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correctly) included comparison to both static
(Mannarini et al., 2016) and time-dependent
(Mannarini & Carelli, 2019) analytical solutions as
well as comparison to the outcomes of another path
planning model (Mannarini et al., 2018). The first step
in evaluation (i.e., assessing whether the model fairly
represents reality) is presented in this work.
The core of the paper is organized into a
description of the evaluation methodology (Section 2)
and a presentation of the results (Section 3), which
precede conclusive remarks and outline (Section 4).
2 METHODOLOGY
In this Section we describe the methodology
employed for this evaluation experiment. The
description comprises the extraction of AIS tracks
from reported raw data (Section 2.1) and the
computation of optimal tracks through VISIR (Section
2.2). The key development enabling the comparison of
AIS and VISIR tracks is the computation of the vessel
speed loss in waves out of AIS kinematic information,
VISIR vessel performance model, and sea state
analysis fields (Section 2.3).
Abbreviations and symbols employed throughout
this text are defined in Table 1.
Table 1. Some abbreviations and symbols employed in this
manuscript.
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Symbol Meaning Units
_______________________________________________
SOG Speed Over Ground kts
STW Speed Through Water kts
COG Course Over Ground deg
HDG Heading deg
EOT Engine Order Telegraph %
UKC Under Keel Clearance m
HWHM Half Width Half Maximum [-]
L
wl Length at the waterline m
B
wl Beam at the waterline m
T
avg Average draught m
P
max (fitted) maximum engine rating kW
V
max (fitted) maximum speed in calm water kts
H
s Significant wave height m
α Wave direction relative to vessel heading deg
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2.1 AIS tracks
Nowadays, a multitude of tracking devices and
systems produce massive amounts of maritime data
on a daily basis. The most commonly used of such
tracking systems is the Automatic Identification
System (AIS), a collaborative, self-reporting system
that allows vessels to broadcast their identification
information, characteristics and destination, along
with other information originating from on-board
devices and sensors, such as location, speed and
heading (M.1371, 2014). AIS messages are broadcast
periodically and they are received by other vessels
equipped with AIS transceivers, as well as by on-
ground stations and satellites.
A growing body of literature describes methods of
exploiting AIS data for safety and optimisation of
seafaring, traffic analysis, anomaly detection, route
extraction and prediction, collision detection, path
planning, weather routing and many more (Tu et al.,
2018). As the amount of available AIS data grows to
massive scales though, researchers are realising that
computational techniques must contend with
difficulties faced when acquiring, storing, and
processing the data. Applying traditional techniques
to data processing can lead to processing times of
several days, if applied to global data sets of
considerable size. Additionally, algorithms are
challenged by difficulties related to the datasets
themselves; including highly skewed, not uniform,
and uncertain data. For example, the update interval
for AIS is not constant, but dependent on a ship’s
behaviour; as such it is common for a vessel to
broadcast its data every three minutes if moving no
faster than 3 knots, while every two seconds if
travelling above 14 knots and changing course. In
such occasions, the collected positions are spatially
and temporally closer. In addition to this, depending
on AIS coastal coverage, there are geographical areas
where huge amounts of data are collected (e.g. busy
ports) while others with much less data. Furthermore,
human errors during data entry generate
discrepancies for example in naming of ports and
areas, generating further uncertainty and ambiguity.
In our previous work (Spiliopoulos et al., 2017), we
proposed an efficient big data approach for building a
global network of sea routes from AIS data. As a first
step of this process we reassign departure and arrival
information for each vessel trajectory as although this
data is existent in AIS it is error prone and often an
issue of confusion. In the present work we consider
vessel trajectories travelling between the ports of
Buenos Aires (Argentina) and Port Elizabeth (South
Africa) from July 2016 until the end of December
2017. These trajectories amounted to more than
160,000 AIS messages in total. Each of these messages
consists of the coordinates of the vessel transmitting
the message, the corresponding kinematic
characteristics of the vessel (such as SOG, COG, and
HDG), and a timestamp. For identification purposes
an anonymised vessel’s identifier and voyage data are
bound to each message.
Within this dataset, we identified 61 different
trajectories in total, each of them being performed by
a different vessel. Moreover 51 of these trajectories
correspond to dry bulk carriers and the remaining 10
trajectories to wet bulk carriers. For each voyage, the
vessel’s dimensions, engine power and maximum
historical speed information were included in our
analysis. The summarised characteristics of the
anonymised vessels in this dataset are shown in Table
2.
Table 2. Vessel characteristics. and stand for average
and standard deviation of the vessel sample.
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Dry bulk Wet bulk
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Number of vessels 51 10
Length [m] 201 182
19 2
Width [m] 32 31
2 2
Engine Power [kW] 8600 9000
1500 2200
Max Speed [knots] 12 12
2 3
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