. Electronic emissions such asradar scans or external communication attempts could reveal theposition of the stealthiest vessel and its susceptibility could beeven higher than that of a conventional vessel. Likewise, vulner-ability is also affected by operational aspects, such as watertightdoors left open at the moment of impact of a weapon or poorperformance of the fire-fighting parties, but these should be veryunlike events onboard a naval ship. Therefore the intrinsic design
Table 1Current UK & US Damage Stability Criteria for surface combatants.
Criteria UK NES 109
Damage lengthLWLo30 m 1-compartme30 moLWLo92 m 2 comp of at92 moLWL max.{15% LWL
Permeability Watertight void 97%Accommodation 95%Machinery 85%Stores etc. 60%
Angle of list or loll o201GZ at C (Fig. 5) 60% of GZmax
Area A1 41.4 Area A2Longitudinal GM 40Buoyancy Longitudinal trim less than that required to cause dow
Fig. 4. Optimization procedure utilizing NAPA macros and modeFro
part of a naval vessel is almost decisive for the probability ofsurvival after a weapon impact.
The difference between the susceptibility and vulnerabilityis that the first can be altered even in later design stages, evenduring the operational life of the ship (use of Radar AbsorbMaterials—RAM, infrared signature suppression devices and lowemission paints), whereas most of the issues that affect vulner-ability will almost certainly characterize the ship throughout herlife. Therefore a generic naval ship design methodology forenhanced survivability should consider the minimization of theship's vulnerability in the early concept design phase.
The tendency during recent decades in surface naval ship designwas to assess and minimize susceptibility through detailed signaturereduction measures. Therefore the probability of detectionwas usuallyestimated and it was considered as input in scenarios simulations. Onthe other hand the probability of staying afloat and upright was lessfrequently taken into account. Most of the simulations assumed asingle-hit-kill probability equal to 1.0 for small naval ships, whereas2 hits were considered adequate for the sinking of larger vessels. Thusthe defence analysis was actually never treating the vulnerability anaval ship as a probabilistic property, but as a property withdeterministic outcome. For the naval architect it is usually enough toassess the adequacy of its design with respect to vulnerability throughthe use of traditional damaged stability requirements introduced bythe various navies, such as those used by the USN and the UK MoD,depicted in Table 1 (Surko, 1994).
U.S.N. DDS-079
nt LWLo100 ft 1-compartmentleast 6 m 100 ftoLWLo300 ft 2 comp, at least 6 mor 21 m} 300 ftoLWL 15% LWL
Watertight Void 95%Accommodation 95%Machinery 85–95%Stores etc. 60–95%Listo151
41.4 Area A2–
n-flooding 3 in margin line
ntier optimization tool (Boulougouris and Papanikolaou, 2004).
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 53
Several software tools have been developed for the assessmentof the survivability of naval ships, e.g. CETENA's S.A.V.I.U.S. (Moliniet al., 2002). Based on related experience in passenger ship design
Fig. 5. Survivability estimation flowchart of the ship aga
and optimization, SDL-NTUA has extended the application of itssurvivability assessment and design software tools on the NAPAsoftware platform (NAPA, 2011) to naval ship design. Using a given
inst a specific threat weapon (Boulougouris, 2003).
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6154
hull geometry and room definition, the display, analysis andoptimization tools (ES.TE.CO., 2003) are interfaced by developedpurpose-specific NAPA-macros creating a handy design environ-ment for the survivability assessment and optimization of navalships (see Fig. 4).
