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A model for risk analysis of RoPax ships - the Gulf of Finland case

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A model for risk analysis of RoPax ships - the Gulf of Finland case
Jakub Montewka
a
∗
, S¨oren Ehlers
b
, Floris Goerland
a
, Tomasz Hinz
c
, PenttiKujala
aa
Aalto University, Department of Applied Mechanics, Marine Technology, Espoo, Finland
b
Norwegian University of Science and Technology, Department of Marine Technology,Trondheim, Norway
c
Waterborne Transport Innovation, Lapino, Poland
Abstract:
The maritime traﬃc is increasing constantly, in terms of number and size of ships. This,on one hand meets the growing demands of the society but on another pose certain risks, both onthe environment and the aforementioned society. Therefore a holistic approach is required in order toestimate these dynamic risks and keep them under control. As the risk is perceived as a combinationof the probability of an accident and its consequences a proper estimation of these two is of highimportance. Therefore this paper introduces a novel approach for estimating the consequences of anopen sea collision between two ships, with the attention on a RoPax ship being considered a struckship. Presented model utilizes the Bayesian network and takes into account composition of maritimetraﬃc in the analysed sea area, ship hydrodynamics, stability, crash-worthiness and collision dynamics.Moreover the accident response is considered with respect to the locations of salvage and rescue ships,evacuation time as well as weather conditions and time of the day at which an accident is probable tohappen.Finally, the new algorithm is combined with an in-house build model estimating the probability of ship-ship collision and the risk expressed in the number of fatalities is obtained and compared withthe social risk acceptance criteria.
Keywords:
Maritime traﬃc, risk, collision consequences, BBN, RoPax
1. INTRODUCTION
Maritime traﬃc poses various risks in terms of fatalities, environmental pollution, or loss of property.In particular, accidents where ships carrying passengers, like RoPax, are involved may pose a high riskwith respect to human casualties. Therefore a number of studies on improvements to RoPax safetyhave been made; see, for example, [1, 2, 3, 4, 5, 6]. However those studies address ship design andless attention has been paid to a holistic risk-based approach to the operation of ships. Although ageneral framework for this purpose is provided by the International Maritime Organisation - see [7]- few researchers have studied this topic in a holistic manner; see [8, 9, 10, 11, 12, 13]. However, thealgorithms presented inhere are generalised and mostly based on accident statistics. Moreover, mostof these models utilise the concept of an event- or fault tree allowing one-way inference; see [9, 11].Thus these models allow measuring the inﬂuence of factors aﬀecting the risk, however it is diﬃcult,but deﬁning the conﬁgurations of the factors leading to risk reduction is not possible.Therefore this paper develops a model that evaluates the operational risk to ships in a holistic andproactive way. This in turn, will allow an insight into the process of risk evolution, as well as deﬁningthe most signiﬁcant and sensitive variables that contribute the most to the risk in order to mitigatethe risk in an optimal way. The model focuses on a selected type of RoPax ship which is considereda characteristic ship for the location being analysed, which is the Gulf of Finland. However, themodular nature of the model allows continuous improvement and adaptation to various locations andconditions. The model is based on a Bayesian Belief Network (BBN) and utilises series of logicallyconnected events, called nodes, among which the relations are given in a probabilistic way, with theprior knowledge obtained in the course of numerical experiments, observation, analysis, and simula-tions. The model assumes that a struck RoPax will be lost if either of two accident scenarios takes
Figure 1: A block diagram of the model for the evaluation of the consequences of a RoPax accident.place: 1- the inner hull of the RoPax that is struck is breached and consequent ﬂooding is experienced;this can result further in the loss of a ship; 2- the RoPax that is struck has no signiﬁcant hull damage;however, the ship is disabled and set adrift, thus experiencing signiﬁcant rolling as a result of waveand wind action, which can result further in the ship capsizing. In the ﬁrst case the critical collisionparameters, such as the striking speed and angle for the given mass ratios, are obtained with theuse of ﬁnite element simulations. In the second case the probability of the disabled ship capsizing iscalculated with the use of the six-degree-of-freedom ship motion model and Monte Carlo simulations.Finally, the model yields the probability of the loss of a RoPax that has been struck, given an opensea collision. This is combined with the probability of the collision, obtained from the dynamic traﬃcsimulator; thus the risk is obtained and presented in the form of an F-N diagram.
