Ocean Engineering 235 (2021) 109396

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Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng

A method for risk analysis of ship collisions with stationary infrastructure

using AIS data and a ship manoeuvring simulator
Axel Hörteborn a, b, *, Jonas W. Ringsberg b
a
SSPA Sweden AB, SE-400 22, Gothenburg, Sweden
b
Chalmers University of Technology, Department of Mechanics and Maritime Sciences, Division of Marine Technology, SE-412 96, Gothenburg, Sweden

A R T I C L E I N F O A B S T R A C T

Keywords: The study presents a methodology that uses AIS data and a ship manoeuvring simulator to simulate and analyse
AIS analysis marine traffic schemes with regard to risks for accidents. An event identification method is presented, which is
Allision energy needed for the accident scenario part of the methodology. This is based on AIS data, where the Great Belt VTS
Event identification
area was used to verify the methodology. Three events that could result in ship-bridge allisions were modelled
Ship-bridge allision
Ship grounding
and simulated in the simulator: drifting ship, sharp turning ship and miss of turning point. The Monte Carlo
Ship manoeuvring simulator method was used to perform large number of simulator runs, including a parameter sensitivity analysis. The
probability of a ship allision against the Great Belt Bridge was calculated to be 0.007. Analysis of the ship-bridge
allision cases was shown to be dominated by the event drifting ship. This event has a relatively low kinetic energy
at the impact, and the expected allision energy for a 1,000-year allision corresponds to a 178 m tanker with
57,870 DWT and ship speed 14.6 knots. Finally, this study presents a mitigation analysis, which shows how the
probability of allisions can be reduced by reducing the ship speed or altering the traffic separation scheme.

1. Introduction where NAl is the number of allisions, N is the number of ships and Pc is
the causation factor. There is limited guidance in Eurocode 1 on how the
The advancement in bridge building engineering during the 20th causation factor should be determined. Pedersen (1995, 2000) proposed
century created an opportunity to build large bridges that span over that it can be estimated using the number of accidents (or allisions for
wide waterways with intensive ship traffic. Risk analysis was used as the ship-bridge contacts) divided by the number of ship passages. Since this
method to ensure that the bridge design and waterway traffic fulfilled approach relies on the number of reported accidents and traffic statistics
expected safety standards. Despite this, 34 major bridge collapses in the area of interest, the accuracy of the value of the calculated
occurred in the period from 1960 to 2007 that were caused by ship- causation factor depends on these data. Hassel et al. (2011) and Psarros
bridge allisions (def.: ship collision with a bridge), which resulted in et al. (2010) found that only approximately 50 percent of all accidents
the loss of more than 340 lives (AASHTO, 2009). In addition to envi­ are reported in accident statistics databases, hence, the causation factor
ronmental and service loads that form the basis of the strength design of is underestimated (and, thereby, the probability of accidents).
a bridge spanning over a waterway, the accidental probability of various This study presents a new methodology that handles the shortcom­
hazardous events and accidental loads must also be considered. ings in the determination of the causation factor in the risk analysis. It
In Europe, the norms and standards for all building codes are uses the approach proposed by Hollnagel et al. (2006) to identify sce­
described in the Eurocode. In Eurocode 1, general equations are pro­ narios that lead to accidents, together with AIS data, to calculate the
posed for the calculation of accidental loads to be used in the design of probability of ship collisions with fixed infrastructure; this approach is
bridges (CEN, 2006). For ship-bridge allisions, these equations are based applied in the study as ship-bridge allision. Hollnagel et al. (2006)
on Eq. (1) with reference to the research presented by Fujii (1983) and proposed that there are different “layers” leading to an accident that
Macduff (1974): should be assessed: root cause, event and the accident itself. For
NAl = N × PC (1) example, an officer on watch falls asleep [root cause], the ship continues
past a turning point [event] and ultimately grounds [accident]. The

* Corresponding author. SSPA Sweden AB, SE-400 22, Gothenburg, Sweden.

E-mail address: Axel.Horteborn@sspa.se (A. Hörteborn).

https://doi.org/10.1016/j.oceaneng.2021.109396
Received 22 October 2020; Received in revised form 11 June 2021; Accepted 25 June 2021
Available online 3 July 2021
0029-8018/© 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

