SELECTED PROBLEMS OF MARITIME TRAFFIC RISK MODELLING.pdf
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Jakub Montewka
Aalto University, School of Science and Technology, Finland
Przemysław Krata
Gdynia Maritime University, Poland
Pentti Kujala
Aalto University, School of Science and Technology, Finland
SELECTED PROBLEMS OF MARITIME TRAFFIC RISK
MODELLING
Abstract
: The paper addresses selected problems of marine traffic risk modelling, in respect to
collision and grounding probability modelling. Two original models are presented, and a case
study regarding ships navigating in selected areas of Gulf of Finland in ice free conditions is
putting forward. Probability of vessel colliding is assessed by means of Minimum Distance To
Collision (MDTC) based model. The model defines in a novel way the collision zone, using
mathematical ship motion model, and recognizes traffic flow as non homogeneous process, unlike
other existing models. Calculations presented address waterways crossing between Helsinki and
Tallinn, where dense cross traffic during certain hours is observed. Risk profile for a certain
period of a day is presented.
For probability of grounding a new approach is proposed, which utilizes the gravity model, where
spatial interactions between objects in different locations are proportional to their respective
importance divided by their distance. A ship at a seaway and navigational obstructions may be
perceived as interacting objects and their repulsion may be modelled by a sort of gravity
formulation.
Keywords
: maritime risk, transportation, navigation, collision, grounding, modelling
1. INTRODUCTION
Maritime traffic risk modelling is a complex process, which takes into account several
aspects, integrating different scientific domains, usually being very remote one from another.
Risk analysis consists of predicting ship accident probability, which means collisions and
groundings. These depend on geographical location of analyzed area, traffic composition,
weather conditions and time of the day. Statistics revealed that these two main types of
accidents are caused mostly by human inappropriate actions, therefore knowledge about
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human behaviour during collision avoidance and grounding avoidance processes is
essential here.
Knowing the probability of an accident, one should assess the consequences of these.
Depending on a ship type involved in an accident, results may be different. In case of a
tanker as a potential outcome of an accident, one may suspect an oil spill, resulting in
environmental loss. In case of a passenger vessel facing an accident, the highest hazard
considered is loss of human lives.
This paper focuses of chosen aspects of marine traffic risk modelling, taking as example
marine traffic in the Gulf of Finland. Method of modelling risk of ship being collided and
being aground is presented, with emphasis put on tankers and passenger ferries. A new
geometrical model for collision frequency assessment, named the MDTC model is used
and a gravity based model for grounding probability calculation is utilized. Consequences
are expressed in costs to incur caused by an oil spill of given magnitude, being a result of a
ship accident.
Existing geometrical models for ship collision frequency prediction simulate marine
traffic as a stationary Poisson process, which not always holds truth. The analysis of AIS
data over the Gulf of Finland revealed that traffic fluctuates, and peak hours may be
defined, regarding both E-W (cargo ships, tankers) and N-S streams (RoPax ferries). These
peak hours affect the probability of collision, which changes over a day.
This paper presents the results of risk analysis carried out for scheduled traffic, taking
into account its non stationary nature. The results are then compared with results obtained
from another version of the MDTC model, which assumes maritime traffic as a stationary
process. The paper addresses only summer traffic, therefore influence of winter related
parameters on risk are not taken into account. This paper does not contain the detailed
description of models applied for risk analysis, as they are described in the literature cited.
Calculations were carried out for two chosen locations of the Gulf of Finland. One is a
junction of two busy waterways, between Helsinki and Tallinn, with RoPax ferries cross
traffic. Another spot is an approach to an oil terminal in Sköldvik, east to Helsinki.
2. MARINE TRAFFIC MODELLING
Presented analysis concerns maritime traffic in the selected areas of the Gulf of Finland.
Data regarding marine traffic concerns all ships above 300 tonnes gross, involved in
international voyages that need to be fitted with the transponder of Automatic
Identification (AIS), according to SOLAS Convention, Regulation 19 of Chapter V. The
analyzed data cover period from 01.06.2006 to 31.06.2006. To compute the traffic volume
in analyzed area two counting gates were established, as depicted in the Fig.1. In gate
number 3, E-W traffic entering the junction was recorded, whereas at gate 2, RoPax
vessels cruising between Helsinki and Tallinn were counted.
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Fig.1. Analyzed waterways junction, with counting gates and main traffic flows [Montewka et al., 2010]
According to the analysis of marine traffic, the following main groups of vessels were
considered: container carriers, tankers, general cargo vessels, ro-ro, cruise ships, and fast
ferries. Marine traffic in the area under analysis was assumed to consist of four main flows:
east, west, north, and south, while the north and south flows are assumed to contain
passenger vessels only (Fig.1). Each flow was modelled with the following input
parameters: overall number of vessels, type of vessels, number of vessels of a given type,
size of vessel of a given type, speed of vessels of a given type, course of vessel, and
position of vessel across the waterway. For modelling purposes most of these values were
approximated by continuous distribution or by histograms. The distribution of the features
being analysed was chosen according to the results of a chi-square test. Those which fitted
the best (obtained the highest value of a chi-square test) were selected as inputs to the
model. In some cases, if none of the available distributions fitted then recorded discrete
values were taken into the model, by random sampling.
