International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 5

Number 3

September 2011

365

1 INTRODUCTION

The MDTC (Minimum Distance To Collision) mod-

el for ship-ship collision probability estimation is a

geometrical model, with a detailed description given

in the following papers: (Montewka et al. 2010),

(Montewka et al. 2011). In order to provide the

probability of an accident, the model uses the com-

monly adopted approach, which combines a fre-

quency of ship-ship meeting situations given an as-

sumption of blind navigation, and a causation factor,

which quantifies the proportion of cases in which

such a meeting ends up as a collision, due to human

or technical reasons.

The causation factor is a sensitive part of a mod-

el, very much location dependent, thus it is not justi-

fied to use the same value for the different models

(Gluver and Olsen 1998). Applying a causation

probability value derived from a study in another sea

area may save some effort, but then the actual condi-

tions are not addressed at all (Hanninen and Kujala

2009).

Two approaches can be recognized in the litera-

ture in order to estimate the causation factor. The

simplified approach is based on a historical data,

where the causation factor is assumed a ratio be-

tween the registered number of accidents and the es-

timated number of collision candidates (Fujii and

Siobara 1971), (MacDuff 1974), (Inoue and Kawase

2007).

A second approach is more sophisticated, based

on the concept of either event tree (Pedersen 1995),

(Martins and Maturana 2010) or Bayesian Networks

(DNV 2003), (Hanninen and Kujala 2009). This way

of modelling is undoubtedly more time consuming

than the first approach, however it allows getting an

insight into the chain of events leading to an acci-

dent instead of providing just a number.

In order to determine the causation factor for the

MDTC model for three different ship-ship encoun-

tering types (crossing, head-on and overtaking), we

based our study on a modified first approach, which

is relatively quick and straightforward thus robust.

We perform two stage analysis, which combines the

statistical data on maritime accidents and an analysis

of near-collisions based on recorded AIS data.

The causation factor is being defined here as a ra-

tio between the modelled number of collision candi-

dates and the actual number of accidents. However

the available statistics on maritime accidents are not

very detailed, and the type of an accident is not in-

cluded there. Thus there is a need to find a proxy be-

tween a recorded number of accidents and a mod-

elled number of collision candidates (Heinrich et al.

1980), (Inoue and Kawase 2007), (Gucma and

Marcjan 2010).

A Method for Assessing a Causation Factor for

a Geometrical MDTC Model for Ship-Ship

Collision Probability Estimation

J. Montewka*, F. Goerlandt, H. Lammi & P. Kujala

*Aalto University, School of Engineering, Finland; Maritime University of Szczecin, Poland

Aalto University, School of Engineering, Finland

ABSTRACT: In this paper a comparative method for assessing a causation factor for a geometrical model for

ship-ship collision probability estimation is introduced. The results obtained from the model are compared

with the results of an analysis of near-collisions based on recorded AIS data and then with the historical data

on maritime accidents in the Gulf of Finland.

The causation factor is obtained for three different meeting types, for a chosen location and prevailing traffic

conditions there.

366

It seems justified to analyze the safety of naviga-

tion on the basis of the numbers of both accidents

and near-miss situations. Such a combination of

analyses may better reflect the collision hazard, as

pointed out by (Inoue et al. 2004) and (Inoue and

Kawase 2007).

In air transportation there has been a tendency to

seek out proxy for aviation safety. One commonly

used measure is that of the ”air-miss”, often called a

”near-miss”. According to (Button and Drexler

2006) ”a near-miss involves an aircraft intruding

upon a predetermined safety zone or envelope

around another aircraft”. The reporting procedures

of near-miss in aviation are well founded providing

valuable statistics. In the maritime sector similar

procedures are missing, thus the near-miss can be

detected only by analysis of recorded data and back

propagation of recorded events.

Following this idea, this paper proposes also a

methodology to evaluate the occurrence of near

ship-ship collisions in an open sea area, based on the

AIS data. The method for near-collisions analysis

presented in this work is rooted in a well-established

concept of a ship domain proposed by (Fujii and

Tanaka 1971). An overview of the near collision de-

tection method is then given and applied to the

summer traffic in the Gulf of Finland.

Finally, we compare the results obtained from the

MDTC model, expressed as the number of ”collision

candidates” with the number of near-collisions and

the number of accidents recorded in the chosen area

of the Gulf of Finland. This approach allows us to

quantify the number of modelled ”collision candi-

dates”, with blind navigation assumption behind, to

the number of cases that ended up as close encoun-

ters, where collision evasive actions were taken.

Such quantification is carried out for three major

types of meeting scenario (crossing, head-on, over-

taking). By combining this accurate enough data

with an average annual number of accidents that

happened (which are random, and almost non pre-

dictable), the causation factor for the MDTC model

is obtained.

2 RESEARCH MODEL

2.1 Accident analysis

The annual number of ship-ship collisions in the an-

alyzed location of the Gulf of Finland (the water-

ways junction between Helsinki and Tallinn) is ob-

tained from HELCOM database, that covers a time

period between 1987 and 2007 (Pettersson et al.