availability of AIS data in combination with the layer approach is the presents the overall methodology, including a brief description of the
key issue in the methodology presented in this study. ship manoeuvre simulator. Chapter 3 introduces the simulation sce­
Fujii (1983) and Macduff (1974) pioneered and established the basic narios in the study, which have been defined for verification and
theory for the current research field. At that time, AIS data were not demonstration purposes of the methodology. The event statistics used in
available. The introduction and availability of AIS recordings have, ac­ these scenarios are presented in Chapter 4. A presentation of the simu­
cording to Svanberg et al. (2019), resulted in new possibilities to lation setup in the ship manoeuvre simulator are presented in Chapter 5
enhance the accuracy in maritime risk assessments. AIS data are, together with the case study area, followed by results and discussions of
therefore, used in this study for two purposes: to represent the real traffic the analyses in Chapter 6. The conclusions are presented in Chapter 7.
statistics of ships passing a waterway; and to benefit from reverse en­
gineering, where advanced numerical simulations are carried out to 2. Methodology
represent failure event statistics that are more valid compared to what
has been reported (i.e. non-reported events and accidents can be The methodology in the study integrates modern simulation and
captured and replicated). analysis tools to ensure safe and robust designs when new bridges that
Computer-based simulation models have been used in the maritime span over waterways are built. It should be noted that it can also be used
field for decades. One example is Källström and Ramzan (1985), who to assess existing bridges if they fulfil today’s design and safety criteria,
used a combination of simulation models and model tests to install the or if mitigation actions need to be activated. This is justified since the
world’s first commercial Tension Leg Platform. Nowadays, there are majority of the bridges that exist were built several decades ago. They
various types of maritime simulation models and software for different were designed based on the marine traffic that was present at that time,
purposes. One simulation model that includes the [event] failure is the considering an extrapolation of its increase and the ideas of which ships
Maritime Transportation System (MTS) model. This model handles the that would be built in the future. It is likely that the assumptions that
ships’ temporospatial positions in a time-domain simulation, but the formed the basis for safety factors in the bridge design are not aligned
hydrodynamic forces are not calculated, making it relatively fast and with today’s marine traffic situation and sizes of ships. One similar
straightforward to use. This type of simulator was used by Ulusçu et al. example where the design criteria had become obsolete is the design of
(2009), who studied the risk of accident in the Strait of Istanbul. van the twin towers of the World Trade Centre in New York (USA) and the
Dorp and Merrick (2011) proposed using the MTS model for risk as­ attack they were subjected to on September 11, 2001. The two towers
sessments in coastal areas. In this model, the traffic was simulated on were designed and constructed in the 1960s to withstand an airplane
routes obtained from AIS data, and the ship failures and errors in the crash. However, 40 years later, both the size of the aircrafts and the
model were simulated based on expert opinions. Goerlandt and Kujala amount of fuel they carry had increased significantly more than ex­
(2011) continued this research and implemented the DMTS model. This pected in the scenarios they were designed to withstand (El-Naby et al.,
simulator is also based on AIS data, but it addresses the meeting situa­ 2014).
tions differently. Goerlandt and Kujala (2011) used a Monte Carlo The methodology in this study has three major parts: collection of
method to estimate the risk of collision and grounding in the Gulf of AIS data, analysis of AIS data for event definition and modelling, and
Finland. Rasmussen et al. (2012) used the ShipRisk software to quantify modelling and simulation of events in a ship manoeuvre simulator. The
the risk to ship traffic in the Fehmarnbelt fixed link project. This soft­ AIS data are used to collect both event and general traffic statistics.
ware is a mixture of the models by Pedersen (1995) and an MTS simu­ Based on the event statistics, different event models are proposed to be
lator. In Rasmussen et al. (2012), the probability of human error, loss of used as input to the simulator, where the evolvement of events is
propulsion, and steering machine failure were analysed. simulated and analysed. It should be noted that one advantage of using a
The purpose of the study is to present new methodology using AIS ship manoeuvre simulator is that not all of the events that are introduced
data and a ship manoeuvring simulator to calculate the accident prob­ or triggered actually lead to an accident. The simulator can thus help us
abilities in marine traffic near bridges spanning over wide waterways. to understand why some events did not result in an accident. It can be
The methodology is verified in a case study on grounding accidents. Its used in investigations as forensic analysis of accidents that actually
wider applicability is presented in a demonstration study where the happened, or it can be used to simulate and analyse the consequence of
probability of ship-bridge allisions is calculated. With the proposed mitigation actions. A schematic of the methodology is shown in Fig. 1;
methodology, it can be numerically shown which ships and traffic sit­ see Chapter 3 for more details how the AIS data are investigated and
uations that are over-represented in failure event analyses; hence, Chapter 5 for more details and a presentation of the simulation setup in
mitigation actions can be proposed that reduce the risk of accidents. It Fig. 7.
can also be used to identify candidate ships that should be used as
“target” ships in bridge concept designs, to ensure sufficient bridge 2.1. Ship manoeuvre simulator
structural strength that can withstand the kinetic energy impacting the
bridge; see Sha and Amdahl (2019). The SEAMAN ship manoeuvre simulator, which was developed by
In the proposed methodology, there is no equation that estimates the SSPA (http://www.sspa.se), was used in this study. The simulator is a
number of allisions; this is the major difference compared to methods software code where the ship’s motions are modelled in all six degrees-
based on Eq. (1). The number of simulations is calculated by equations, of-freedom. It is a module-based software where the definition of the
but the simulations give the number of allisions. Another difference ship model’s characteristics is divided into subsystems, e.g. the hull,
compared to previous research is that the methodology includes engine, propeller and rudder. The simulator includes spatial-temporal
methods to obtain location-specific failure events regarding both dura­ subsystems and numerical codes that calculate the forces acting on the
tion and frequency. The proposed methodology can thus be applied to ship that are induced by the wind, waves and currents; shallow water
study risk mitigation options in location-specific areas. Note, however, and bank effects are also considered (Andreasson et al., 2005; Ottosson
that a limitation is that only single ships can be studied in each simu­ and Bystrom, 1991). Total force equilibrium of the ship model is solved
lation. This is because the event statistics are gathered from single-ship in a nonlinear mathematical model in every time step according to a
situations, and it is challenging to model all human decisions that could procedure presented in Ottosson (1994).
be made in an autopilot logic. Apart from the probability of allision, the A SEAMAN ship model requires several hundreds of parameters to
methodology also enables estimations of the design energy the structure accurately represent a ship and its characteristics in the simulator. A
needs to withstand. This is possible since the kinetic energy just before ship’s hydrodynamics and resistance properties can be fine-tuned if test
the allision is captured for all simulated allisions. data are available from model testing. When new models are defined in
The remainder of the paper is structured as follows. Chapter 2 the simulator, a procedure for parameter sensitivity study of the ship

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 1. Schematic of the methodology presented in the study.

model’s parameters is always carried out. For example, to ensure that event or simulation scenario determined by the user. The batch mode
the manoeuvrability of the ships used in this study was correctly was used in this study since it significantly reduced the simulation time
modelled in SEAMAN, each ship model was simulated and verified and there was no need to survey the simulations in real time on a screen.
against the zig-zag and turning circle tests from the IMO’s “Standards for It was also a necessity because of the large number of simulations carried
ship manoeuvrability” (IMO, 2002). Running these tests in a simulation out using the Monte Carlo method; see Chapters 5 and 6.
context have also been applied by others like Budak and Beji (2020),
who used the tests to ensure the ship’s manoeuvrability while imple­ 3. Definition and identification of failure events using AIS
menting a course-keeping autopilot.
Fig. 2 presents a screen shot from a simulation when the simulator is Simulation and analysis of ship accidents and their causes can be
run in desktop mode in real time. It can also be run in batch mode with carried out in multiple ways. Pedersen (1995, 2020) proposed a method
an autopilot navigating the ship according to a pre-defined route, failure based on the work of Fujii (1983) and Macduff (1974). In this method,

Fig. 2. Example from a SEAMAN simulator run in desktop mode (screen shot). It shows the history of the ship’s manoeuvres when it leaves the port and its nav­
igation trajectory when it enters the fairway.