2. MODELS AND METHODS
The paper introduces a model ﬁtting called the Formal Safety Assessment (FSA), addressing its secondstep, called risk analysis, see [7]. The model consists of four major parts: a part estimating the collisionrelevant parameters; a part evaluating the probability of a ship capsizing as a result of ﬂooding or deadship conditions (DSC); a part governing the response to an accident, and, ﬁnally, a part comprisingthe results of the model. The relations between these parts, as well as the model architecture, aredepicted in Figure 1.The model utilises a BBN developed by means of an available software package called GeNIe, see [14].The BBN contains continuous nodes with distributions obtained either by means of an experimentor a literature survey. In order to determine which factors are essential and thus should be modelledwith greater caution, a sensitivity analysis is carried out at the initial stage of the development of themodel, see [15]. Therefore the most sensitive nodes of the model refer to the weather conditions, theprobability of a ship sinking as a result of ﬂooding, the parameters describing a collision scenario (massratio, collision angle, collision speed), and the probability of the ship capsizing in DSC. These weretailored to the speciﬁc ship type and location by means of the experiments and methods described inthe following sections. The distributions for the remaining nodes, with a lower impact on the outcomeof the model, are based on the generic data available in the literature.
2.1. Collision parameters
One of the inputs for the model is maritime traﬃc data in terms of traﬃc composition, ship types,ship sizes, collision angles, collision speed, and the time of day of a potential collision. These are
derived from a dynamic marine traﬃc simulation model, which takes the inputs from the AutomaticIdentiﬁcation System (AIS), augmented with harbour statistics concerning the cargo types that aretraded, see [16]. Additionally, the collision speed and angle are modelled using a two-step procedure,where in the ﬁrst step the initial data from the maritime traﬃc simulator are provided, while inthe second these data are considered the input values for the statistical models providing the actualcollision parameters and their distributions.There are several diﬀerent models estimating the collision speed and collision angle; see [17]. For thepurposes of this study, the model introduced by L¨utzen, see [18], is adopted. This approach takes intoaccount the changes in the ships initial speeds and courses resulting from the evasive actions taken.Thus the following two assumptions are made: 1- the velocity of a striking ship
V
A
follows a uniformdistribution for velocities between zero and 75 per cent of her initial speed, then decreases triangularlyto zero; 2 - the velocity of a struck ship
V
B
is approximated by a triangular distribution with a mostlikely value equal to zero and a maximum value equal to her initial speed; the initial values of
V
A
and
V
B
are obtained from the dynamic traﬃc simulator; assumption 3 - the collision angle is uniformlydistributed between 10 and 170 degrees.The distribution of the actual collision speed is estimated by means of the dynamic marine traﬃcsimulator, following the ﬁve-step random sampling Monte Carlo procedure: step 1 - randomly samplethe speed of a striking ship, create the distribution around it and random sample again from thedistribution (
V
A
); step 2 - in the same way sample the speed of a struck ship (
V
B
); step 3 - randomlysample the collision angle from the uniform distribution; step 4 - calculate the relative speed atwhich ship A hits ship B, (
V
(
A,B
)
); step 5 - calculate a normal to the hull of struck ship
B
, whichis considered the collision speed,
V
(
A,B
)
⊥
. For each collision encounter obtained from the dynamictraﬃc simulator, the above procedure was repeated to obtain a set of distributions of a collision speedgiven a collision angle. These collision speed values are ordered according to the collision angle andare divided into three groups: 10-45 degrees, 45-135 degrees and 135-170 degrees. Finally, threecontinuous distributions for the three groups of collision angles were obtained and embedded into theBBN, yielding the distribution of collision speeds given the collision angle, see also Figure 5.
2.2. The probability of an inner hull rupture
To determine the probability of a rupture of the inner hull of a RoPax given a collision, two parametersare considered as input variables: the collision speed and the ratio of the ships’ masses. If the collisionspeed for a given encounter exceeds the critical speed, then the hull of a struck ship is breached. Thecritical collision speed, given the collision angle, is determined using the concept of collision energy,which is evaluated for the reference RoPax considered to be a struck ship, the given collision encounters,the collision angle, and the location along the hull of the struck ship. For the main characteristicsof the struck ship see Table 1. The following sizes of striking ship are considered with respect to thestruck RoPax: a similar size (mass ratio 1.0), a ship smaller by 25 per cent (mass ratio 1.33), a shiplarger by 25 per cent (mass ratio 0.8), and a ship larger by 70 per cent (mass ratio 0.6). Thereforethe mass ratios that are analysed cover almost 80 per cent of maritime traﬃc in the Gulf of Finland.The remaining share belongs mostly to ratios higher than 1.3, which can be assumed to be less criticalconcerning hull rupture for the usual blunt bow shapes, as well as a certain percentage of ratios lowerthan 0.6, which are not taken into account.The available energy for structural deformations is obtained according to the calculation model intro-duced in [19]. This model estimates the dynamics of a ship collision and the share of energy availablefor ship motions and structural deformations. As a result of the combination of this dynamic sim-ulation procedure and the non-linear ﬁnite element method a good estimation of structural damagein various collision scenarios with oblique angles and varying eccentricities of the contact point canbe achieved. For the purpose of collision simulations the solver LS-DYNA version 971 is used. TheANSYS parametric design language is used to build the ﬁnite element model of the reference RoPaxvessel. A three-dimensional model is built between two transverse bulkheads spaced at 26.25 m apart