5. Vulnerability estimation
Risk Based Design (RBD) is defined as “a formalized methodol-ogy that integrates systematically risk assessment in the designprocess with prevention/reduction of risk embedded as a designobjective, alongside “conventional” design objectives” (Vassalos, inPapanikolaou, 2009a). In this respect the probabilistic damagestability framework is a tool for RBD. The authors have presentedearlier a generic concept for the design of both merchant and navalships of enhanced survivability (Papanikolaou and Boulougouris,1998; Boulougouris and Papanikolaou, 2003; Boulougouris et al.,2004). It is based on the fundamental probabilistic damagestability concept originally introduced by Wendel (1960) and itsderivatives (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 theship's damage stability:
−
The probability that a ship compartment or group of compart-ments i may be flooded (damaged), pi.−
The probability of survival after flooding the ship compartmentor group of compartments i under consideration, si.The total probability of survival is expressed by the attainedsubdivision index A which is given by the sum of the products ofpi, and si for each compartment and compartment group, i, alongthe ship's length:
A¼∑ipisi ð3Þ
The IMO damage stability regulations for dry cargo andpassenger ships (IMO MSC.216(82)) require that this attainedsubdivision index should be greater than a required subdivision
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.1 0.2 0.3 0.4 0.5Non dimensio
Impa
ct p
oint
Pro
babi
lity
Den
sity
Dis
tribu
tion
Normal Density Longitudinal Distribution
Piecewise Linear Density LongitudinalDistributionSOLAS B1
Mine Longitudinal Density Distribution
Fig. 6. Comparison of alternative longitudinal damage distrib
index R. The parameters in the formula determining R are relatedto ship's size and the number of people/live saving appliancesonboard (passenger ships). The required subdivision index of aship is so selected to correspond to the mean value of the attainedsubdivision indexes of a sample of ships of assumed comparablerisk exposure (similar size and people at risk) with acceptabledamage stability/survival characteristics (IMO MSC.216(82)); or tothe attained subdivision index of sample ships of acceptable risk,which has been rationally determined following a Cost BenefitAnalysis (GOALDS, 2009–2012).
Likewise for a naval ship's damage stability there is a prob-ability of hit by a threat weapon, causing ship's flooding of one ormore compartments or group of compartments. The likely damagecan be at any position along the ship and its extent depends onboth the characteristics of the threat (weapon) and the character-istics of the target (ship). It is easily understood that the prob-ability distribution of the damage of a naval ship relatessusceptibility with vulnerability characteristics. The estimation ofthe survivability for a given design against a specific threatweapon is following the flowchart in Fig. 5.
The probability of survival of a particular function of the shipcan be extracted from the total attained index, which representsship's floatability and stability after damage. If jn¼{j1,j2,j3,…,jn} theset of compartments that host all systems of the particularfunction F, then the damage of any set j that includes j* willimpair the ship from function F. Therefore the probability ofsurvival of the particular function is calculated using the followingformula:
Sf ¼∑ipisi−∑
jpjsj ð4Þ
where j are all damage cases which include the compartment setj*.
6. Determining pi
During the initial stages of a naval ship's design, when there is alack of refined estimations for the threat's signature distributionalong the ship we may assume that the probability of weapon
0.6 0.7 0.8 0.9 1nal Length
utions (see Boulougouris and Papanikolaou, 2003).
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 55
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 withactual or virtual engagement scenarios, the authors have proposedfor air-to-surface missile (ASM) threats a piecewise linear distri-bution with the maximum probability amidships, whereas forcontact mines we may assume a linear distribution (Boulougourisand Papanikolaou, 2003; Harmsen and Krikke, 2000) (see Fig. 6).
Thus the impact point probability density function in themissile's case with a piecewise linear distribution is
Imp ðxÞ ¼ 4x x≤0:5−4xþ4 x40:5
(ð5Þ
whereas in the case of a normal distribution it would be
ImpðxÞ ¼ 1ffiffiffiffiffiffi2π
psexp −
12s2
ðx−0:5Þ2� �
ð6Þ
where s the standard deviation. In Fig. 6 both these distributionsare compared with the longitudinal distribution assumed in SOLASA.265 for passenger ships. The damage length probability densitydistribution is based on the concept of the Damage Function usedin the theory of Defence Analysis (Przemieniecki, 1994). The well-known log-normal distribution shown in Fig. 7 is considered themost appropriate for this case. Therefore the damage lengthprobability density distribution is give by the following formula:
DamðyÞ ¼ 1ffiffiffiffiffiffi2π
pβy
exp −ln2ðy=αÞ
2β2
" #ð7Þ
Fig. 7. Lognormal damage function.