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

situations are defined that can result in an accident, an approach that Rasmussen et al. (2012) and Kaneko (2012).
has been applied by among others Montewka et al. (2012) and Goerlandt The AIS data were used to identify drifting ships by following the AIS
and Kujala (2011). Pedersen’s situation-based approach can be effi­ trajectories and applying the following criteria as filters:
ciently used in mathematical models that do not involve or need a ship
manoeuvring simulator or detailed modelling of the ship’s motions and • speed over ground (SOG): should be less than 2 knots.
dynamics. However, one shortcoming is that it relies on historical • course over ground (COG): should differ more than 20◦ from the
events/accidents and data for known traffic situations and ships, which heading.
often are related to very low probabilities, and, hence the method is • duration: longer than 5 min.
sensitive to the access to and quality of data (Chen et al., 2019). The
advantage of the approach is that analyses can be made with low Each candidate ship that fulfilled these criteria was manually
modelling and computation efforts, which often are suitable in risk an­ checked to ensure that there were no obvious reasons for their drifting
alyses that involve the Monte Carlo method. behaviour, which would then result in the candidate being removed
The ship manoeuvre simulator presented in Chapter 2 was used in from the sample. Examples of such candidates that should be excluded as
this study instead of Pedersen’s approach. The advantage of the simu­ drifting ships are slow steaming ships and ships that intervene with
lator approach is that it opens up new possibilities to simulate, assess other ships, e.g. ships that pickup pilots or change crew. The duration of
and execute risk analysis of existing and future marine traffic situations the event for a drifting ship was defined by the position report where the
that may involve infrastructure offshore. The gain of this approach is ship started to lose speed (or its last known position) to the position
that specific details of the trace from event to accident can be obtained report where the ship recovered control and started to either pick up
and analysed. This includes data of ship types, weather situations, ship speed again or anchored.
operation profiles, fairway layouts and infrastructure objects, which can In the simulator, a drifting ship is modelled as fully operational for
be modelled and systematically varied in parametric studies; it does not the first 60 s in a simulation case whereafter the propulsion system is
need an explicit value or expression of the causation factor, which is turned off. At this instant, the ship begins to lose speed, and the autopilot
required in Pedersen’s approach. The drawback is that it requires some tries to keep the ship’s course on track for as long as possible. This setup
more modelling and computation efforts, but the simulator software correlates with the most common ship behaviours from AIS data ob­
used in this study offers batch mode simulations to overcome the chal­ servations from the ship traffic studied in Chapter 4; complete blackout
lenge. In addition, instead of defining and analysing accidents, three (including the steering engine) was not observed. The simulation in the
types of events are identified in the study as relevant and critical for simulator continues for the duration of the event, which can either be
ship-bridge allisions in relatively narrow waterways: drifting of the ship, the duration as measured from AIS data (see above), from a pre-defined
sharp turning of a ship and miss of a turning point. They are similar to time by the user when the propulsion system is turned on again, or when
the categorisation presented in Ulusçu et al. (2009), van Dorp and the ship is anchored. In this study, the first option was used. Fig. 3 shows
Merrick (2011) and Rassmusen et al. (2012); see a discussion in Chapter an example from a comparison of results from a simulator simulation
6.4 for other types of events. (green ship contours) and the real AIS track (grey ship contours) for the
The AIS data of the marine traffic in the area are needed to model, same case of a drifting ship. This example shows that the simulator
simulate and analyse the events. Since 2002, ships larger than 300 gross almost replicates the AIS track.
tonnes must have an AIS transponder, which means that this informa­
tion has been available after 2002. AIS messages are separated in two 3.2. Event “sharp turning ship”
message types: position report and metadata message (Raymond, 2019).
At sea, every ship issues a position report every 2–10 s, depending on the The sharp turning ship event is defined as a ship that may suffer from
ship’s speed and turning rate. In this study, this information is handled a malfunction in the rudder giving rise to a locked rudder that turns the
both as “single points” and after post-processing as “trajectories”, ship distinctly to starboard or port; see Pedersen et al. (2020) for the
defined by multiple points and represented by lines connecting similar category III type of accident for a similar situation or event. In the
points. The trajectories then contain data from both the position reports current study, it is assumed that when this event occurs, the ship de­
and the metadata messages data and are stored in a PostgreSQL database creases its speed to gain time to repair/fix the rudder problem. When the
with the spatial extension PostGIS. For more details about how the ship’s speed decreases, and there is no rudder effect that can be
trajectories were constructed with a Douglas-Peucker compression, see controlled by the crew, it looks as if the ship is drifting in the AIS data.
Hörteborn et al. (2019) or a similar method presented in Zhao and Shi Thus, the principles and filters used to identify drifting ships can initially
(2019) and Wei et al. (2020). be applied to identify candidates for the current event. To distinguish
The following subchapters present how AIS data were used to this event from the event drifting ship, the following complementary
quantify frequencies and durations for the three events of drifting ship, criteria are used:
sharp turning ship and miss of turning point. Each subchapter ends with
a summary of how the simulation of the event was implemented in the • a ship that continuously loses its speed, without an instant sharp
simulator’s autopilot. In short, the event identification using AIS data turn, is categorised as a candidate for the event drifting ship.
was carried out in two steps. First, an automatic filter with specified • a ship that starts its drifting with an instant turn and has a rudder
conditions that helped define an event was applied to the AIS trajec­ malfunction is categorised as a candidate for the event sharp turning
tories, followed by a second manual step applied to the remaining tracks ship.
that could not be identified as a clear event among the three categories.
Events identified by the AIS data were also used in the process of cali­ The duration of the sharp turning ship event for a ship was defined by
brating the autopilot’s behaviour, for example, related to the time to the position reported where the ship started to turn sharply, to the po­
turn off the steering system and lock the rudder’s position. sition reported where the ship recovered control and started to either
pick up speed again or anchored.
3.1. Event “drifting ship” Modelling this event in the simulator is challenging, since, in reality,
the crew of a ship will react and act differently in each scenario to a
The drifting ship event is defined as a ship that appears to drift with malfunction of the rudder. Nevertheless, the simulator setup to simulate
the waves, the wind and the current with no possibility to turn on its this event is in the study is defined as a fully operational ship the first 60
engine. It is assumed that the probability that the drifting ship event will s of the simulation case whereafter the rudder is set to either full star­
occur is the same along the fairway; see Furnes and Amdahl (1980), board or full port. After another 60 s in the simulation, the engine is

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 4. Sharp turning ship: simulated track (contours plotted in green, one
position every 20 s connected with a blue line) overlaid the real AIS data
(contours plotted in red). (For interpretation of the references to colour in this
figure legend, the reader is referred to the Web version of this article.)

(2020) for the category II type of accident for a similar situation or

event. The event is exemplified in Fig. 5, where the blue line shows a
ship (traveling from south west to north east), failing to follow the
expected/normal traffic behaviour. The ship passes through the border
(line 3) of the Traffic Separation Scheme (TSS). After some time, the
“mistake” is observed, and the ship turns back to the main navigation
lane of the fairway. The reason for the occurrence of this event can have
various root causes, such as fatigued crew (falling asleep), rudder stuck
mid ship, human errors during navigation, etc.
The AIS data were used to identify miss of turning point ships by
following the AIS trajectories and applying the following criteria as fil­
ters, here presented related to the example in Fig. 5:

Fig. 3. Drifting ship event: simulated track (contours plotted in green, one
position every 20 s connected with a blue line) overlaid the real AIS data
(contours plotted in grey). (For interpretation of the references to colour in this
figure legend, the reader is referred to the Web version of this article.)

turned off, and after another 5 min, the rudder is assumed functional
again and set to mid ship position. This sequence, times and behaviours
were determined from the authors’ experiences from analyses of AIS
data, parametric studies in the simulator and attempts to mimic real
events in the simulator’s environment. Fig. 4 shows an example from a
comparison of results from a simulator simulation (green ship contours)
and the real AIS track (red ship contours) for the same case of a sharp
turning ship. The turn is initiated with constant speed, indicating that it
is a sharp turning point event and not a case of loss of propulsion (i.e.
drifting event). This example shows that the simulator almost replicates
the AIS track for this event.

3.3. Event “miss of turning point”

The miss of turning point event is defined as a ship that continues

straight ahead, passing a marked or expected turning point, but manages Fig. 5. An example of a ship that fails to turn at a marked turning point; the
to correct its course later to the main navigation lane; see Pedersen et al. example is taken from the TSS Bornholmsgat area.