Special attention was paid on tankers. Based on the recorded data, tanker traffic in the
Gulf of Finland was assumed to consist of two major types of tankers: crude oil tankers
(25%) and oil product tankers (70%), the remaining 5% includes chemical and gas tankers
which were not considered in the analysis presented. Although tanker traffic is season
dependent (Montewka, Krata, Kujala, 2010), this paper addresses only summer traffic. The
main dimensions of tankers (their length, breadth and maximum design draught) were
estimated with the use of triangle distributions, and the minimum, maximum and mean
values adopted are presented in Figure 2. The triangle distributions were the ones that
fitted best the observed discrete data.
25
Logistic(12.7; 1.2)
0,35
20
0,3
0,25
15
0,2
10
0,15
0,1
5
0,05
0
0
0 2 4 6 8 0 2 4 6 8
Velocity [kn]
mode
max
min
Gas
Crude oil
Oil products
Chemical
Fig.2. Distributions of the main parameters of tankers navigating in the Gulf of Finland
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Velocity of the tankers was modelled by a Logistic distribution, which fitted the best the
recorded values (Figure 2), and follows the formula:
⎛
⎞
⎛ −
x
α
⎞
2
⎜
⎝
⎟
⎠
sec
h
0
.
⎜
⎝
⎟
⎠
β
v
=
f
(
x
)
=
,
( 1)
4
β
where
sech
is a hyperbolic secant function,
x
is a random variable (velocity),
α
is a location
parameter and equals 12.7, and
β
is a scale parameter which equals 1.2. The courses of the
vessels were modelled by either distributions or a sampling method from the recorded AIS
data. Another important factor, that was neglected in previous geometrical models used for
collision probability assessment was daily variations of marine traffic. As the marine
traffic in the analyzed area is dominated by RoPax vessels, which follow their schedules,
modelling this kind of traffic flow by means of a stationary Poisson process may be
questionable. Daily variations in north- and southbound RoPax traffic between Helsinki
and Tallinn as well as in the east- and westbound traffic of cargo ships are depicted in
figures 3 and 4.
Monthly intensity of northbound traffic
Monthly intensity of southbound traffic
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
Time of the day [hrs]
Time of the day [hrs]
Fig.3. The marine traffic intensity of N-S flow, recorded between Helsinki and Tallinn
Monthly intensity of westbound traffic
Monthly intensity of eastbound traffic
260
240
240
220
220
200
200
180
180
160
160
140
140
120
120
100
100
80
80
Time of the day [hrs]
Time of the day [hrs]
Fig.4. The marine traffic intensity of E-W flow, recorded between Helsinki and Tallinn
From the data presented, certain peaks can be recognized, both for the N-S and the E-W
flows. It may be noted that time of the day for peaks for N-S traffic generally differ from
peaks for E-W traffic. And usually rush hours for N-S traffic do not correspond the rush
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hours for E-W flow. Thus modelling the marine traffic flow in analyzed location as a
constant number is burden with high uncertainty, and may lead to the underestimation of
the results (a number of collision candidates and risk of collision).
500
400
300
200
100
0
1
3
5
7
9
11
13
15
17
19
21
Time of the day [hrs]
Time dependent process
23
Stationary process
Fig.5. A number of collision candidates obtained from the MDTC model for constant and time varying traffic
flows
The comparison of results obtained from MDTC model, expressed as a number of
collision candidates, is depicted in Fig. 5. During experiment, at first traffic intensity was
assumed to be stationary, and number of collision a candidate was calculated, which was
not depending on time of the day. Secondly traffic intensity was modelled according to the
AIS data recorded, and number of collision candidates calculated depended significantly
on time of the day.
In Fig.5 substantial differences can be recognized, especially during peak hours, where
the number of collision candidates is almost three times higher in comparison with results
obtained from the model with constant intensity. This obviously translates directly into risk
level.
3. PROBABILITY OF ACCIDENT MODELLING
Probability of ship colliding and grounding was modelled by means of two original
models, which have been developed by the authors. A model which assesses the
probability of collision is called the MDTC model and was described in detail in
(Montewka et al., 2010) and after improvements in (Montewka J, Ståhlberg K et al., 2010).
A grounding model is a gravity model, which considers a ship and surrounding her
obstacles the imaginary masses which affect each other, an initial description of the model
was given in (Krata, 2007).
Due to the existing detailed description of the MDTC model in the references, only the
main idea is presented in this paper. However the description of the gravity model
presented here is lacking in the literature, therefore more space will be devoted to it.
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