Fig. 8. Damage extent o
where
α¼ffiffiffiffiffiffiffiffiffiffiffiffiffiLSSLSK
p, β¼ 1
2ffiffiffi2
pzSS
lnLSSLSK
� �,
where LSK is the sure kill length which means that d(LSK)¼0.98, LSSis the sure save length which means d(LSS)¼0.02 and zSS isconstant equal to 1.45222.
For defining the damage extent range, it is a common approachin naval ship design to consider 2 or 3 damaged compartmentsaround the detonation compartment, as shown in Fig. 8, especiallyin case of absence of blast resistant bulkheads (Erkel and Galle,2003). More detailed estimates may result from a careful riskassessment based on live firing tests analysis, the analysis of datafrom actual engagements, empirical formulas linking the damagerange with the type and the weight of the warhead or from the useof damage lengths/extents defined in current deterministicdamage stability regulations for naval ships.
In the later case, which is the one proposed by the authors, afirst approximation of the LSS can be taken according to navalcodes NES 109 and DDS-079 and it would be 0.15L (see Table 1).The LSK has been assumed equal to 0.02L (Fig. 9).
Using on the above the probability of a damage lying betweenthe boundaries x1 and x2 of a naval ship's compartment is
pijx2x1 ¼Z y
0DamðyÞ
Z x2−ðy=2Þ
x1 þðy=2ÞImpðxÞdx dy ð8Þ
The equations resulting from a substitution of the piecewiselinear Imp(x) into Eq. (8) were presented earlier in Boulougourisand Papanikolaou (2004).
The vertical extent of damage may also vary depending on theweapon's characteristics. In a surface combatant such as a frigateor a destroyer there are 3 vertical watertight boundaries, namelythe tanktop, the damage control deck and the main deck. An air-delivered weapon (e.g. guided missile) is more likely to causelarger damage above waterline, leaving the tanktop deck probablyintact, whereas an underwater weapon such as a contact-mineor a torpedo is likely to leave the damage control deck intact.The problem with an underwater explosion is that modern under-keel torpedoes may cause a extensive damage to the hull girder ofeven cruiser sized ship, often sufficient to cause breaking andsinking of the ship. Such cases are not covered by the proposedmethodology as the maintenance of the structural integrity is aprerequisite for the examination of the damaged stability (Fig. 10).
For a hit by an air-delivered weapon, a linear distribution forthe probability density function of the vertical extent of damagecan be used. Its maximum is at the main deck and the minimum atthe keel. The opposite is valid for an underwater weapon. In orderto take into account both threats a weighting factor can be appliedaccording to an operational analysis of the potential threats. Thedamage penetration distribution is not an ‘issue’ for surface
n naval ship profile.
Fig. 9. Damage extent on naval ship profile.
Fig. 10. Vertical watertight boundaries.
Table 2Proposed damage stability criteria for naval combatants.
si¼1 φroll¼251 wind speed¼accord. to DDS-079-1.A1≥1.4 A2 Min Freeboard≥3 in.þ0.5� (Hs(0.99)-8 ft)
si¼P(Hs≤8 ft) Ship meets DDS-079 damaged stability criteriasi¼0 φroll¼111 Wind speed¼accord. to DDS-079-1
A1≤1.05 A2 Margin line immerses.
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6156
combatants, as commonly a longitudinal watertight subdivisionthat may result to asymmetrical flooding conditions is avoided bydesign.
7. Survival index Si
The probability of survival of a ship after damage in waves canbe estimated using:
−
A probabilistic damage stability quasi-static approach adjustedfor the currently valid, semi-empirical deterministic criteria fornaval ships (probabilistic quasi-static study approach).−
A probabilistic damage stability approach in which the assess-ment of the probable damage scenarios is accomplished by atime domain flooding and/or capsizing simulation code (prob-abilistic dynamic flooding/capsizing approach).7.1. Probabilistic damage stability quasi-static approach
A methodology implementing the probabilistic survivabilityassessment approach to ship design within a formalised optimiza-tion scheme was earlier proposed (Boulougouris et al., 2004). Itconsiders the probability of survival damages based on quasi-staticsurvival criteria, like those of the RN and the USN. They take intoaccount data of real damage incidences of WWII and they provedto be quite reliable for some time in the past. The philosophybehind the earlier proposed methodology regarding the transfor-mation of the deterministic naval ship criteria into a probabilisticassessment procedure was following the approach of IMOResolution A.265 for passenger ships.