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

• the ship should cross the pre-defined TSS border lines, i.e. the border calculated by dividing the number of events with the number of sailing
lines 1, 3 and 4 in Fig. 5. hours. The “miss of turning point” frequency was calculated by dividing
• the COG should differ less than 5◦ between the crossing of lines 1 and the number of events with the number of ships making the turn. These
3. frequencies together with the data from Rasmussen et al. (2012) are
• the SOG should differ less than 1 knot between the crossing of lines 1 shown in Table 2.
and 3. The event frequency for “drifting ship” is in same order of magnitude
in the three studies. The values for the Great Belt VTS and Rasmussen
Similar to the other event categories, every ship that fulfilled these et al. (2012) show very good agreement; thus, the method described in
criteria was manually checked to ensure that there were no obvious or Chapter 3.1 for this event was considered verified. The lower value for
other reasons for its behaviour and choice of path. For example, a ship the Great Belt VTS area compared to the TSS Bornholmsgat area is due to
with a distance smaller than its own ship domain to another ship was the ships in the former area being able to manoeuvre more easily and
excluded, since its path could have been affected by the other ship (i.e. safely and anchor outside the fairway if they experience minor trouble,
intentional and voluntary miss of turning point to avoid an incident). such as a partial blackout. It should be noted that with the event iden­
The definition of the size of the ship domain followed the method pre­ tification method presented in Chapter 3.1, it is not possible to differ­
sented in Hörteborn et al. (2019). entiate these events from planned anchoring. In the case study in
The duration of the miss of turning point event for a ship was defined Chapter 5, simulations and analyses of the Great Belt VTS area, this
by the position of the expected turning point and the position reported event’s frequency was set to 0.65 × 10− 4/hour.
where the ship actually turned. The expected turning point here is the The event frequency for “sharp turning ship” differs some between
point where the majority of all ships turn to follow the TSS; see line 2 in the different studies. However, only two cases were identified for the
Fig. 5, which marks when ships are supposed to make the turn in the two studies in the Great Belt VTS area, which are too few to rely on when
example. generating statistics. It was assumed that the value of this event’s fre­
Modelling this event in the simulator was done in the case study as quency should be somewhat lower than the average value from the three
follows. The ship is run as expected during the initial 2 min of the studies, it was set to 0.070 × 10− 4/hour. A sensitivity analysis in which
simulation in order to ensure that it is on the correct navigation path. this event’s frequency is increased 50 percent is presented in Chapter
After that, the autopilot is turned off, and the rudder is locked in mid- 6.4.
ship position and remains so for the remaining time duration of the The event frequency for “miss of turning point” shows relatively
event. good conformity between the three studies; the value from Rasmussen
et al. (2012) is, instead of calculating the event frequency in terms of
4. Event statistics occurrences per turn, based on “human failure” and event frequency per
hour as the unit. Based on the same reasons as for the “drifting ship”
This chapter present event statistics and durations for the events event, an event frequency of 1.55 × 10− 4/turn was used in the simula­
defined in Chapter 3. The case study presented in Chapters 5 and 6 tions and analyses in Chapter 5. However, it should be noted the dura­
emphasises the Great Belt VTS area. However, in this chapter, the sta­ tion time of the event was found to be notably different between these
tistics and analyses of the TSS Bornholmsgat area and the results re­ three studies, see the following chapter for the analysis.
ported in Rasmussen et al. (2012) are included for comparison purposes.
The AIS data were based on the marine traffic in the Great Belt VTS 4.2. Event durations
and TSS Bornholmsgat areas during the period 2014 to 2019 obtained
from DMA (2020). The data were analysed with the methodology pre­ The definition of the duration of each event was defined in Chapter 3.
sented in Chapter 3. Rasmussen et al. (2012) presented their results for Fig. 6 presents a summary of the durations for the “drifting ship” and
“human failure” in the Kadetrenden area using AIS data from 2007 to “sharp turning ship” event categories. The symbols in the figure repre­
2010, and their statistics for “loss of propulsion” and “steering machine sent results from the AIS data processing, while the lines represent fitted
failure” were based on four years of incident reports from the Great Belt curves according to the distributions presented in Table 3. For the
VTS. former category, the results are presented separately for the Great Belt
VTS, the TSS Bornholmsgat and Rasmussen et al. (2012). For the sharp
turning ship event, there were too few cases in the Great Belt VTS and
4.1. Event frequencies
the TSS Bornholmsgat areas to make a distribution. To overcome this
was six event durations from a third area, the Kiel Canal, included to
It assumed that the probability of occurrence and the duration of the
make this distribution (this area is discussed in Chapter 6.5). However,
events defined in Chapter 3 are independent of ship type and size. In
the event had similar durations in all areas, so they were fitted to one
total, 153 events were identified in the Great Belt VTS and TSS Born­
common distribution representing the event.
holmsgat areas using the event identification methods described in
The results in the figure show that the duration of the drifting ship
Chapter 3. Table 1 presents a summary of the number of events for each
event is the shortest in the Great Belt VTS area. It can be explained by the
event category, together with the number of sailing hours that were used
fact that this area offers the best opportunity to anchor. The event
to identify the “drifting ship” and “sharp turning ship”. Two waypoints
in these areas were used to define the event “miss of turning point”, and
the number of turns at these waypoints are also presented in the table. Table 2
Summary of event frequencies where * refers to “loss of propulsion”, ** to
The frequency for “drifting ship” and “sharp turning ship” was
“steering machine failure” and *** to “human failure” in Rasmussen et al.
(2012).
Table 1
Event category Great Belt VTS TSS Rasmussen et al.
Number of events, hours and turns in respective area.
Bornholmsgat (2012)
Data analysis Great Belt VTS TSS Bornholmsgat
Drifting ship 0.65 × 10− 4/ 0.91 × 10− 4/hour 0.6 × 10− 4/hour*
Number of drifting ship events 34 65 hour
Number of sharp turning ship events 2 5 Sharp turning 0.038 × 10− 4/ 0.092 × 10− 4/ 0.1 × 10− 4/hour**
Number of sailing hours 522,296 713,531 ship hour hour
Number of miss of turning point events 19 26 Miss of turning 1.55 × 10− 4/ 2.10 × 10− 4/turn 2.5 × 10− 4/hour***
Number of turns at waypoints 122,319 124,705 point turn

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 6. Duration of the events drifting ship (individually: Great Belt VTS, TSS Bornholmsgat, Rasmussen et al. (2012)) and sharp turning ship (summary of all: Kiel
Canal, Great Belt VTS, Bornholmsgat TTS). The dots represent the measurements, and the lines are the result of the curve fitting presented in Table 3.

Fig. 7. Schematic of deterministic (d) and randomly generated (mc) parameters in the SEAMAN simulator simulations.

category “miss of turning point” is not included in the figure, but its
Table 3
statistical distributions are presented in Table 3.
Statistical distributions and their parameters for duration of events (time in
hours). The parameters correspond to σ = standard deviation, ι = location, λ =
scale and μ = mean value.
4.3. Accident statistics in the areas

Event category Great Belt TSS Rasmussen et al.

Collection of accident statistics in the Great Belt VTS area was
VTS Bornholmsgat (2012)
emphasised since this area was used in the simulator case study in
Drifting ship Lognormal Lognormal Weibull Chapter 5. Three sources were used to ensure that the majority of ac­
σ = 0.71 σ = 0.87 σ = 0.5
ι = 0.021 ι = 0.1 λ = 0.605
cidents reported between 2010 and 2019 in the area were collected. In
λ = 0.69 λ = 0.97 the accident records of IHS Fairplay (2020), five strandings, two colli­
Sharp turning ship Lognormal: σ = 1.2; ι = 0.06 λ = n/a sions, one contact and one fire accident were reported. In addition to
0.54 these accidents, the Norwegian Maritime Authority (Sjofartsdirektor­
Miss of turning Normal Normal Less than 0.33
atet, 2020) reported one fire accident, and no additional accidents were
point μ = 0.064 μ = 0.19
σ = 0.015 σ = 0.047 found reported in the EMCIP database (EMCIP, 2020).