2010). During this time, three accidents of this type

took place. Two of them happened during summer

time, and one was related to the ice conditions,

which are out of scope of the analysis presented in

this paper.

According to the aforementioned statistics there

was, on average, one summer collision per ten years.

This assumption is simplified, as the rate of collision

occurence is random, as the first collision happened

in 1996, second in 2001 and between the years 2001

and 2007 no summer collision happened in the area

of investigation. Notwithstanding, we assume that

the annual ship-ship collision frequency in the ana-

lyzed area equals 0.1.

Unfortunately, the database provided by HEL-

COM does not contain any information regarding

type of ship-ship encounter, at which the accident

took place. Thus it is not feasible to compare a mod-

elled number of collision candidates in given en-

counter type (crossing, head-on, overtaking) with an

appropriate number of the accidents. At this point

the results of near- collisions analysis are utilized

and considered a proxy between a model and the

recorded accident data.

Figure 1: The ship domain applied in the near-collision analy-

sis, with the following axes: a = 1.6LOA, b = 4LOA (Wang et

al. 2009)

2.2 Near-collisions analysis

The near-collision analysis applied in this paper is

based on a concept of a ship domain, which accord-

ing to definition given by (Goodwin 1975), is the ar-

ea around the vessel which the navigator would like

to keep free of other vessels, for safety reasons.

Since the first introduction of the ship domain

concept by (Fujii and Tanaka 1971), various re-

searchers have attempted to quantify the size of this

domain. An overwiev of the different proposed do-

mains is given in (Wang et al. 2009). Even though

the ship domain is a well established concept, certain

problems with the application can be identified as

pointed out by (Jingsong et al. 1993). Domains can

be classified by their shape: circular, elliptical and

polygonal domains. A distinction can also be made

between fuzzy domains and crisp domains. Fuzzy

domains such as that proposed by (Pietrzykowski

2008) and (Wang 2010) seem preferable in terms of

367

safety analysis of marine traffic, but are at present

still under development. Crisp domains use a simple

classification of a situation between safe or unsafe,

which evidently is a simplification. Moreover, the

sizes of the domains proposed in the literature vary

quite significantly (Wang et al. 2009).

In this paper, the smallest ship domain found in

the literature, by (Fujii and Tanaka 1971), is applied.

This is justifiable, since the aim of the method pro-

posed in this paper is finding the most critical en-

counters between ships. This domain is defined as an

ellipse with the major axis along the ship’s length

(LOA)and the minor axis perpendicular to the ship’s

beam, as illustrated in Figure 1. The half-length of

the major axis is taken as 4LOA while the half-

length of the minor axis is taken as 1.6LOA. A

number of comments should be made in the use of

this domain:

− the domain is symmetric, which implies that the

possible influence of the COLREGs is not taken

into account;

− another consequence of this symmetry is the fact

that passing behind the stern is considered as

dangerous as passing in front of the bow;

− in the meeting between ships, the largest ship has

the largest domain; this means that for the largest

vessel, the situation is classified as dangerous,

whereas for the smallest vessel, the situation may

still be evaluated as safe;

− the domain is affected by ship length only, neither

ship type nor hydrometeorological conditions are

included in the analysis.

However the latter can be supported by the recent

research, which revealed that the ship domain has a

relatively low correlation with the sea state and wind

force (Kao et al. 2007).

In this section, a brief description of analysis of

AIS data in order to estimate a number of near-

collisions in the selected area of the Gulf of Finland

is given. Recorded AIS data consists of millions of

data points, containing static and dynamic infor-

mation regarding a ship. In order to analyze the mar-

itime traffic in the GOF, this data need to be grouped

into routes. Routes are defined here as a set of trajec-

tories between a departure and arrival harbor as in-

troduced by (Goerlandt and Kujala 2011). The AIS

data is first gathered per ship, based on the MMSI

number. After sorting this data chronologically, the

data per ship is further split up to form individual

ship trajectories, using a methodology described by

(Aarsther and Moan 2009). These trajectories are

then further processed and grouped per route. The

sample rate of these vessel positions in the trajecto-

ries is about 5 minutes on average. In order to enable

a comparison between vessel positions at exactly the

same time instant, the trajectory data is artificially

enhanced to contain data for each second. The ex-

trapolation for the vessel position is performed using

an algorithm suitable for data in the WGS-84 refer-

ence frame following (Vincenty 1975). The ship

speed is linearly interpolated between known values.

It should also be noted that certain vessel types are

not taken into account into the analysis, like tugs are

left out of the analyzed database. This is done be-

cause these vessels are meant to operate in a close

vicinity of merchant vessels. The near collision de-

tection algorithm is shown in Figure 2.

The basic idea is to scan the database for events

where the ship contour of one vessel (i.e. the ship

area in terms of ship length and width) enters the

ship domain of another vessel. If the domain is vio-

lated, the event is labeled as a near collision and rel-

evant details such as time of occurrence, location,

encounter type, ship types and ship flags are stored

for further analysis. The near collision detection al-

gorithm is encoded in MATLAB.

Figure 2: Near collision detection algorithm