It is well established that in all relevant damage stabilitycriteria there is an underlying assumption that the sea conditionsat the time of damage are “moderate”. This constraint was hereinlifted for naval ship operating conditions with the requirement fora specific survival sea state in case of damage. This would allowthe correction of these requirements by consideration of the
probability of exceedance of the wave height considered as basisfor the current deterministic RN and USN criteria, namely asignificant wave height Hs of merely 8 ft. This wave height wasused in the above criteria for the determination of φroll, namely theroll amplitude due to wave action. It was also the underlyingassumption behind the guidelines for establishing the watertightfeatures/closures to prevent progressive flooding. Thus, anyattempt to change the wave amplitude must take into accountchanges in both φroll as well as the margin line or equivalent. Theintroduction of a nominal operating area and related seawayconditions is in line with relevant classification rules and regula-tions for structural loading; it has been also used in a variety ofrecent IMO regulations regarding passenger ship safety (HighSpeed Code-MSC.97(73), SOLAS Res. 14-Stockholm agreement,SOLAS 2009 and Safe Return to Port ).
Another important environmental parameter is the windspeed. Given the small probability of exceeding the values givenby the U.S. Navy standards for warships (namely, about 33 knotsfor a 3500 tons frigate), this value could be left unchanged.Alternatively the Kruseman wind wave relationship can be usedfor determining the mean wind velocity (Palazzi and Kat, 2003):
Vm ¼ 372� H1:829s
T2:66p
ðm=sÞ ð9Þ
where Hs the significant wave height and Tp the peak period. Theabove formula gives the same mean wind velocity with that usedin DDS-079 for 8 ft significant wave height, for a peak period ofapproximately 6 s.
The following survival criteria, shown in Table 2, could beapplied in the frame of a probabilistic approach for the surviva-bility of naval ships (see Fig. 11 for the meaning of the variousnotions of the righting arm curve). For intermediate stages,interpolant values can be used.
Implementing the above criteria for ships operating in NorthAtlantic P (Hs≤8 ft) would be 0.56 and for East Mediterranean Sea0.90 (Athanassoulis and Skarsoulis, 1992). Therefore, a combatant,meeting the U.S. Navy criteria for warships, should have – accord-ing to the proposed criteria – 56% probability of survival in theNorth Atlantic for a damage length not exceeding the currentregulations (Ochi, 1978). This probability will increase to 90%probability of survival in the Mediterranean Sea. Obviously asimilar methodology can be introduced for auxiliary naval vessels.The minimum required values for compliance could be estimatedafter application of the above procedure to sample/existing ships.
Fig. 11. Damage stability criteria.
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 57
7.2. 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 probabilityof survival in any damage condition. It could be used repeatedlyfor a large range of conditions and provides the designer with amore accurate picture of the attained survivability of a designunder assessment. Several time domain ship motions flooding/capsize simulation programs were developed and presented in thepast, 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 andflooding with satisfactory accuracy, but at the expense of appreci-able computing time. Related work on the assessment of navalships survival by time domain simulations were presented inseveral 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 indexwhen using a time domain simulation programme is that given/assuming adequate buoyancy (including reserve buoyancy), themain risk is the probability of capsize. The latter is assumed to bedirectly related to the probability of exceeding a critical roll angle:P(φ4φcritical). Using a time simulation programme (e.g. FREDYN)the critical roll angle is determined, and then the probabilityof capsize (or exceeding the critical roll angle) may be determinedby the following formula (Perrault et al., 2010):
Pðϕ4ϕcriticalÞ ¼∑∑∑∑pðVÞpðβÞpðHs,TpÞpðϕ4ϕcriticaljV ,β,Hs,TpÞð10Þ
where V is the vessel's speed, β is its heading, Hs the significantwave height, Tp the peak wave period, and their joint probabilitydensity is p(Hs,Tp). The final term, p(φ4φcritical| V,β, Hs,Tp) is theconditional probability of exceeding the critical roll angle given aspecific combination of speed heading and seaway conditions. It isdetermined by multiple simulations using a fitted distribution or adistribution-free probability method.