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

5. Description of simulator simulations and case study allisions with a probability level of 1 × 10− 3. The procedure to identify
ships that follow this criterion was as follows. The allision energies from
The chapter presents a case study where the SEAMAN simulator was a complete simulation set in the simulator were sorted from the highest
used to simulate and analyse the marine traffic situation in the Great Belt to lowest. The probability for the worst allision in the same set of sim­
VTS area. Chapter 5.1 presents how the simulator simulations were ulations is then 1/YR, and the second worst (or worse) has a probability
planned and setup followed by specific details and descriptions of the of occurring 2/YR. For this analogy, with simulator simulations of YR =
case study in Chapter 5.2. 10,000 times, the 10th worst allision corresponds to the worst allision
that has the highest probability to occur in 1,000 years. If YR is increased
to 100,000, the 100th worst allision corresponds to the allision energy
5.1. Simulator simulations and setup with a probability to occur corresponding to 1 × 10− 3.
The SEAMAN simulator has two major parts in the simulator model:
The simulations in the SEAMAN simulator were run in sets, where a model of the ship and a model of the environment (called “world”).
each set contained 90 batches of simulations. The 90 batches were based Fig. 7 presents a schematic of the parameters of these models that have
on three event categories, 15 types of ships and two directions of ship either been deterministic, d, or randomly generated, mc, in Monte Carlo
routes; see Chapter 3 for event categorisation and Chapter 5.2 for ship simulations. The deterministic parameters were the three batch pa­
types and route directions specific for the case study marine traffic rameters (i.e. event categories, ship types and direction on route), and
situation. the seven randomly generated parameters were described by statistical
The number of simulations in each batch, for the drifting ship and distributions.
sharp turning ship events, was calculated using Eq. (2):
5.2. Case study: the Great Belt VTS area
15 ∑
∑ 2
NSim,i = Pft,i × NCat,jk × tN,jk × YR (2)
j=1 k=1 The chapter presents the case study area in detail. It is presented
from which the values and settings of the parameters lateral offset,
where NSim,i is the number of simulations for event i (1 = drifting ship; 2 route, ship, ship speeds and environmental variables were collected. The
= sharp turning ship), Pft,i is the event probability per hour for the event properties of the events were presented in Chapter 3 and their durations
under study (see event frequency in Chapter 4.1), NCat,j,k is the estimated in Chapter 4.2.
number of ships per year for ship type j on a route k in the area, tN,j,k is The Great Belt VTS was chosen as the case study area since it has
the average time ship type j sails on the route k, and YR is the number of been studied by other researchers from a ship-bridge allision perspec­
repetitions of one year’s traffic the simulation should represent. tive; for an example, see Gluver and Olsen (1998). According to statistics
The starting position of a ship in a simulation for an event varied in accident databases, numerous groundings in the area have been re­
between the simulations. It was assumed that the starting position of a ported during the past few years (EMSA, 2019), and historic AIS data are
ship (i.e. its position in the fairway when the simulation starts) follows available for the area (DMA, 2020). Fig. 8 presents a map of the marine
the traffic separation scheme and spatially follows an even distribution traffic passing the area, and Fig. 9 presents histograms of the distribution
along the route. The distance between starting positions, Dsp,ijk, was in ship length, ship speed and lateral distribution for the marine traffic
calculated according to Eq. (3), where NSim,i was calculated according to that passed the Great Belt Bridge during 2019. The marine traffic is
Eq. (2), where Lr,k is the length of the simulated route. spread laterally over the fairway, which, according to IALA (2014), can
/ be represented by the normal distribution. In this study, this distribution
Dsp,ijk = Lr,k NSim,i . (3)
is checked/updated at every waypoint for all traffic in 2019 since the
The number of simulations in each batch for the miss of turning point properties of the distribution may vary in the fairway (here, called
event (i = 3) was calculated using Eq. (4): offset). By means of the offset (normal) distributions, indicated as
Lateral offsetmc in Fig. 7, a unique route could be generated for each
15 ∑
∑ 2
NSim,i = PCSA,i × NCat,jk × NT,jk × YR . (4) simulator simulation.
j=1 k=1 Most of the traffic that passes the area follows the south-north T-
route. It is divided into a deep water route and a normal route, see Fig. 8.
where PCSA,i is the probability that a ship misses a turn, and NT,jk is the Statistics of the marine traffic in the area during 2019 shows that 19,507
number of turns the ship j makes on its route k. According to Chapter 3.3, ships passed under the Great Belt Bridge, divided into 7,225 general
these simulations started 2 min prior to the point where the turn was cargo ships, 5,242 tanker ships, 2,094 RoPax/RoRo ships, 1,488
missed; a turning point was laterally distributed in accordance with their container ships, 1,484 bulk carriers and 1,974 unknown ship types. The
unique route. length distribution of each ship type is presented in Fig. 10.
The majority of the simulator simulations ended without ship The results in the figure were used to define 15 representative ships
grounding or ship-bridge allision. However, for the simulations that in the simulator that together reflected the marine traffic in the area
ended with an allision, the allision energy was calculated according to during 2019. Table 4 presents some of the ships specifics, ship speed
Eq. (5), where M is the ship’s displacement, v the ship speed and E is the (normally distributed, Speedsmc in Fig. 7) and the number of ships going
allision energy. Note that this is the largest theoretical energy that may north and south (NCat in Eqs (2) and (4)). The three largest ships with
cause damage to the ship and the bridge structures, since the formula is regards to draught—Bulk, 226 m; Tanker, 241 m; Tanker, 260 m—used
simplistic it does not include detailed energy distribution which could be the deep water route in Fig. 8; all other ships use the normal route.
studied by external dynamics simulations; see Yu et al. (2016) and Lu
et al. (2016). 5.3. Metocean statistics for the Great Belt VTS area
/
E = (Mv2 ) 2 (5)
The metocean statistics for the area were downloaded from the
A central part of the presented methodology is the bridge design Copernicus Marine Service (2020). The wind statistics for the period
criteria. According to Johansen and Askeland (2019), there are different 2015 to 2020 are presented in Fig. 11 as a wind rose plot for the location
ways to interpret these criteria where the authors proposed to use of an latitude 55.25◦ and longitude 11.0◦ . The current statistics for the period
FN-curve to better represent both the probability and the consequence. 2016 to 2020 are presented in Fig. 12 as a current rose plot for the
In this study, a risk criterion with a threshold of 1 × 10− 3 was selected, location latitude 55.2◦ and longitude 11.0◦ . The data in the rose plots are
which means that a bridge struck by a ship should withstand and survive used to define the wind and current loads in the simulator model; see

8
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Moctar, 2018). The probability to encounter different wave heights in

the range 0–2.5 m in the area is presented in Fig. 13. This figure show
that the probability to encounter waves larger than 1.5 m is very low, i.e.
waves have a minor effect on a ship’s manoeuvrability in the area.
Hence, it was assumed that waves could be disregarded in the simulator
model, which also reduce the computational efforts (less simulation
time). To conclude, the influence from wind and current have a great
effect on the drift force, and, hence, they were included in the simulator
model, which, in this study, was defined as a four degrees-of-freedom
ship model (heave and pitch were not considered).