- see Figure 2 - and the translational degrees of freedom are restricted in the plane of the bulkheadlocations, whereas the remaining edges are free. The structure is modelled using four nodded, quadri-lateral Belytschko-Lin-Tsay shell elements with ﬁve integration points through their thickness. Thecharacteristic element length in the contact region is 50 mm in order to account for non-linear struc-tural deformations, such as buckling and folding. The element length-dependent material relation andfailure criterion is utilised for the simulations, see [20]. Crash worthiness simulations employing thismaterial model have been found to be suﬃciently accurate compared to large-scale experiments; see[21]. Standard LS-DYNA hourglass control and automatic single surface contact (friction coeﬃcientof 0.3) is used for the simulations. Moreover, the collision simulations are displacement-controlled.The rigid bow is moved into the side structure of the ship in a quasi-static fashion. Hence, this ap-proach results in the maximum energy absorption of the side structure alone, which is needed for acomparison and can be considered conservative and therefore suitable for fast prediction.As a result, the relative energy available for structural deformations as a function of the longitudinalstriking location is obtained for a mass ratio of 1.0; see Figure 3 and then scaled to account for theremaining mass ratios. Finally the critical striking speeds for a given mass ratio, striking angle, andstriking location along the hull of the struck ship, causing an inner hull breach, are evaluated.Table 1: The characteristics of the RoPax vessel that was analysed.
Length Breadth Draught Displacement[m] [m] [m] [t]
188.3 28.7 6.0 19610.0Figure 2: FEM model and vertical striking locations.Figure 3: Relative available deformation energy versus relative striking location and striking angle.
2.3. The probability of a ship capsizing as a result of ﬂooding while in damagedcondition
As a result of a ship-ship collision, where the collision speed exceeds the threshold for breaching theinner hull, the ingress of water can be expected; however, it does not always lead to catastrophicﬂooding. The model assumes that ﬂooding contributing to the loss of the ship occurs if the wave ishigher than a critical height and at least the main car deck is ﬂooded. To determine the probability of the ship loss resulting from ﬂooding the concept of a ”capsize band” is utilised. The band is a functionof wave height and ship stability, and within the band a transition between two states, named ”safe”and ”unsafe”, takes place, see [2]. The band begins at a wave height that does not cause the shipto capsize (
P
capsize
= 0) and ends at the wave height where the loss of the ship is always expected(
P
capsize
= 1). The capsize boundaries are symmetrical around the value of the critical wave height(CWH), which corresponds to
P
capsize
= 0
.
5. For the purpose of this study four damage stabilityconditions of a RoPax corresponding to the four values of the CWH are assumed; these are 5.5 m,3.5 m, 2.5 m, and 2.0 m, with appropriate bandwidths around them; see [2]. Therefore the weatherconditions are categorised into three groups, called the instances of a variable
weather
:
good
,
moderate
,and
bad
, where
moderate
corresponds to the capsize band,
good
means no capsizing at all, and
bad
represents sea conditions in which the ship will always capsize if the car deck is ﬂooded. Dependingon the stability of a ship thus the CWH these instances take diﬀerent values, see Table 2. Then theprobabilities of the occurrence of these instances for each CWH are calculated on the basis of thewave data for the Gulf of Finland, see [22]. Finally, each instance is modelled by means of a uniformdistribution, where the limits correspond to the probabilities of the occurrence of a given wave height,see Table 3.The damage stability conditions analysed in this paper consider a RoPax experiencing ﬂooding of the main car deck and two of the compartments beneath. The conditional probability of such hugeconsequences of a collision (
damage
−
extent
−
significant
) is estimated by taking into account themass ratio of the ships colliding and the speed and angle of the collision, this yields 0.2, versus 0.16derived from the historical data, see [4]. Additionally, the time taken to capsize as a result of ﬂoodingis based on the results of numerical simulations, see [6].Finally, the mean value of the probability of a RoPax capsizing, given the collision and resultingﬂooding yields 5
.
40
×
10
−
3
.Table 2: The capsize bands applied in the model.
CWH Weather[m]
good moderate bad
[m] [m] [m]
2.0
<
1.3 1.3-2.8
>
2.82.5
<
1.5 1.5-3.4
>
3.43.5
<
2.0 2.0-4.8
>
4.85.5
<
3.5 3.5-7.2
>
7.2Table 3: The prior probabilities for the variable
weather
.
Variable instance Variable values Boundaries of [m] the distribution
Good 0 - 3.5 0.54 - 0.92Moderate 1.3 - 7.2 0.08 - 0.29Bad 2.8 - 7.2 0.00 - 0.10

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