The drawback of this approach is the vast number of requiredcalculations and the associated computing time that makes itdifficult to implement it in a formalised optimization procedureinvolving the assessment of hundreds of thousands of designs, asproposed 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 considera-tion of extinguishing water, the necessary number of simulation
runs for the evaluation of just one design is 92,160 and theassociated computing time on a desktop computer several tensof hours (Harmsen and Krikke, 2000). Limiting the headings tobeam seas at zero forward speed, without considering the firefighting water, the number of runs drops to 1440. Obviously, amore detailed analysis can be performed for the identified criticaldamage cases.
7.3. Flooding simulation by the pressure-correction method
In the present study, the NAPA dynamic flooding simulationtool was tested and implemented in the probabilistic assessmentframework. The principles of the method were presented inRuponen (2007). At each time step the conservation of mass issatisfied in each flooded room, both for water and air. Theequation of continuity stipulatesZΩ
∂ρ∂t
dΩ¼−ZSρv dS ð11Þ
where ρ is the density of the fluid, v the velocity vector and S thesurface that bounds the control volume Ω. The velocities in theopenings are calculated using Bernoulli's equation for a streamlinefrom a point in the middle of a flooded room A to a point in theopening B:Z B
A
dpρ
þ 12ðu2
B−u2AÞþgðhB−hAÞ ¼ 0 ð12Þ
where p is the air pressure, u is the flow velocity and h is theheight for a reference level. The velocity at the centre of the roomis assumed zero. The flow is considered inviscid and irrotational,but semi-empirical discharge coefficients are used for the pressurelosses in flooding openings and pipes. For the latter, the dischargecoefficient 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 ofvolumes (cells). Each room is a single computational cell. The fluxthrough a cell face is possible only with an opening that connectsthe room with another one or the sea (environment). The water islevel in the room, thus sloshing effects are not taken into account.The volume in each room is calculated using the water depth in itand the heel and trim angles Thus, the progress of floodwater issolved implicitly on the basis of the pressures in the rooms and thevelocities in the openings (Metsä et al., 2008). The underlyingconcept is that the equation of continuity and the linearization ofthe momentum equation (Bernoulli) are used for the correction of
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6158
the pressures until the iteration is converged and both are satisfiedat the same time.
The tool allows also the estimation of the dynamic roll motionof the ship. However, in contrast to the more accurate time domainsimulation tools (CAPSIM, FREDYN, PROTEUS), that allow theconsideration of 6 degrees of freedom motions in seaways, theNAPA approximate tool is limited to the roll motion caused byflooding only, whereas trim and draught are treated in a quasi-static way. The resulting roll motion is based on given values forthe natural roll period and damping and the impact of seaway istaken in an approximate way into account (Metsä et al., 2008).
The main drawback, when applying this tool to the estimationof the survivability index, is its quasi-static nature with respect tothe ship motions, whereas the currently implemented maximumwave 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 floodingcan be systematically explored, taking into account moderatemotions of the ship in beam waves with a significant height ofDWL/2. The main advantage, on the other side, offered by this toolis its fast execution, allowing the assessment of many damagescenarios within reasonable time.
Table 4Pi for frigate’ 1-comp damages.
Room NZ x1 x2 x1u x2u J pi
Room01 1 0 8.4 0.000 0.061 0.061 0.0014
8. Case study
A generic frigate model defined in the NAPA software tool(Napa, 2011) was used to demonstrate the implementation of themethodology. The ship's main particulars are given in Table 3 andthe 3D hull model in Fig. 12. The arrangement is typical for thissize of naval combatant with 2 passageways, one at each side ofthe ship, running along the whole damage control deck. The shiphas: two main engine rooms (one for the diesel engines and onefor the gas turbine), separated by a reduction gear room and twoauxiliary machinery rooms (forward the GT room and aft of the DEroom). The hull is subdivided in 17 zones by 16 watertighttransverse bulkheads. Horizontal watertight boundaries areformed by four decks, namely main deck (1st deck), the bulkhead
Fig. 12. Frigate 3D hull model.Source: NAPA 2011.2.