6. Results

The simulator runs were defined in three categories divided into ten
simulation sets for (i) investigation of the influence from random seeds
in the generation of random variables, (ii) a sensitivity study of the
parameters, and (iii) demonstration of examples of risk mitigation; see
Table 5 for an overview of all simulation sets. The simulation of a single
ship’s voyage took approximately 2 s on an Intel Core i7-2600 3.4 GHz
processor with 16 GB RAM memory and 64Bit architecture. One set of
simulations consist of some four million ship voyages, which needed
approximately 80 h to complete using eight processors.
The three sets, 1A, 1B and 1C, relate to the random seed study. They
have the same input, but the random seed for the generation of random
variables (mc in Fig. 7) is varied, which resulted in different values of the
random variables. Hence, by defining the random seed, a simulation
could be reproduced, ensuring that new combinations of random vari­
ables were generated (Harris et al., 2020). The number of simulations
needed in the set was determined by a criterion defined in this study
stating that the difference in allision energy between the simulation sets
should not differ more than five percent.
The five sets in 2–4 in Table 5 were defined for sensitivity study
analysis purposes in which the probabilities and duration time of the
events were studied. The input data were based on the TSS Born­
holmsgat area. One set investigated the increased probability and
duration time of the event drifting ship, and another set investigated a
fifty percent increase in probability of the event sharp turning ship. The
miss of turning point event was separated into three sets: increase of
both probability and duration time, increase of only the probability and
increase of only the duration time.
Sets 5 and 6 were defined and used in examples of risk mitigation to
demonstrate how the methodology presented in the study can be uti­
lised. In set 5, a speed limitation of 12 knots was enforced, and in set 6,
the navigation path was altered to force the traffic to navigate 2.6
nautical miles straight prior to the Great Belt Bridge instead of 1.6
nautical miles, which is the normal navigation path.

6.1. Analysis of the number of simulated traffic years (YR)

Fig. 8. Map presenting the marine traffic in the Great Belt VTS area.
Sets 1A, 1B and 1C were used to investigate how many traffic years
(YR) need to be simulated according to the discussion in Chapter 5.1.
Fig. 7.
Table 6 presents the results from the simulator simulations with YR =
The length of a colour bar in Fig. 11 indicates the probability of a
10,000 traffic years (or repetitions of one year). There is a difference in
specific wind speed and wind direction. For example, the wind di­
the number of groundings and allisions because of the different random
rections around 11 percent of the time are from the south-west, where
seeds, which also affects the maximum allision energy and the 1,000-
the wind speed is 2.5 percent of the time less than 3 m/s, 6 percent of the
year allision energy for each simulation set. As described in Chapter
time between 3 and 6 m/s, 3 percent of the time between 6 and 9 m/s,
5.1 the 1,000-year allision energy represents the worst allision that has a
and less than 0.5 percent of the time it is faster than 9 m/s. The wind rose
probability of 1 × 10− 3 to occur. Because the 1,000-year allision energy
plot in Fig. 11 shows that the dominant wind directions are from the
differs more than 30 percent between the sets, YR was too low and was
west and the south-west, and that the wind speed is often below 9 m/s.
increased to 100,000. The results from these simulations are presented
Wind speeds larger than 9 m/s come from the west and sometimes from
in Table 7. They show that the number of groundings is, on average,
the east, but rarely from other directions. The current rose plot in Fig. 12
50,887. This gives a probability of 0.51 groundings per year, which,
shows that there are currents in the area that are dominated by the di­
compared to the accident statistics for the area, demonstrates a good
rections north north-west and south south-east.
agreement since five groundings were reported during a ten-year period
Forces from secondary waves induce drift forces on ships, and waves
(see Chapter 4.3). The average number of allisions is 721, which gives a
up to 2 m have some effects on a ship’s manoeuvrability (Chillcce and el
probability of 0.007 allisions per year, or one allision every 139 years.

9
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 9. Histograms of ship length, ship speed and lateral distribution of the marine traffic passing the Great Belt Bridge in 2019.

Fig. 10. Number of ships (y-axis) versus the length distribution of the ship types (x-axis) that passed under the Great Belt Bridge in 2019.

The 1,000-year allision energy shows some difference between the sets, ship event results, but there was a large effect with regard to the miss of
but the deviation is less than five percent, which is acceptable. The turning point event. Simulations with a longer duration time show a
average allision energy was calculated to 1,624 MJ, which represents a larger probability for grounding and allision accidents. The miss of
178 m tanker with 57,870 DWT at ship speed 14.6 knots. turning point thus shows the highest probability for a grounding or
allision accident. Fig. 15 presents the results from simulation set 1A to
illustrate the paths of ships that collided with the bridge. Using the
6.2. Analysis of the duration time parameter methodology presented in this study and these results, it is possible to
propose and analyse mitigation actions that can help reduce or possibly
Fig. 14 presents the results from an analysis of all simulations in avoid ship-bridge allisions.
simulation set 1A in Table 7, emphasising the influence from the
parameter duration time in the three event categories. The green line
represents the distribution of all simulations, while the blue dotted and 6.3. Analysis of two mitigation methods
the red dashed lines represent the distributions for the events that ended
in grounding or allision accidents, respectively. The results show that Two mitigations were analysed by simulation sets 5 and 6: reduction
the duration time in the drifting ship event had a small influence of maximum allowed ship speed and change of point where ships should
compared to the overall distribution and probability that lead to an make an earlier turn (change navigation path) to pass under the bridge,
allision. The duration time had a minor influence on the sharp turning respectively. These two mitigation options were included to showcase

10
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Table 4
List of ships modelled in the simulator and used in the case study; σ = standard deviation and μ = mean value.
Ship type Length (m) Beam (m) Draught (m) Displacement (tonnes) μ speed, (knots) σ speed, (knots) North going South going

Container 134 21 7.13 7,698 14.6 2.25 246 183

Container 170 26 9.3 23,027 14.3 2.81 540 315
Container 255 36 10.2 55,727 15.3 2.35 268 268
General Cargo 73 12 4.1 4,850 9.3 3.76 1,896 2,022
General Cargo 125 18 6.8 13,048 10.3 2.72 643 595
General Cargo 161 25 9.1 30,056 13.4 2.76 2,491 1,523
Bulk 169 27 9.23 55,459 11.5 1.78 790 339
Bulk 226 33 12.8 72,611 11.3 1.53 441 93
Tanker 79 13 4.8 6,538 10.2 1.97 136 131
Tanker 132 21 7.6 12,617 12.0 1.89 496 506
Tanker 178 28 9.9 57,870 12.6 1.70 1,545 374
Tanker 241 41 12 78,459 11.8 1.67 395 220
Tanker 260 45 11.8 164,820 11.8 2.00 481 365
RoPax 194 30 6.5 29,500 17.5 2.66 685 580
RoPax 252 31 6.5 36,256 16.9 1.66 485 462