Table 3Main particulars.
Length, waterline (m) 138.0Breadth, waterline (m) 15.85DWL (m) 4.90Depth (m) 9.40Displ. (end of life) (ton) 5435
deck (2nd deck), the 3rd deck, and the tanktop (4th deck). A totalof 495 different damage cases have been defined extendingdamages up to 6 zones.
The ship has a displacement of 4940 t at the full load conditionwithout the future growth margin and the vertical centre ofgravity is 6.45 m above baseline resulting to a GMcorr of 1.194 m.The ship fulfils at this condition all the intact and damagestability criteria of DDS-079. The 15%L damage length results to4-compartment damages for most cases for this ship. The high D/Tratio results to a substantial amount of reserved buoyancy bydesign.
In order to investigate the impact of the metacentric height onsurvivability, the attained survivability index using the probabil-istic damage stability quasi-static approach was calculated for twodifferent values, namely GM of 0.8 and 1.14 m. For the investiga-tion of the influence of the operational area, two differentscenarios were used. The first assuming P(Hs≤8 ft)¼0.8 andHs(0.99)¼4 m (East Med.) and a second one with P(Hs≤8 ft)¼0.56 and Hs(0.99)¼10 m (North Atlantic). A natural roll period of10 s, typical for combatants of this size was used in the calcula-tions. Various values of damping ratios were used ranging from0.01 to 0.03.
The formulas for the calculation of the probabilities of damagepi using Eq. (8) were applied to the sample ship and the results forthe one compartment damages are given in Table 4.
The calculations have shown that for the given arrangement,damage length and longitudinal distribution, 1 compartment casescontribute approximately 0.2 to the attained index, whereas 2,3 and 4 compartment cases contribute approximately 0.58, 0.18and 0.03 respectively (see Fig. 13). Therefore the design that fulfilsthe survivability criteria for all damage cases of flooding of up to3 compartments will have a probability of survival of at least 0.96.
Room02 1 8.4 14.4 0.061 0.104 0.043 0.0011Room03 1 14.4 20.4 0.104 0.148 0.043 0.0018Room04 1 20.4 29.4 0.148 0.213 0.065 0.0102Room05 1 29.4 37.8 0.213 0.274 0.061 0.0111Room06 1 37.8 48 0.274 0.348 0.074 0.0249Room07 1 48 53.4 0.348 0.387 0.039 0.0033Room08 1 53.4 58.8 0.387 0.426 0.039 0.0037Room09 1 58.8 69.6 0.426 0.504 0.078 0.0416Room10 1 69.6 77.4 0.504 0.561 0.057 0.0169Room11 1 77.4 86.4 0.561 0.626 0.065 0.0229Room12 1 86.4 91.2 0.626 0.661 0.035 0.0019Room13 1 91.2 100.2 0.661 0.726 0.065 0.0173Room14 1 100.2 109.8 0.726 0.796 0.070 0.0162Room15 1 109.8 121.8 0.796 0.883 0.087 0.0195Room16 1 121.8 130.8 0.883 0.948 0.065 0.0048Room17 1 130.8 138 0.948 1.000 0.052 0.0007
Fig. 13. Contributions of the various damage cases to the total index.
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 59
The results for the particular design considering up to6-compartment damage cases resulted to an attained index ofA¼0.95 for the Mediterranean scenario, using a metacentric
Fig. 14. Subdivision and survivability index for North Atlantic operation with GM 1.2 m.the web version of this article.)
Fig. 15. Floating position for
height of 0.8 m while for the same loading condition the attainedindex is reduced to A¼0.89 for the North Atlantic scenario.The ship at her design full loading condition (GMint¼1.194) has
(For interpretation of the references to colour in this figure, the reader is referred to
damage including Z4–9.
00
5
10
15
Fig. 16. Heel's time history for damage in zones Z4–9.
00 100 200 300 400 500 600
6.1
6.2
6.3
6.4
Fig. 17. Draught's time history for damage in zones Z4–9.
0 100 200 300 400 500 60000
5
10
15
20
Fig. 18. Heel's time history for damage in zones Z4–9 using compartmentsopenings.
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–6160
an attained index of A¼0.94 for the North Atlantic scenario. Thelocal survivability indices for this case are shown in Fig. 14. Thedamage case for which the ship has si¼1.0 are shown with greencolour, while the orange indicates values below 1.0. The red boxesindicate case where the ship is not going to survive. Using suchfigures the designer may identify potential weaknesses of thedesign, compare different designs on the bases of their surviva-bility index and integrate the methodology into a formalisedmulti-objective optimization procedure (Boulougouris andPapanikolaou, 2004).
The survivability of the mobility function can be calculatedusing Eq.(4), where j are all the main engine room compartments;in this case rooms 7, 8 and 9. This would result in a mobilitysurvivability index of Sf¼0.90 for the North Atlantic scenario at thedesign full load condition.
For those cases where the ship has a survivability index lessthan 1.0 and especially for those where soP(Hso8 ft) a morerefined investigation is necessary using the probabilistic dynamicflooding/capsizing approach. The damages may be defined both by
−
rooms flooded and open to sea, while internal openings areused for the progressive flooding−
damage holes modelled as openingsAn example investigation of the impact of the intermediatestages of flooding is shown in Fig. 15. The ship is subject to a 6-compartment asymmetrical damage extending from Zone 4 up to
Zone 9. Waves with height of 2.4 m and period equal to ship'snatural period (10 s) are assumed exciting the ship. In Fig. 16 theheel time history is shown assuming that the damaged compart-ments are open to sea. The relevant draught history is presented inFig. 17. From the results it is apparent that the ship will heel up to201 before she will stabilize at 10.41. If the compartments areassumed interconnected through their openings, then the resultsshow much higher max roll angles exceeding 201, as shown inFig. 18. The designer should examine carefully such results anddecide whether the ship should be considered as survivable insuch a case, or using additional measures (e.g. counter-flooding) toattempt to minimize the list of the ship.
9. Conclusions
The application of a risk-based approach to ship design requiresthe availability of (Papanikolaou, 2009b):
−
safety-performance prediction tools − adequate risk models and − an optimization platformThe authors have presented in the past the optimization plat-form of NTUA-SDL (Boulougouris and Papanikolaou, 2004). Thispaper supplements their previous work introducing a risk modelfor the probabilistic assessment of battle damages and a safety-performance prediction method for calculating the probability ofsurvival as well as maintaining vital functions of a naval ship. Thisintroduces the minimization of risk (and therefore the maximiza-tion of survivability) as an additional design objective in thedesign procedure materializing the RBD process.
The introduced method has been applied to a generic frigatedesign operating in specified seaway conditions and typical resultsof this study were presented and discussed. Probabilistic damagestability quasi-static derived survivability indices were used forthe attained survivability index assessment. Additionally, criticalcases were examined using flooding simulations that implementthe pressure-correction method. The software tool implementingthe proposed methodology is part of the design and optimizationtools suite developed by SDL-NTUA using the NAPA softwareplatform. Links to other numerical tools for the calculation of theresistance, the wave field around the ship, the seakeeping perfor-mance and the signature assessment software (e.g. RCS) are inplace. The suite allows the designer to start from initial
E. Boulougouris, A. Papanikolaou / Ocean Engineering 65 (2013) 49–61 61
requirements and develop optimal design solutions with respectto formulated assessment criteria.
In the next stage, the present methodology will be furtherdeveloped to enable the implementation of Monte Carlo typeanalysis for the assessment of the survivability index of parame-trically generated design alternatives. This will lead eventually toformal multi-objective optimizations. Other enhancements are theintegration of more refined hydrodynamic software tools, likenon-linear time domain simulation tools (such as CAPSIM) forbetter capturing the dynamic behaviour of the ship in extremeseaways in damaged conditions as the present NAPA time domaintool is limited to moderate sea states only.
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