Fig. 11. Wind rose plot presenting the probability of wind speeds and wind Fig. 12. Current rose plot presenting the probability of current speeds and
directions. Data source: Copernicus Marine Service (2020), current directions. Data source: Copernicus Marine Service (2020),
reanalysis-era5-single-levels. BALTICSEA_ANALYSIS_FORECAST_PHY_003_006.

possibilities with the methodology. They were designed based on similar

ship fairway-bridge crossings. The results presented in Table 8 show that
both these actions have a positive effect on reducing the number of
accidents. The reason why the allision energy is significantly reduced is
simply because many of the allision cases in set 1A did not occur for the
miss of turning point event, which formerly gave the largest collision
energies. It should be noted that the suggested mitigation actions have
not been confirmed as realistic measures to be enforced in the area;
however, with the methodology presented in this study, it is shown that
they are worth investigating further, especially if marine traffic density
and ship sizes continue to increase in the area. This is also supported by
Pedersen et al. (2020), who recommended doing scenario-based simu­
lations as a preparation for future changes and estimations of ship traffic
Fig. 13. Probability of occurrence of the wave height (m) at latitude
situations and risk assessments.
55.0–56.0◦ and longitude 10.4–11.4◦ . Data source: Copernicus Marine Service
(2020), GLOBAL_REANALYSIS_WAV_001_032-TDS, period 1993 to 2018.
6.4. Sensitivity analysis

A sensitivity study analysis was carried out to investigate how the

probabilities and duration time parameters from the simulation sets

11
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Table 5
Overview and definition of ten simulation sets run in the SEAMAN simulator. The parameters of the events and their details are presented in Chapters 4.1 and 4.2.
ID Seed Description of event and simulation set

1A 0 Drifting ship – probability: 0.65 × 10− 4; duration: σ = 0.71, ι = 0.021, λ = 0.69

1B 1 Sharp turning ship – probability: 0.70 × 10− 5; duration: σ = 1.2, ι = 0.06, λ = 0.54
1C 2 Miss of turning point – probability: 1.55 × 10− 5; duration: σ = 0.015, μ = 0.064
2 0 Drifting ship – probability: 0.91 × 10− 4; duration: σ = 1.2, ι = 0.1, λ = − 0.4
The other events were modelled as defined in set 1
3 0 Sharp turning ship – probability: 1.05 × 10− 5
The other events were modelled as defined in set 1
4A 0 Miss of turning point – probability: 2.1 × 10− 4, duration: σ = 0.047, μ = 0.19
The other events were modelled as defined in set 1
4B 0 Miss of turning point – probability: 2.1 × 10− 4, duration for miss of turning point and the other events were modelled as defined in set 1
4C 0 Miss of turning point – duration: σ = 0.047 μ = 0.19, probability for miss of turning point and the other events were modelled as defined in set 1
5 0 Maximum ship speed: 12
Event probabilities and durations as defined in set 1
6 0 Longer straight navigation distance prior to the bridge
Event probabilities and durations as defined in set 1

Table 6 turning point. This has not been studied in detail in similar in­
Results from simulation sets 1A, 1B and 1C with YR = 10,000. vestigations and models within the same research area (e.g. Goerlandt
and Kujala, 2011; Hansen et al., 2013; van Dorp and Merrick, 2011). It is
Id Number of Number of Number Maximum 1,000-year
simulations groundings of allision expected recommended that a stronger emphasis should be placed on this
allisions energy (MJ) allision parameter in future work, as the manner which the duration time varies
energy (MJ) for different ship traffic areas, ship types and sizes should be studied in
1A 395,770 5,165 59 2,308 MJ 1,220 MJ more depth.
1B 395,770 5,214 67 2,315 MJ 1,620 MJ
1C 395,770 5,065 56 1,967 MJ 1,403 MJ
6.5. Applicability of proposed methodology
affect the results, except for 1B, 1C, 5 and 6. Those sets were excluded
In Chapter 4, the methods described in Chapter 3 were used to obtain
because there was no need to include all the random seed simulation sets
event statistics in two areas. These areas have their differences when it
or the simulation sets that were defined for the mitigation study. The
comes to geography; however, they are both considered to be open sea
results are presented in Table 9.
and have well-defined sailing paths (partly regulated by TSS). Another
Simulation sets 2 and 4 were based on the event statistics from the
area with well-defined sailing paths is the Kiel Canal; the methods to
TSS Bornholmsgat area. Set 2 has a higher probability for drifting ship
identify events were applied in this area, as well, but it was concluded
compared to simulation set 1A. This increased the number of groundings
that the methods were not applicable here. With the assumption that all
and allisions by about 25 percent. It did not, however, affect the 1,000-
the events led to accidents, and that all the accidents here were reported,
year allision energy. Set 3 has a 50 percent higher probability for sharp
the accidents from 2017 reported to IHS Fairplay and EMCIP were
turning ship compared to simulation set 1A, which also showed a minor
studied. The records give a higher frequency here for the loss of pro­
increase in the number of groundings and allisions but no influence on
pulsion and rudder failure, but they are in the same magnitude as in the
the 1,000-year allision energy.
areas included in this paper. Although, it should also be noted that
For the miss of turning point in set 4A, the case study simulations
rudder failures in the accident records include more types of events than
show that this event has the largest influence and is, thereby, the most
described in Chapter 3.2.
sensitive to the results. The increase of probability and duration were
There are other events that were not investigated in the study that
separated into 4B and 4C, to further investigate this event type and its
could result in an allision. One example of such an event is “cowboy
effect on the result. An increase of only the event probability from 1.55
ships”, which was introduced by Pyman et al. (1983). The event defines
× 10− 4 to 2.1 × 10− 4 raised the number of allisions caused by miss of
ships that do not follow the intended navigation path and make turns at
turning point from 0.25 percent per year to 0.32 percent per year and the
wrong locations in the fairway and traffic scheme. The cause behind the
expected 1,000-year allision energy by approximate 13 percent. How­
event could be crew/captains influenced by alcohol, malfunction of
ever, an increase of the average duration from 0.064 h to 0.19 h affected
navigation aids, acts of terrorism, etc. This type of event was excluded
the number of allisions by 2,900 percent and the expected 1,000-year
from the study, since no method was found to model, identify and
allision energy by 251 percent. A comparison between the allision en­
quantify the event. Another example of event that was not considered in
ergy from sets 4C and 1A is illustrated in Fig. 16. An allision energy of
the study is the category IV scenario proposed in Pedersen et al. (1995,
approximately 4,268 MJ represents a 260 m tanker with 164,820 DWT
2020), which refers to a ship that makes an evasive manoeuvre because
at ship speed 14 knots or a larger tanker with 237,100 DWT at ship speed
of another ship near a bridge. This event was not considered in the study
12 knots.
for the same reasons as the cowboy ship event.
The results in Fig. 16 show that some of the results are sensitive to the
Compared to previous research and methods in, e.g., Ulusçu et al.
value of the parameter duration time, especially for the event miss of
(2009), van Dorp and Merrick (2011) and Goerlandt and Kujala (2011),

Table 7
Results from simulation sets 1A, 1B and 1C with YR = 100,000; number of allision accidents caused by D = drifting ship, ST = sharp turning ship, MTP = miss of turning
point.
Id Number of simulations Number of groundings Number of allisions (D, ST, MTP) Maximum allision energy (MJ) 1,000-year expected allision energy (MJ)

1A 3,959,282 50,258 710 (376, 85, 249) 3,221 1,667

1B 3,959,282 51,198 722 (385, 97, 240) 4,634 1,601
1C 3,959,282 51,206 730 (395, 87, 248) 2,708 1,605

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A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 14. Analysis of the effects from the parameter duration time (simulation set 1A) on the probability density distributions for all simulations, groundings and
accidents for the three studied events.

Table 8
Results from simulation sets 1A (reference), 5 and 6 with YR = 100,000; number
of allision accidents caused by D = drifting ship, ST = sharp turning ship, MTP =
miss of turning point.
Id Number of Number of Number of Maximum 1000-year
simulations groundings allisions allision expected
(D, ST, energy (MJ) allision
MTP) energy (MJ)

1A 3,959,282 50,258 710 (376, 3,221 1,667

85, 249)
5 3,959,282 32,003 436 (347, 1,030 12
89, 0)
6 3,962,135 50,255 484 (402, 2,258 22
82, 0)

Table 9
Results from simulation sets 1A (reference), 2, 3 and 4 with YR = 100,000;
number of allision accidents caused by D = drifting ship, ST = sharp turning
ship, MTP = miss of turning point.
Fig. 15. Illustration of ten percent of the paths of ships from simulation set 1A
Id Number of Number of Number of Maximum 1000-year
that collided with the bridge. The green line represents the drifting ship event,
simulations groundings allisions allision expected
the blue line the sharp turning ship event and the red line the miss of turning (D, ST, energy (MJ) allision
point event. (For interpretation of the references to colour in this figure legend, MTP) energy (MJ)
the reader is referred to the Web version of this article.)
1A 3,959,282 50,258 710 (376, 3,221 1,667
85, 249)
the proposed methodology includes calculation of the hydrodynamic 2 4,221,089 65,516 985 (651, 3,221 1,667
forces. It also contains methods for obtaining local event failure fre­ 85, 249)
3 3,994,525 54,268 800 (376, 3,221 1,667
quencies and durations. The study has demonstrated that the proposed
175, 249)
methodology can be applied to allision case studies while other models 4A 5,169,542 1,020,580 27,954 4,822 4,268
in the literature often emphasize open sea and coastal areas. Finally, a (376, 85,
difference between the proposed methodology and equation-based 27,493)
models (e.g., Pedersen, 1995, 2020) is that the probability and conse­ 4B 5,169,542 60,662 777 (376, 3,221 1,880
85, 316)
quence of an event are analysed together instead of separately.
4C 3,959,282 748,053 20,606 5,054 4,179
The proposed methodology can be used both to analyse the risk of (376, 85,
existing bridges and in the planning phase of new bridges. The risk 20,145)
defined in Eq. (1) has the terms (accumulated) probability and

13
A. Hörteborn and J.W. Ringsberg Ocean Engineering 235 (2021) 109396

Fig. 16. A log-log diagram presenting the probability of allision energy for the simulation sets 1A and 4C for the three studied events. The allision energy is
calculated in accordance with Eq. (4).

consequence, which were also analysed for each simulation case in the confirmed that the methodology could predict the probability of ship
methodology. This definition of risk and the way to present accumulated groundings corresponding to the accident statistics from the past ten
probability in Fig. 16 is similar to Johansen and Askeland (2019) who years in the same area. It was concluded that the presented methodology
used an FN-curve as the design criterion for bridge design. Note that the can be used to simulate and analyse traffic situation schemes in costal
FN-curve has the number of fatalities on the x-axis and Fig. 16 has the waterways to calculate the probability that a ship accident will occur.
allision energy. In future research, the allision energy could be trans­ The ship-bridge allision case study of the Great Belt Bridge showed in
lated to damages to the bridge and thereafter converted to number of a sensitivity study that the parameter duration time of an event has a
fatalities. large influence on the results. It is thus recommended to carry out a
parametric sensitivity study of this parameter. In the current case study,
7. Conclusions it was shown to have a relatively large influence, especially on the miss
of turning point event and the subsequent way the ship’s situation in the
The study presented a methodology using AIS data, a ship manoeu­ simulator runs evolved.
vring simulator and the Monte Carlo method to calculate the accident A sensitivity study of the number of simulated traffic years showed
probabilities in marine traffic near bridges spanning over wide water­ that 100,000 traffic years were required to satisfy the convergence cri­
ways. The methodology was verified in a case study on grounding ac­ terion defined in the study. The probability for a ship allision against the
cidents, and its wider applicability was presented in a case study where Great Belt Bridge was calculated to be 0.007. An analysis of all ship-
the probability of ship-bridge allisions was calculated. With the pro­ bridge allision cases showed that it was dominated by the drifting ship
posed methodology, ships and traffic situations that were over- event. The expected allision energy for the 1,000-year allision was
represented in the failure event analyses in the case study’s marine calculated to be 1,624 MJ, which can be represented by a 178 m tanker
traffic area were numerically shown, and mitigation actions were pro­ with 57,870 DWT and ship speed 14.6 knots. However, if the duration of
posed that can reduce the probability of ship-bridge allisions. Ships that the event miss of turning point was increased to the same duration as in
represent the 1,000-year allision energy were identified, which can be the TSS Bornholmsgat the expected allision energy for a 1,000-year
used as target ships in bridge structural strength assessments and whose allision was increased to 4,268 MJ, which can be represented by a
kinetic energy impact a bridge must withstand. 260 m tanker with 164,820 DWT at ship speed 14 knots or a larger
An event-based approach was proposed for the identification of tanker with 237,100 DWT at ship speed 12 knots.
events that should be simulated and analysed if they can lead to a Two mitigation actions were studied: change of the traffic separation
maritime accident. This is based on an analysis of AIS data of the traffic scheme and limitation of the ship speed. Both of these actions will give
separation scheme of the area of interest. Event detection criteria for the crew more time to act and react in case they lose the manoeu­
three events, drifting ship, sharp turning ship and miss of turning point, vrability of the ship; hence, the probability of an allision was reduced.
were proposed. The marine traffic areas Great Belt VTS and TSS Born­ The methodology presented in the study and its results show that it
holmsgat were analysed to estimate the event frequency. The results can be applied either in the planning phase of a new bridge over a
were compared with results in Rasmussen et al. (2012), and there was waterway if the AIS data in the area are known, or in the assessment of
good agreement for the drifting ship and miss of turning point events. marine traffic situations near existing bridges where the marine traffic
For the sharp turning ship event, too few events in the AIS data were may have changed since they were designed and built. The methodology
found to form representative statistical conclusions. is not limited to ship-bridge allisions; it can also be used to assess the
The Great Belt VTS area was used in a verification study that probability of collisions with other infrastructures offshore or other

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